SubsurfaceDataAnalytics_Feature_Transformations.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "## Subsurface Data Analytics \n",
    "\n",
    "### Feature Transformations for Subsurface Data Analytics in Python \n",
    "\n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Subsurface Machine Learning: Feature Transformations for Subsurface Data Analytics \n",
    "\n",
    "Here's a demonstration of feature transformations for subsurface modeling in Python. This is part of my Subsuface Machine Learning Course at the Cockrell School of Engineering at the University of Texas at Austin.  \n",
    "\n",
    "#### Feature Transformations\n",
    "\n",
    "There are many reasons that we may want to perform feature transformations.\n",
    "\n",
    "* the make the features consistent for visualization and comparison\n",
    "\n",
    "* to avoid bias or impose feature weighting for methods (e.g. k nearest neighbours regression) that rely on distances calculated in predictor feature space\n",
    "\n",
    "* the method requires the variables to have a specific range or distribution:\n",
    "\n",
    "    * artificial neural networks may require all features to range from [-1,1] \n",
    "    * parital correlation coefficients require a Gaussian distribution.\n",
    "    * statistical tests may require a specific distribution\n",
    "    * geostatistical sequential simulation requires an indicator or Gaussian transform \n",
    "\n",
    "Feature transformations is a common basic building blocks in many machine learning workflows.  \n",
    "\n",
    "* Let's learn how to perform feature transformations.\n",
    "\n",
    "#### Objective \n",
    "\n",
    "In the Stochastic Machine Learning class, I want to provide hands-on experience with solving complicated subsurface modeling problems with data analytics, machine learning. Python provides an excellent vehicle to accomplish this. I have coded a package called GeostatsPy with GSLIB: Geostatistical Library (Deutsch and Journel, 1998) functionality that provides basic building blocks for building subsurface modeling workflows. \n",
    "\n",
    "The objective is to remove the hurdles of subsurface modeling workflow construction by providing building blocks and sufficient examples. This is not a coding class per se, but we need the ability to 'script' workflows working with numerical methods.    \n",
    "\n",
    "#### Getting Started\n",
    "\n",
    "Here's the steps to get setup in Python with the GeostatsPy package:\n",
    "\n",
    "1. Install Anaconda 3 on your machine (https://www.anaconda.com/download/). \n",
    "2. From Anaconda Navigator (within Anaconda3 group), go to the environment tab, click on base (root) green arrow and open a terminal. \n",
    "3. In the terminal type: pip install geostatspy. \n",
    "4. Open Jupyter and in the top block get started by copy and pasting the code block below from this Jupyter Notebook to start using the geostatspy functionality. \n",
    "\n",
    "You will need to copy the data file to your working directory.  They are available here:\n",
    "\n",
    "* Tabular data - unconv_MV_v4.csv at https://git.io/fhHLT.\n",
    "\n",
    "#### Importing Packages\n",
    "\n",
    "We will import the GeostatsPy package.  \n",
    "\n",
    "* we will use a convenient transformation method\n",
    "\n",
    "There are examples below with GeostatsPy functions. You can go here to see a list of the available functions, https://git.io/fh4eX, and for other example workflows and source code. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "import geostatspy.GSLIB as GSLIB          # GSLIB utilies, visualization and wrapper\n",
    "import geostatspy.geostats as geostats    # GSLIB methods convert to Python        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will also need some standard packages. These should have been installed with Anaconda 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np                        # ndarrys for gridded data\n",
    "import pandas as pd                       # DataFrames for tabular data\n",
    "import os                                 # set working directory, run executables\n",
    "import matplotlib.pyplot as plt           # for plotting\n",
    "from scipy import stats                   # summary statistics\n",
    "import math                               # trigonometry etc.\n",
    "import scipy.signal as signal             # kernel for moving window calculation\n",
    "import random                             # for randon numbers\n",
    "import seaborn as sns                     # for matrix scatter plots\n",
    "from scipy import linalg                  # for linear regression\n",
    "from sklearn import preprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Declare Functions\n",
    "\n",
    "Let's define a single function to streamline plotting correlation matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def histograms(df):\n",
    "\n",
    "    pormin = min(df['Por']); pormax = max(df['Por']); \n",
    "    porname = 'Porosity (%)'; portitle = 'Porosity' # user specified min and max values, and labels for plotting\n",
    "    permmin = min(df['Perm']); permmax = max(df['Perm']);\n",
    "    permname = 'Permeability (mD)'; permtitle = 'Permeability'     \n",
    "    AImin = min(df['AI']); AImax = max(df['AI']);\n",
    "    AIname = 'Acoustic Impedance (kg/m2s*10^6)'; AItitle = 'Acoustic Impedance'\n",
    "    brmin = min(df['Brittle']); brmax = max(df['Brittle']);\n",
    "    brname = 'Brittleness Ratio (%)'; brtitle = 'Brittleness'\n",
    "    TOCmin = min(df['TOC']); TOCmax = max(df['TOC']);\n",
    "    TOCname = 'Total Organic Carbon (%)'; TOCtitle = 'Total Organic Carbon' \n",
    "    VRmin = min(df['VR']); VRmax = max(df['VR']);\n",
    "    VRname = 'Vitrinite Reflectance (%)'; VRtitle = 'Vitrinite Reflectance'\n",
    "    prodmin = min(df['Prod']); prodmax = max(df['Prod']);\n",
    "    prodname = 'Normalized Initial Production (MCFPD)'; prodtitle = 'Normalized Initial Production'\n",
    "    \n",
    "    plt.subplot(331)\n",
    "    GSLIB.hist_st(df['Por'].values,pormin,pormax,log=False,cumul = False,bins=20,weights = None,xlabel=porname,title=portitle)\n",
    "\n",
    "    plt.subplot(332)\n",
    "    GSLIB.hist_st(df['Perm'].values,permmin,permmax,log=False,cumul = False,bins=20,weights = None,xlabel=permname,title=permtitle)\n",
    "\n",
    "    plt.subplot(333)\n",
    "    GSLIB.hist_st(df['AI'].values,AImin,AImax,log=False,cumul = False,bins=20,weights = None,xlabel=AIname,title=AItitle)\n",
    "\n",
    "    plt.subplot(334)\n",
    "    GSLIB.hist_st(df['Brittle'].values,brmin,brmax,log=False,cumul = False,bins=20,weights = None,xlabel=brname,title=brtitle)\n",
    "\n",
    "    plt.subplot(335)\n",
    "    GSLIB.hist_st(df['TOC'].values,TOCmin,TOCmax,log=False,cumul = False,bins=20,weights = None,xlabel=TOCname,title=TOCtitle)\n",
    "\n",
    "    plt.subplot(336)\n",
    "    GSLIB.hist_st(df['VR'].values,VRmin,VRmax,log=False,cumul = False,bins=20,weights = None,xlabel=VRname,title=VRtitle)\n",
    "\n",
    "    plt.subplot(338)\n",
    "    GSLIB.hist_st(df['Prod'].values,prodmin,prodmax,log=False,cumul = False,bins=20,weights = None,xlabel=prodname,title=prodtitle)\n",
    "\n",
    "    plt.subplots_adjust(left=0.0, bottom=0.0, right=3.0, top=3.5, wspace=0.2, hspace=0.2)\n",
    "    plt.savefig('hist_Porosity_Multiple_bins.tif',dpi=600,bbox_inches=\"tight\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set the Working Directory\n",
    "\n",
    "I always like to do this so I don't lose files and to simplify subsequent read and writes (avoid including the full address each time). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "os.chdir(\"c:/PGE383\")                     # set the working directory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loading Tabular Data\n",
    "\n",
    "Here's the command to load our comma delimited data file in to a Pandas' DataFrame object.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('unconv_MV_v4.csv')      # load our data table (wrong name!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualizing the DataFrame would be useful and we already learned about these methods in this demo (https://git.io/fNgRW). \n",
    "\n",
    "We can preview the DataFrame by utilizing the 'head' DataFrame member function (with a nice and clean format, see below). With the head command, add parameter 'n=13' to see the first 13 rows of the dataset.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Well</th>\n",
       "      <th>Por</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "      <th>Brittle</th>\n",
       "      <th>TOC</th>\n",
       "      <th>VR</th>\n",
       "      <th>Prod</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>12.08</td>\n",
       "      <td>2.92</td>\n",
       "      <td>2.80</td>\n",
       "      <td>81.40</td>\n",
       "      <td>1.16</td>\n",
       "      <td>2.31</td>\n",
       "      <td>1695.360819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>12.38</td>\n",
       "      <td>3.53</td>\n",
       "      <td>3.22</td>\n",
       "      <td>46.17</td>\n",
       "      <td>0.89</td>\n",
       "      <td>1.88</td>\n",
       "      <td>3007.096063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>14.02</td>\n",
       "      <td>2.59</td>\n",
       "      <td>4.01</td>\n",
       "      <td>72.80</td>\n",
       "      <td>0.89</td>\n",
       "      <td>2.72</td>\n",
       "      <td>2531.938259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>17.67</td>\n",
       "      <td>6.75</td>\n",
       "      <td>2.63</td>\n",
       "      <td>39.81</td>\n",
       "      <td>1.08</td>\n",
       "      <td>1.88</td>\n",
       "      <td>5288.514854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>17.52</td>\n",
       "      <td>4.57</td>\n",
       "      <td>3.18</td>\n",
       "      <td>10.94</td>\n",
       "      <td>1.51</td>\n",
       "      <td>1.90</td>\n",
       "      <td>2859.469624</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>14.53</td>\n",
       "      <td>4.81</td>\n",
       "      <td>2.69</td>\n",
       "      <td>53.60</td>\n",
       "      <td>0.94</td>\n",
       "      <td>1.67</td>\n",
       "      <td>4017.374438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>13.49</td>\n",
       "      <td>3.60</td>\n",
       "      <td>2.93</td>\n",
       "      <td>63.71</td>\n",
       "      <td>0.80</td>\n",
       "      <td>1.85</td>\n",
       "      <td>2952.812773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>11.58</td>\n",
       "      <td>3.03</td>\n",
       "      <td>3.25</td>\n",
       "      <td>53.00</td>\n",
       "      <td>0.69</td>\n",
       "      <td>1.93</td>\n",
       "      <td>2670.933846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>12.52</td>\n",
       "      <td>2.72</td>\n",
       "      <td>2.43</td>\n",
       "      <td>65.77</td>\n",
       "      <td>0.95</td>\n",
       "      <td>1.98</td>\n",
       "      <td>2474.048178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>13.25</td>\n",
       "      <td>3.94</td>\n",
       "      <td>3.71</td>\n",
       "      <td>66.20</td>\n",
       "      <td>1.14</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2722.893266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>11</td>\n",
       "      <td>15.04</td>\n",
       "      <td>4.39</td>\n",
       "      <td>2.22</td>\n",
       "      <td>61.11</td>\n",
       "      <td>1.08</td>\n",
       "      <td>1.77</td>\n",
       "      <td>3828.247174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>12</td>\n",
       "      <td>16.19</td>\n",
       "      <td>6.30</td>\n",
       "      <td>2.29</td>\n",
       "      <td>49.10</td>\n",
       "      <td>1.53</td>\n",
       "      <td>1.86</td>\n",
       "      <td>5095.810104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>13</td>\n",
       "      <td>16.82</td>\n",
       "      <td>5.42</td>\n",
       "      <td>2.80</td>\n",
       "      <td>66.65</td>\n",
       "      <td>1.17</td>\n",
       "      <td>1.98</td>\n",
       "      <td>4091.637316</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "    Well    Por  Perm    AI  Brittle   TOC    VR         Prod\n",
       "0      1  12.08  2.92  2.80    81.40  1.16  2.31  1695.360819\n",
       "1      2  12.38  3.53  3.22    46.17  0.89  1.88  3007.096063\n",
       "2      3  14.02  2.59  4.01    72.80  0.89  2.72  2531.938259\n",
       "3      4  17.67  6.75  2.63    39.81  1.08  1.88  5288.514854\n",
       "4      5  17.52  4.57  3.18    10.94  1.51  1.90  2859.469624\n",
       "5      6  14.53  4.81  2.69    53.60  0.94  1.67  4017.374438\n",
       "6      7  13.49  3.60  2.93    63.71  0.80  1.85  2952.812773\n",
       "7      8  11.58  3.03  3.25    53.00  0.69  1.93  2670.933846\n",
       "8      9  12.52  2.72  2.43    65.77  0.95  1.98  2474.048178\n",
       "9     10  13.25  3.94  3.71    66.20  1.14  2.65  2722.893266\n",
       "10    11  15.04  4.39  2.22    61.11  1.08  1.77  3828.247174\n",
       "11    12  16.19  6.30  2.29    49.10  1.53  1.86  5095.810104\n",
       "12    13  16.82  5.42  2.80    66.65  1.17  1.98  4091.637316"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(n=13)                             # we could also use this command for a table preview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset has features from 200 unconventional wells including: \n",
    "\n",
    "0. well index\n",
    "1. well average porosity (%) \n",
    "2. permeability (mD)\n",
    "3. accoustic impedance (kg/m2s*10^6)\n",
    "4. brittness ratio (%) \n",
    "5. total organic carbon (%) \n",
    "6. vitrinite reflectance (%)\n",
    "8. normalized initial production 90 day average (MCFPD). \n",
    "\n",
    "Note, the dataset is synthetic, but has realistic ranges and general multivariate relationships.\n",
    "\n",
    "Ranking features is really an effort to understand the features and their relationships with eachother.  We will start with basic data visualization and move to more complicated methods such are partial correlation and recursive feature elimination.\n",
    "\n",
    "### Summary Statistics\n",
    "\n",
    "In any multivariate work we should start with the univariate analysis, summary statistics of one variable at a time. The summary statistic ranking method is qualitative, we are asking:\n",
    "\n",
    "* are there data issues?\n",
    "* do we trust the features? do we we trust the features all equally?\n",
    "* are there issues that need to be taken care of before we develop any multivariate workflows?\n",
    "\n",
    "There are a lot of efficient methods to calculate summary statistics from tabular data in DataFrames. The describe() command provides count, mean, minimum, maximum, and quartiles all in a compact data table. We use transpose() command to flip the table so that features are on the rows and the statistics are on the columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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       "    <tr>\n",
       "      <th>Well</th>\n",
       "      <td>200.0</td>\n",
       "      <td>100.500000</td>\n",
       "      <td>57.879185</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>50.750000</td>\n",
       "      <td>100.500000</td>\n",
       "      <td>150.250000</td>\n",
       "      <td>200.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Por</th>\n",
       "      <td>200.0</td>\n",
       "      <td>14.991150</td>\n",
       "      <td>2.971176</td>\n",
       "      <td>6.550000</td>\n",
       "      <td>12.912500</td>\n",
       "      <td>15.070000</td>\n",
       "      <td>17.402500</td>\n",
       "      <td>23.550000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Perm</th>\n",
       "      <td>200.0</td>\n",
       "      <td>4.330750</td>\n",
       "      <td>1.731014</td>\n",
       "      <td>1.130000</td>\n",
       "      <td>3.122500</td>\n",
       "      <td>4.035000</td>\n",
       "      <td>5.287500</td>\n",
       "      <td>9.870000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AI</th>\n",
       "      <td>200.0</td>\n",
       "      <td>2.968850</td>\n",
       "      <td>0.566885</td>\n",
       "      <td>1.280000</td>\n",
       "      <td>2.547500</td>\n",
       "      <td>2.955000</td>\n",
       "      <td>3.345000</td>\n",
       "      <td>4.630000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Brittle</th>\n",
       "      <td>200.0</td>\n",
       "      <td>48.161950</td>\n",
       "      <td>14.129455</td>\n",
       "      <td>10.940000</td>\n",
       "      <td>37.755000</td>\n",
       "      <td>49.510000</td>\n",
       "      <td>58.262500</td>\n",
       "      <td>84.330000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TOC</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.990450</td>\n",
       "      <td>0.481588</td>\n",
       "      <td>-0.190000</td>\n",
       "      <td>0.617500</td>\n",
       "      <td>1.030000</td>\n",
       "      <td>1.350000</td>\n",
       "      <td>2.180000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>VR</th>\n",
       "      <td>200.0</td>\n",
       "      <td>1.964300</td>\n",
       "      <td>0.300827</td>\n",
       "      <td>0.930000</td>\n",
       "      <td>1.770000</td>\n",
       "      <td>1.960000</td>\n",
       "      <td>2.142500</td>\n",
       "      <td>2.870000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Prod</th>\n",
       "      <td>200.0</td>\n",
       "      <td>3864.407081</td>\n",
       "      <td>1553.277558</td>\n",
       "      <td>839.822063</td>\n",
       "      <td>2686.227611</td>\n",
       "      <td>3604.303507</td>\n",
       "      <td>4752.637556</td>\n",
       "      <td>8590.384044</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count         mean          std         min          25%  \\\n",
       "Well     200.0   100.500000    57.879185    1.000000    50.750000   \n",
       "Por      200.0    14.991150     2.971176    6.550000    12.912500   \n",
       "Perm     200.0     4.330750     1.731014    1.130000     3.122500   \n",
       "AI       200.0     2.968850     0.566885    1.280000     2.547500   \n",
       "Brittle  200.0    48.161950    14.129455   10.940000    37.755000   \n",
       "TOC      200.0     0.990450     0.481588   -0.190000     0.617500   \n",
       "VR       200.0     1.964300     0.300827    0.930000     1.770000   \n",
       "Prod     200.0  3864.407081  1553.277558  839.822063  2686.227611   \n",
       "\n",
       "                 50%          75%          max  \n",
       "Well      100.500000   150.250000   200.000000  \n",
       "Por        15.070000    17.402500    23.550000  \n",
       "Perm        4.035000     5.287500     9.870000  \n",
       "AI          2.955000     3.345000     4.630000  \n",
       "Brittle    49.510000    58.262500    84.330000  \n",
       "TOC         1.030000     1.350000     2.180000  \n",
       "VR          1.960000     2.142500     2.870000  \n",
       "Prod     3604.303507  4752.637556  8590.384044  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe().transpose()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's remove the well index as we will not want to transform it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Por</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "      <th>Brittle</th>\n",
       "      <th>TOC</th>\n",
       "      <th>VR</th>\n",
       "      <th>Prod</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12.08</td>\n",
       "      <td>2.92</td>\n",
       "      <td>2.80</td>\n",
       "      <td>81.40</td>\n",
       "      <td>1.16</td>\n",
       "      <td>2.31</td>\n",
       "      <td>1695.360819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12.38</td>\n",
       "      <td>3.53</td>\n",
       "      <td>3.22</td>\n",
       "      <td>46.17</td>\n",
       "      <td>0.89</td>\n",
       "      <td>1.88</td>\n",
       "      <td>3007.096063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>14.02</td>\n",
       "      <td>2.59</td>\n",
       "      <td>4.01</td>\n",
       "      <td>72.80</td>\n",
       "      <td>0.89</td>\n",
       "      <td>2.72</td>\n",
       "      <td>2531.938259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>17.67</td>\n",
       "      <td>6.75</td>\n",
       "      <td>2.63</td>\n",
       "      <td>39.81</td>\n",
       "      <td>1.08</td>\n",
       "      <td>1.88</td>\n",
       "      <td>5288.514854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.52</td>\n",
       "      <td>4.57</td>\n",
       "      <td>3.18</td>\n",
       "      <td>10.94</td>\n",
       "      <td>1.51</td>\n",
       "      <td>1.90</td>\n",
       "      <td>2859.469624</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Por  Perm    AI  Brittle   TOC    VR         Prod\n",
       "0  12.08  2.92  2.80    81.40  1.16  2.31  1695.360819\n",
       "1  12.38  3.53  3.22    46.17  0.89  1.88  3007.096063\n",
       "2  14.02  2.59  4.01    72.80  0.89  2.72  2531.938259\n",
       "3  17.67  6.75  2.63    39.81  1.08  1.88  5288.514854\n",
       "4  17.52  4.57  3.18    10.94  1.51  1.90  2859.469624"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.iloc[:,1:]\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We should also take a look at the histograms. We will use our convenient function (declared above) to visualize all the distribuitons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "histograms(df)                       # our function to visualize all feature histograms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are just a couple slighly negative values, let's just truncate them at zero. We   can use this command below to set all TOC values in the DataFrame that are less than 0.0 as 0.0, otherwise we keep the original TOC value.\n",
    "\n",
    "### Truncation\n",
    "\n",
    "It is possible that the features may extend beyond the palusible range of values.\n",
    "\n",
    "* truncation is simply assigning values outside the range with a specific value\n",
    "\n",
    "* it is common to assign the minimum permissible value to outliers on the lower tail and visa versa\n",
    "\n",
    "Truncation can be handled easily with numpy operators applied to the feature array within the Pandas DataFrame\n",
    "\n",
    "```python\n",
    "num = df._get_numeric_data() \n",
    "num[num < data_min] = data_min\n",
    "num[num > data_max] = data_max\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Por</th>\n",
       "      <td>200.0</td>\n",
       "      <td>14.991150</td>\n",
       "      <td>2.971176</td>\n",
       "      <td>6.550000</td>\n",
       "      <td>12.912500</td>\n",
       "      <td>15.070000</td>\n",
       "      <td>17.402500</td>\n",
       "      <td>23.550000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Perm</th>\n",
       "      <td>200.0</td>\n",
       "      <td>4.330750</td>\n",
       "      <td>1.731014</td>\n",
       "      <td>1.130000</td>\n",
       "      <td>3.122500</td>\n",
       "      <td>4.035000</td>\n",
       "      <td>5.287500</td>\n",
       "      <td>9.870000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AI</th>\n",
       "      <td>200.0</td>\n",
       "      <td>2.968850</td>\n",
       "      <td>0.566885</td>\n",
       "      <td>1.280000</td>\n",
       "      <td>2.547500</td>\n",
       "      <td>2.955000</td>\n",
       "      <td>3.345000</td>\n",
       "      <td>4.630000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Brittle</th>\n",
       "      <td>200.0</td>\n",
       "      <td>48.161950</td>\n",
       "      <td>14.129455</td>\n",
       "      <td>10.940000</td>\n",
       "      <td>37.755000</td>\n",
       "      <td>49.510000</td>\n",
       "      <td>58.262500</td>\n",
       "      <td>84.330000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TOC</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.991950</td>\n",
       "      <td>0.478264</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.617500</td>\n",
       "      <td>1.030000</td>\n",
       "      <td>1.350000</td>\n",
       "      <td>2.180000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>VR</th>\n",
       "      <td>200.0</td>\n",
       "      <td>1.964300</td>\n",
       "      <td>0.300827</td>\n",
       "      <td>0.930000</td>\n",
       "      <td>1.770000</td>\n",
       "      <td>1.960000</td>\n",
       "      <td>2.142500</td>\n",
       "      <td>2.870000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Prod</th>\n",
       "      <td>200.0</td>\n",
       "      <td>3864.407081</td>\n",
       "      <td>1553.277558</td>\n",
       "      <td>839.822063</td>\n",
       "      <td>2686.227611</td>\n",
       "      <td>3604.303507</td>\n",
       "      <td>4752.637556</td>\n",
       "      <td>8590.384044</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count         mean          std         min          25%  \\\n",
       "Por      200.0    14.991150     2.971176    6.550000    12.912500   \n",
       "Perm     200.0     4.330750     1.731014    1.130000     3.122500   \n",
       "AI       200.0     2.968850     0.566885    1.280000     2.547500   \n",
       "Brittle  200.0    48.161950    14.129455   10.940000    37.755000   \n",
       "TOC      200.0     0.991950     0.478264    0.000000     0.617500   \n",
       "VR       200.0     1.964300     0.300827    0.930000     1.770000   \n",
       "Prod     200.0  3864.407081  1553.277558  839.822063  2686.227611   \n",
       "\n",
       "                 50%          75%          max  \n",
       "Por        15.070000    17.402500    23.550000  \n",
       "Perm        4.035000     5.287500     9.870000  \n",
       "AI          2.955000     3.345000     4.630000  \n",
       "Brittle    49.510000    58.262500    84.330000  \n",
       "TOC         1.030000     1.350000     2.180000  \n",
       "VR          1.960000     2.142500     2.870000  \n",
       "Prod     3604.303507  4752.637556  8590.384044  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num = df._get_numeric_data()              # get the numerical values\n",
    "num[num < 0] = 0                          # truncate negative values to 0.0\n",
    "df.describe().transpose()                 # get the summary statistics of all features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the summary statistics again to confirm that we were successful in truncating TOC to $\\ge 0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Por</th>\n",
       "      <td>200.0</td>\n",
       "      <td>14.991150</td>\n",
       "      <td>2.971176</td>\n",
       "      <td>6.550000</td>\n",
       "      <td>12.912500</td>\n",
       "      <td>15.070000</td>\n",
       "      <td>17.402500</td>\n",
       "      <td>23.550000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Perm</th>\n",
       "      <td>200.0</td>\n",
       "      <td>4.330750</td>\n",
       "      <td>1.731014</td>\n",
       "      <td>1.130000</td>\n",
       "      <td>3.122500</td>\n",
       "      <td>4.035000</td>\n",
       "      <td>5.287500</td>\n",
       "      <td>9.870000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AI</th>\n",
       "      <td>200.0</td>\n",
       "      <td>2.968850</td>\n",
       "      <td>0.566885</td>\n",
       "      <td>1.280000</td>\n",
       "      <td>2.547500</td>\n",
       "      <td>2.955000</td>\n",
       "      <td>3.345000</td>\n",
       "      <td>4.630000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Brittle</th>\n",
       "      <td>200.0</td>\n",
       "      <td>48.161950</td>\n",
       "      <td>14.129455</td>\n",
       "      <td>10.940000</td>\n",
       "      <td>37.755000</td>\n",
       "      <td>49.510000</td>\n",
       "      <td>58.262500</td>\n",
       "      <td>84.330000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TOC</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.991950</td>\n",
       "      <td>0.478264</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.617500</td>\n",
       "      <td>1.030000</td>\n",
       "      <td>1.350000</td>\n",
       "      <td>2.180000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>VR</th>\n",
       "      <td>200.0</td>\n",
       "      <td>1.964300</td>\n",
       "      <td>0.300827</td>\n",
       "      <td>0.930000</td>\n",
       "      <td>1.770000</td>\n",
       "      <td>1.960000</td>\n",
       "      <td>2.142500</td>\n",
       "      <td>2.870000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Prod</th>\n",
       "      <td>200.0</td>\n",
       "      <td>3864.407081</td>\n",
       "      <td>1553.277558</td>\n",
       "      <td>839.822063</td>\n",
       "      <td>2686.227611</td>\n",
       "      <td>3604.303507</td>\n",
       "      <td>4752.637556</td>\n",
       "      <td>8590.384044</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count         mean          std         min          25%  \\\n",
       "Por      200.0    14.991150     2.971176    6.550000    12.912500   \n",
       "Perm     200.0     4.330750     1.731014    1.130000     3.122500   \n",
       "AI       200.0     2.968850     0.566885    1.280000     2.547500   \n",
       "Brittle  200.0    48.161950    14.129455   10.940000    37.755000   \n",
       "TOC      200.0     0.991950     0.478264    0.000000     0.617500   \n",
       "VR       200.0     1.964300     0.300827    0.930000     1.770000   \n",
       "Prod     200.0  3864.407081  1553.277558  839.822063  2686.227611   \n",
       "\n",
       "                 50%          75%          max  \n",
       "Por        15.070000    17.402500    23.550000  \n",
       "Perm        4.035000     5.287500     9.870000  \n",
       "AI          2.955000     3.345000     4.630000  \n",
       "Brittle    49.510000    58.262500    84.330000  \n",
       "TOC         1.030000     1.350000     2.180000  \n",
       "VR          1.960000     2.142500     2.870000  \n",
       "Prod     3604.303507  4752.637556  8590.384044  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe().transpose()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the summary statistics you can see that the truncation was successful, we now have a minimum of 0.0.\n",
    "\n",
    "### Affine Correction\n",
    "\n",
    "The affine correction is the transform of the feature distribution to a new mean and variance.\n",
    "\n",
    "* this is a shift and stretch / squeeze of the original property distribution\n",
    "\n",
    "* no shape change is assumed\n",
    "\n",
    "The following equation is applied to each sample in the original distribution\n",
    "\n",
    "\\begin{equation}\n",
    "y = \\frac{\\sigma_y}{\\sigma_x}\\left( x - \\overline{x} \\right) + \\overline{y}\n",
    "\\end{equation}\n",
    "\n",
    "where $\\sigma_x$ is the original standard deviation, $\\sigma_y$ is the target standard deviation, $\\overline{x}$ is the original mean and $\\overline{y}$ is the target mean.\n",
    "\n",
    "* there is a affine function in GeostatsPy that we may use\n",
    "\n",
    "* the function is not set up to accept multiple features at once so we will just transform a single feature\n",
    "\n",
    "Let's transform porosity to have an arbitrary mean and standard deviation ($\\overline{x} = 1.0$ and $\\sigma_x = 1.0$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Por</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "      <th>Brittle</th>\n",
       "      <th>TOC</th>\n",
       "      <th>VR</th>\n",
       "      <th>Prod</th>\n",
       "      <th>aPor</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12.08</td>\n",
       "      <td>2.92</td>\n",
       "      <td>2.80</td>\n",
       "      <td>81.40</td>\n",
       "      <td>1.16</td>\n",
       "      <td>2.31</td>\n",
       "      <td>1695.360819</td>\n",
       "      <td>0.017744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12.38</td>\n",
       "      <td>3.53</td>\n",
       "      <td>3.22</td>\n",
       "      <td>46.17</td>\n",
       "      <td>0.89</td>\n",
       "      <td>1.88</td>\n",
       "      <td>3007.096063</td>\n",
       "      <td>0.118968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>14.02</td>\n",
       "      <td>2.59</td>\n",
       "      <td>4.01</td>\n",
       "      <td>72.80</td>\n",
       "      <td>0.89</td>\n",
       "      <td>2.72</td>\n",
       "      <td>2531.938259</td>\n",
       "      <td>0.672323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>17.67</td>\n",
       "      <td>6.75</td>\n",
       "      <td>2.63</td>\n",
       "      <td>39.81</td>\n",
       "      <td>1.08</td>\n",
       "      <td>1.88</td>\n",
       "      <td>5288.514854</td>\n",
       "      <td>1.903875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.52</td>\n",
       "      <td>4.57</td>\n",
       "      <td>3.18</td>\n",
       "      <td>10.94</td>\n",
       "      <td>1.51</td>\n",
       "      <td>1.90</td>\n",
       "      <td>2859.469624</td>\n",
       "      <td>1.853263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>14.53</td>\n",
       "      <td>4.81</td>\n",
       "      <td>2.69</td>\n",
       "      <td>53.60</td>\n",
       "      <td>0.94</td>\n",
       "      <td>1.67</td>\n",
       "      <td>4017.374438</td>\n",
       "      <td>0.844403</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>13.49</td>\n",
       "      <td>3.60</td>\n",
       "      <td>2.93</td>\n",
       "      <td>63.71</td>\n",
       "      <td>0.80</td>\n",
       "      <td>1.85</td>\n",
       "      <td>2952.812773</td>\n",
       "      <td>0.493495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>11.58</td>\n",
       "      <td>3.03</td>\n",
       "      <td>3.25</td>\n",
       "      <td>53.00</td>\n",
       "      <td>0.69</td>\n",
       "      <td>1.93</td>\n",
       "      <td>2670.933846</td>\n",
       "      <td>-0.150962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>12.52</td>\n",
       "      <td>2.72</td>\n",
       "      <td>2.43</td>\n",
       "      <td>65.77</td>\n",
       "      <td>0.95</td>\n",
       "      <td>1.98</td>\n",
       "      <td>2474.048178</td>\n",
       "      <td>0.166205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>13.25</td>\n",
       "      <td>3.94</td>\n",
       "      <td>3.71</td>\n",
       "      <td>66.20</td>\n",
       "      <td>1.14</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2722.893266</td>\n",
       "      <td>0.412516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>15.04</td>\n",
       "      <td>4.39</td>\n",
       "      <td>2.22</td>\n",
       "      <td>61.11</td>\n",
       "      <td>1.08</td>\n",
       "      <td>1.77</td>\n",
       "      <td>3828.247174</td>\n",
       "      <td>1.016483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>16.19</td>\n",
       "      <td>6.30</td>\n",
       "      <td>2.29</td>\n",
       "      <td>49.10</td>\n",
       "      <td>1.53</td>\n",
       "      <td>1.86</td>\n",
       "      <td>5095.810104</td>\n",
       "      <td>1.404506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>16.82</td>\n",
       "      <td>5.42</td>\n",
       "      <td>2.80</td>\n",
       "      <td>66.65</td>\n",
       "      <td>1.17</td>\n",
       "      <td>1.98</td>\n",
       "      <td>4091.637316</td>\n",
       "      <td>1.617075</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Por  Perm    AI  Brittle   TOC    VR         Prod      aPor\n",
       "0   12.08  2.92  2.80    81.40  1.16  2.31  1695.360819  0.017744\n",
       "1   12.38  3.53  3.22    46.17  0.89  1.88  3007.096063  0.118968\n",
       "2   14.02  2.59  4.01    72.80  0.89  2.72  2531.938259  0.672323\n",
       "3   17.67  6.75  2.63    39.81  1.08  1.88  5288.514854  1.903875\n",
       "4   17.52  4.57  3.18    10.94  1.51  1.90  2859.469624  1.853263\n",
       "5   14.53  4.81  2.69    53.60  0.94  1.67  4017.374438  0.844403\n",
       "6   13.49  3.60  2.93    63.71  0.80  1.85  2952.812773  0.493495\n",
       "7   11.58  3.03  3.25    53.00  0.69  1.93  2670.933846 -0.150962\n",
       "8   12.52  2.72  2.43    65.77  0.95  1.98  2474.048178  0.166205\n",
       "9   13.25  3.94  3.71    66.20  1.14  2.65  2722.893266  0.412516\n",
       "10  15.04  4.39  2.22    61.11  1.08  1.77  3828.247174  1.016483\n",
       "11  16.19  6.30  2.29    49.10  1.53  1.86  5095.810104  1.404506\n",
       "12  16.82  5.42  2.80    66.65  1.17  1.98  4091.637316  1.617075"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['aPor'] = GSLIB.affine(df['Por'].values,tmean = 1.0,tstdev = 1.0)  \n",
    "df.head(n = 13)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check the summary statistics of our new feature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    200.000000\n",
       "mean       1.000000\n",
       "std        1.002509\n",
       "min       -1.848142\n",
       "25%        0.298639\n",
       "50%        1.026605\n",
       "75%        1.813617\n",
       "max        3.887855\n",
       "Name: aPor, dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['aPor'].describe().transpose()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's remove the affine transformed feature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df.drop(columns = ['aPor'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standardization\n",
    "\n",
    "Standardization is the transform of the feature distribution to a mean of zero and a variance of one.\n",
    "\n",
    "* this is a shift and stretch / squeeze of the original property distribution\n",
    "\n",
    "* no shape change is assumed\n",
    "\n",
    "The transform is effectively a specific case of the affine correction, with $\\overline{y} = 0$ and $\\sigma_y = 1.0$.\n",
    "\n",
    "\\begin{equation}\n",
    "y = \\frac{1}{\\sigma_x}\\left( x - \\overline{x} \\right)\n",
    "\\end{equation}\n",
    "\n",
    "where $\\sigma_x$ is the original standard deviation and $\\overline{x}$ is the original mean.\n",
    "\n",
    "Let's standardize the feature to have:\n",
    "\n",
    "* mean = 0.0\n",
    "* variance = standard deviation = 1.0\n",
    "\n",
    "To do this we:\n",
    "\n",
    "1. instantiate the StandardScaler from scikit learn. We assign it as 'scaler' so we can use it to conveniently reverse the transformation if we like. We will need to do that to get our predictions back into regular production units.\n",
    "\n",
    "```python\n",
    "scaler = StandardScaler()\n",
    "```\n",
    "\n",
    "2. we then extract all the values from our DataFrame and apply the by-column standardization.  The result is a 2D ndarray\n",
    "\n",
    "```python\n",
    "sfeatures = scaler.fit_transform(df_mv.values)\n",
    "```\n",
    "3. we make an new empty DataFrame\n",
    "\n",
    "```python\n",
    "df_nmv = pd.DataFrame()\n",
    "```\n",
    "\n",
    "4. then we add the transformed value to the new DataFrame while keeping the sample index and feature names from the old DataFramae\n",
    "\n",
    "```python\n",
    "df_nmv = pd.DataFrame(sfeatures, index=df_mv.index, columns=df_mv.columns)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Por</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "      <th>Brittle</th>\n",
       "      <th>TOC</th>\n",
       "      <th>VR</th>\n",
       "      <th>Prod</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.982256</td>\n",
       "      <td>-0.817030</td>\n",
       "      <td>-0.298603</td>\n",
       "      <td>2.358297</td>\n",
       "      <td>0.352257</td>\n",
       "      <td>1.152048</td>\n",
       "      <td>-1.399936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.881032</td>\n",
       "      <td>-0.463751</td>\n",
       "      <td>0.444147</td>\n",
       "      <td>-0.141332</td>\n",
       "      <td>-0.213702</td>\n",
       "      <td>-0.280931</td>\n",
       "      <td>-0.553322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.327677</td>\n",
       "      <td>-1.008148</td>\n",
       "      <td>1.841224</td>\n",
       "      <td>1.748113</td>\n",
       "      <td>-0.213702</td>\n",
       "      <td>2.518377</td>\n",
       "      <td>-0.859996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.903875</td>\n",
       "      <td>1.401098</td>\n",
       "      <td>-0.599240</td>\n",
       "      <td>-0.592585</td>\n",
       "      <td>0.184565</td>\n",
       "      <td>-0.280931</td>\n",
       "      <td>0.919141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.853263</td>\n",
       "      <td>0.138561</td>\n",
       "      <td>0.373409</td>\n",
       "      <td>-2.640962</td>\n",
       "      <td>1.085907</td>\n",
       "      <td>-0.214280</td>\n",
       "      <td>-0.648602</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Por      Perm        AI   Brittle       TOC        VR      Prod\n",
       "0 -0.982256 -0.817030 -0.298603  2.358297  0.352257  1.152048 -1.399936\n",
       "1 -0.881032 -0.463751  0.444147 -0.141332 -0.213702 -0.280931 -0.553322\n",
       "2 -0.327677 -1.008148  1.841224  1.748113 -0.213702  2.518377 -0.859996\n",
       "3  0.903875  1.401098 -0.599240 -0.592585  0.184565 -0.280931  0.919141\n",
       "4  0.853263  0.138561  0.373409 -2.640962  1.085907 -0.214280 -0.648602"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scaler = StandardScaler()                                   # instantiate the scaler \n",
    "sfeatures = scaler.fit_transform(df.values)              # standardize all the values extracted from the DataFrame \n",
    "df_st = pd.DataFrame()                                     # instantiate a new DataFrame\n",
    "df_st = pd.DataFrame(sfeatures, index=df.index, columns=df.columns) # copy the standardized values into the new DataFrame\n",
    "df_st.head()                                               # preview the the new DataFrame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's close the loop and reverse the transformation and confirm that we get back to the original data.\n",
    "\n",
    "To do this we:\n",
    "\n",
    "5. call the 'fit' features' scaler's inverse transform function transformed value to the new DataFrame while keeping the sample index and feature names from the old DataFramae\n",
    "\n",
    "```python\n",
    "rfeatures = scaler.inverse_transform(df_st.values)\n",
    "```\n",
    "\n",
    "the output from this is a 2D numpy array. \n",
    "\n",
    "6. We will put it into a new DataFrame.\n",
    "\n",
    "```python\n",
    "df_reverse = pd.DataFrame(rfeatures, index=df.index, columns=df.columns)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Por</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "      <th>Brittle</th>\n",
       "      <th>TOC</th>\n",
       "      <th>VR</th>\n",
       "      <th>Prod</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12.08</td>\n",
       "      <td>2.92</td>\n",
       "      <td>2.80</td>\n",
       "      <td>81.40</td>\n",
       "      <td>1.16</td>\n",
       "      <td>2.31</td>\n",
       "      <td>1695.360819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12.38</td>\n",
       "      <td>3.53</td>\n",
       "      <td>3.22</td>\n",
       "      <td>46.17</td>\n",
       "      <td>0.89</td>\n",
       "      <td>1.88</td>\n",
       "      <td>3007.096063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>14.02</td>\n",
       "      <td>2.59</td>\n",
       "      <td>4.01</td>\n",
       "      <td>72.80</td>\n",
       "      <td>0.89</td>\n",
       "      <td>2.72</td>\n",
       "      <td>2531.938259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>17.67</td>\n",
       "      <td>6.75</td>\n",
       "      <td>2.63</td>\n",
       "      <td>39.81</td>\n",
       "      <td>1.08</td>\n",
       "      <td>1.88</td>\n",
       "      <td>5288.514854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.52</td>\n",
       "      <td>4.57</td>\n",
       "      <td>3.18</td>\n",
       "      <td>10.94</td>\n",
       "      <td>1.51</td>\n",
       "      <td>1.90</td>\n",
       "      <td>2859.469624</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Por  Perm    AI  Brittle   TOC    VR         Prod\n",
       "0  12.08  2.92  2.80    81.40  1.16  2.31  1695.360819\n",
       "1  12.38  3.53  3.22    46.17  0.89  1.88  3007.096063\n",
       "2  14.02  2.59  4.01    72.80  0.89  2.72  2531.938259\n",
       "3  17.67  6.75  2.63    39.81  1.08  1.88  5288.514854\n",
       "4  17.52  4.57  3.18    10.94  1.51  1.90  2859.469624"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rfeatures = scaler.inverse_transform(df_st.values)\n",
    "df_reverse = pd.DataFrame(rfeatures, index=df.index, columns=df.columns) # copy the standardized values into the new DataFrame\n",
    "df_reverse.head() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can confirm the result is the same as the original, prior to standardization DatatFrame.\n",
    "\n",
    "We were just testing, so let's get rid of (delete) the new DataFrame.  We can use the following to delete an instantiated object in Python.\n",
    "\n",
    "```python\n",
    "del df_reverse\n",
    "```\n",
    "\n",
    "For more complicated workflows it may be a good idea to remove intermediate products to save memmory and to prevent clutter!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "del df_reverse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normalization\n",
    "\n",
    "Also known as the min / max transform, recales the features to have a minimum of 0 and a maximum of 1.\n",
    "\n",
    "\\begin{equation}\n",
    "y = \\frac{x - min(x)}{max(x) - min(x)}\n",
    "\\end{equation}\n",
    "\n",
    "where $min(x)$ and $max(x)$ are the minimum and maximum values for each feature.\n",
    "\n",
    "* scikit learn has a built in min / max transform method\n",
    "\n",
    "```python\n",
    "min_max_scaler = preprocessing.MinMaxScaler()\n",
    "scaled_array = min_max_scaler.fit_transform(float_array)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Por</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "      <th>Brittle</th>\n",
       "      <th>TOC</th>\n",
       "      <th>VR</th>\n",
       "      <th>Prod</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.325294</td>\n",
       "      <td>0.204805</td>\n",
       "      <td>0.453731</td>\n",
       "      <td>0.960076</td>\n",
       "      <td>0.532110</td>\n",
       "      <td>0.711340</td>\n",
       "      <td>0.110384</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.342941</td>\n",
       "      <td>0.274600</td>\n",
       "      <td>0.579104</td>\n",
       "      <td>0.480038</td>\n",
       "      <td>0.408257</td>\n",
       "      <td>0.489691</td>\n",
       "      <td>0.279628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.439412</td>\n",
       "      <td>0.167048</td>\n",
       "      <td>0.814925</td>\n",
       "      <td>0.842894</td>\n",
       "      <td>0.408257</td>\n",
       "      <td>0.922680</td>\n",
       "      <td>0.218322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.654118</td>\n",
       "      <td>0.643021</td>\n",
       "      <td>0.402985</td>\n",
       "      <td>0.393378</td>\n",
       "      <td>0.495413</td>\n",
       "      <td>0.489691</td>\n",
       "      <td>0.573983</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.645294</td>\n",
       "      <td>0.393593</td>\n",
       "      <td>0.567164</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.692661</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.260581</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Por      Perm        AI   Brittle       TOC        VR      Prod\n",
       "0  0.325294  0.204805  0.453731  0.960076  0.532110  0.711340  0.110384\n",
       "1  0.342941  0.274600  0.579104  0.480038  0.408257  0.489691  0.279628\n",
       "2  0.439412  0.167048  0.814925  0.842894  0.408257  0.922680  0.218322\n",
       "3  0.654118  0.643021  0.402985  0.393378  0.495413  0.489691  0.573983\n",
       "4  0.645294  0.393593  0.567164  0.000000  0.692661  0.500000  0.260581"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm_scaler = preprocessing.MinMaxScaler()                 # instantiate the scaler \n",
    "nfeatures = norm_scaler.fit_transform(df.values)           # standardize all the values extracted from the DataFrame \n",
    "df_n = pd.DataFrame(nfeatures, index=df.index, columns=df.columns) # copy the standardized values into the new DataFrame\n",
    "df_n.head() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check the summary statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Por</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.496538</td>\n",
       "      <td>0.174775</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.374265</td>\n",
       "      <td>0.501176</td>\n",
       "      <td>0.638382</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Perm</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.366219</td>\n",
       "      <td>0.198057</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.227975</td>\n",
       "      <td>0.332380</td>\n",
       "      <td>0.475686</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AI</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.504134</td>\n",
       "      <td>0.169220</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.378358</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.616418</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Brittle</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.507180</td>\n",
       "      <td>0.192526</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.365377</td>\n",
       "      <td>0.525548</td>\n",
       "      <td>0.644809</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TOC</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.455023</td>\n",
       "      <td>0.219387</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.283257</td>\n",
       "      <td>0.472477</td>\n",
       "      <td>0.619266</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>VR</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.533144</td>\n",
       "      <td>0.155066</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.432990</td>\n",
       "      <td>0.530928</td>\n",
       "      <td>0.625000</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Prod</th>\n",
       "      <td>200.0</td>\n",
       "      <td>0.390241</td>\n",
       "      <td>0.200408</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.238229</td>\n",
       "      <td>0.356681</td>\n",
       "      <td>0.504843</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count      mean       std  min       25%       50%       75%  max\n",
       "Por      200.0  0.496538  0.174775  0.0  0.374265  0.501176  0.638382  1.0\n",
       "Perm     200.0  0.366219  0.198057  0.0  0.227975  0.332380  0.475686  1.0\n",
       "AI       200.0  0.504134  0.169220  0.0  0.378358  0.500000  0.616418  1.0\n",
       "Brittle  200.0  0.507180  0.192526  0.0  0.365377  0.525548  0.644809  1.0\n",
       "TOC      200.0  0.455023  0.219387  0.0  0.283257  0.472477  0.619266  1.0\n",
       "VR       200.0  0.533144  0.155066  0.0  0.432990  0.530928  0.625000  1.0\n",
       "Prod     200.0  0.390241  0.200408  0.0  0.238229  0.356681  0.504843  1.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_n.describe().transpose()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's close the loop and reverse the transformation (back-transform) and confirm that we get back to the original data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>Por</th>\n",
       "      <th>Perm</th>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12.08</td>\n",
       "      <td>2.92</td>\n",
       "      <td>2.80</td>\n",
       "      <td>81.40</td>\n",
       "      <td>1.16</td>\n",
       "      <td>2.31</td>\n",
       "      <td>1695.360819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12.38</td>\n",
       "      <td>3.53</td>\n",
       "      <td>3.22</td>\n",
       "      <td>46.17</td>\n",
       "      <td>0.89</td>\n",
       "      <td>1.88</td>\n",
       "      <td>3007.096063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>14.02</td>\n",
       "      <td>2.59</td>\n",
       "      <td>4.01</td>\n",
       "      <td>72.80</td>\n",
       "      <td>0.89</td>\n",
       "      <td>2.72</td>\n",
       "      <td>2531.938259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>17.67</td>\n",
       "      <td>6.75</td>\n",
       "      <td>2.63</td>\n",
       "      <td>39.81</td>\n",
       "      <td>1.08</td>\n",
       "      <td>1.88</td>\n",
       "      <td>5288.514854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.52</td>\n",
       "      <td>4.57</td>\n",
       "      <td>3.18</td>\n",
       "      <td>10.94</td>\n",
       "      <td>1.51</td>\n",
       "      <td>1.90</td>\n",
       "      <td>2859.469624</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Por  Perm    AI  Brittle   TOC    VR         Prod\n",
       "0  12.08  2.92  2.80    81.40  1.16  2.31  1695.360819\n",
       "1  12.38  3.53  3.22    46.17  0.89  1.88  3007.096063\n",
       "2  14.02  2.59  4.01    72.80  0.89  2.72  2531.938259\n",
       "3  17.67  6.75  2.63    39.81  1.08  1.88  5288.514854\n",
       "4  17.52  4.57  3.18    10.94  1.51  1.90  2859.469624"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rfeatures = norm_scaler.inverse_transform(df_n.values)\n",
    "df_reverse = pd.DataFrame()                                     # instantiate a new DataFrame\n",
    "df_reverse = pd.DataFrame(rfeatures, index=df.index, columns=df.columns) # copy the standardized values into the new DataFrame\n",
    "df_reverse.head() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can confirm the result is the same as the original, prior to standardization DataFrame.\n",
    "\n",
    "Once again we were just testing, so let's delete the back-transformed DataFrame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "del df_reverse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### L1 / L2 Normalizer\n",
    "\n",
    "Another type of normalization is performed independently on each sample to force the $L1$ or $L2$ norm to be 1.0.\n",
    "\n",
    "For the L1 norm:\n",
    "\n",
    "\\begin{equation}\n",
    "\\sum^m_{i,\\alpha = 1} x_{i, \\alpha} = 1.0, \\quad i = 1, \\ldots, n\n",
    "\\end{equation}\n",
    "\n",
    "where we have $x_{i, \\alpha}, \\alpha = 1, \\dots, m$ features over $i = 1, \\dots, n$ samples.\n",
    "\n",
    "For the L2 norm:\n",
    "\n",
    "\\begin{equation}\n",
    "\\sum^m_{i,\\alpha = 1}\\left( x_{i, \\alpha} \\right)^2 = 1.0, \\quad i = 1, \\ldots, n\n",
    "\\end{equation}\n",
    "\n",
    "where we have $x_{i, \\alpha}, \\alpha = 1, \\dots, m$ features over $i = 1, \\dots, n$ samples.\n",
    "\n",
    "* this may be applied in text classification or clustering\n",
    "\n",
    "We demonstrate the L1 and L2 normalizer below.\n",
    "\n",
    "* there is no reverse to this transform\n",
    "\n",
    "Let's start with the $L2$ norm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Por</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "      <th>Brittle</th>\n",
       "      <th>TOC</th>\n",
       "      <th>VR</th>\n",
       "      <th>Prod</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.007117</td>\n",
       "      <td>0.001720</td>\n",
       "      <td>0.001650</td>\n",
       "      <td>0.047957</td>\n",
       "      <td>0.000683</td>\n",
       "      <td>0.001361</td>\n",
       "      <td>0.998820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.004116</td>\n",
       "      <td>0.001174</td>\n",
       "      <td>0.001071</td>\n",
       "      <td>0.015352</td>\n",
       "      <td>0.000296</td>\n",
       "      <td>0.000625</td>\n",
       "      <td>0.999872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.005535</td>\n",
       "      <td>0.001022</td>\n",
       "      <td>0.001583</td>\n",
       "      <td>0.028740</td>\n",
       "      <td>0.000351</td>\n",
       "      <td>0.001074</td>\n",
       "      <td>0.999569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.003341</td>\n",
       "      <td>0.001276</td>\n",
       "      <td>0.000497</td>\n",
       "      <td>0.007527</td>\n",
       "      <td>0.000204</td>\n",
       "      <td>0.000355</td>\n",
       "      <td>0.999965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.006127</td>\n",
       "      <td>0.001598</td>\n",
       "      <td>0.001112</td>\n",
       "      <td>0.003826</td>\n",
       "      <td>0.000528</td>\n",
       "      <td>0.000664</td>\n",
       "      <td>0.999972</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Por      Perm        AI   Brittle       TOC        VR      Prod\n",
       "0  0.007117  0.001720  0.001650  0.047957  0.000683  0.001361  0.998820\n",
       "1  0.004116  0.001174  0.001071  0.015352  0.000296  0.000625  0.999872\n",
       "2  0.005535  0.001022  0.001583  0.028740  0.000351  0.001074  0.999569\n",
       "3  0.003341  0.001276  0.000497  0.007527  0.000204  0.000355  0.999965\n",
       "4  0.006127  0.001598  0.001112  0.003826  0.000528  0.000664  0.999972"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import Normalizer\n",
    "l2normalizer = Normalizer(norm = 'l2') \n",
    "l2features = l2normalizer.fit_transform(df)                                                             # standardize all the values extracted from the DataFrame \n",
    "df_nL2 = pd.DataFrame()                                      # instantiate a new DataFrame\n",
    "df_nL2 = pd.DataFrame(l2features, index=df.index, columns=df.columns) # copy the standardized values into the new DataFrame\n",
    "df_nL2.head() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's demonstrate the $L1$ norm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Por</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "      <th>Brittle</th>\n",
       "      <th>TOC</th>\n",
       "      <th>VR</th>\n",
       "      <th>Prod</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.007117</td>\n",
       "      <td>0.001720</td>\n",
       "      <td>0.001650</td>\n",
       "      <td>0.047957</td>\n",
       "      <td>0.000683</td>\n",
       "      <td>0.001361</td>\n",
       "      <td>0.998820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.004116</td>\n",
       "      <td>0.001174</td>\n",
       "      <td>0.001071</td>\n",
       "      <td>0.015352</td>\n",
       "      <td>0.000296</td>\n",
       "      <td>0.000625</td>\n",
       "      <td>0.999872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.005535</td>\n",
       "      <td>0.001022</td>\n",
       "      <td>0.001583</td>\n",
       "      <td>0.028740</td>\n",
       "      <td>0.000351</td>\n",
       "      <td>0.001074</td>\n",
       "      <td>0.999569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.003341</td>\n",
       "      <td>0.001276</td>\n",
       "      <td>0.000497</td>\n",
       "      <td>0.007527</td>\n",
       "      <td>0.000204</td>\n",
       "      <td>0.000355</td>\n",
       "      <td>0.999965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.006127</td>\n",
       "      <td>0.001598</td>\n",
       "      <td>0.001112</td>\n",
       "      <td>0.003826</td>\n",
       "      <td>0.000528</td>\n",
       "      <td>0.000664</td>\n",
       "      <td>0.999972</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Por      Perm        AI   Brittle       TOC        VR      Prod\n",
       "0  0.007117  0.001720  0.001650  0.047957  0.000683  0.001361  0.998820\n",
       "1  0.004116  0.001174  0.001071  0.015352  0.000296  0.000625  0.999872\n",
       "2  0.005535  0.001022  0.001583  0.028740  0.000351  0.001074  0.999569\n",
       "3  0.003341  0.001276  0.000497  0.007527  0.000204  0.000355  0.999965\n",
       "4  0.006127  0.001598  0.001112  0.003826  0.000528  0.000664  0.999972"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import Normalizer\n",
    "l1normalizer = Normalizer(norm = 'l1') \n",
    "l1features = l2normalizer.fit_transform(df)                                                             # standardize all the values extracted from the DataFrame \n",
    "df_nL1 = pd.DataFrame()                                      # instantiate a new DataFrame\n",
    "df_nL1 = pd.DataFrame(l1features, index=df.index, columns=df.columns) # copy the standardized values into the new DataFrame\n",
    "df_nL1.head() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Binary or Indictor Transform\n",
    "\n",
    "For the many problems that we need to perform a binary transform to convert our continuous feature to 0's and 1's based on a threshold, $x_t$\n",
    "\n",
    "* for the binary transform, $x_i = 0$ if $<= x_t$ and $x_i = 1$ otherwise\n",
    "* for the indicator transform, $x_i = 1$ if $<= x_t$ and $x_i = 0$ otherwise\n",
    "\n",
    "There is a scikit-learn function for the binary transform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "       [1.]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import Binarizer\n",
    "binarizer = Binarizer(threshold = 13.0) \n",
    "bPor = binarizer.fit_transform(df['Por'].values.reshape(-1, 1))                                                         # standardize all the values extracted from the DataFrame \n",
    "bPor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### K Bins Discretization\n",
    "\n",
    "With K bins discretization we bin the range of the feature into K bins and then expand each sample for our continuous feature to k features with the assignment of a value of 1 if the sample is within a bin and 0 if outsize the bin\n",
    "\n",
    "* strategies include uniform width bins (uniform) and uniform number of data in each bin (quantile)\n",
    "\n",
    "Let's make 5 uniform bins and then concatenate the original porosity values so we can compare the original porosity values and our K bins discretization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12.08,  0.  ,  1.  ,  0.  ,  0.  ,  0.  ],\n",
       "       [12.38,  0.  ,  1.  ,  0.  ,  0.  ,  0.  ],\n",
       "       [14.02,  0.  ,  0.  ,  1.  ,  0.  ,  0.  ],\n",
       "       ...,\n",
       "       [12.12,  0.  ,  1.  ,  0.  ,  0.  ,  0.  ],\n",
       "       [15.55,  0.  ,  0.  ,  1.  ,  0.  ,  0.  ],\n",
       "       [20.89,  0.  ,  0.  ,  0.  ,  0.  ,  1.  ]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import KBinsDiscretizer\n",
    "kbins = KBinsDiscretizer(n_bins=5, strategy='uniform') \n",
    "kbins_por = kbins.fit_transform(df['Por'].values.reshape(-1, 1))                                                         # standardize all the values extracted from the DataFrame \n",
    "np.concatenate((df['Por'].values.reshape(-1, 1),kbins_por.toarray()),axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the bin boundaries to better understand the result above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([array([ 6.55,  9.95, 13.35, 16.75, 20.15, 23.55])], dtype=object)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kbins.bin_edges_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Spot check the first sample, $12.08\\%$ porosity is $\\in [9.95\\%,13.35\\%]$ so we have a 1 in the second bin (second column in our table) and zeros in the other bins. \n",
    "\n",
    "### Gaussian Transform / Gaussian Anamorphosis\n",
    "\n",
    "This is a quantile transformation of the feature to follow a Gaussian distribution. We actually map each of the quantiles from the original feature distribution to the target distribution. This is required for a wide range of statistical methods.\n",
    "\n",
    "\\begin{equation}\n",
    "y = G_y^{-1}(F_x(x))\n",
    "\\end{equation}\n",
    "\n",
    "where $G_y$ is the Gaussian cumulative distribution function and $F_x$ is the original feature cumulative distribution function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Por</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "      <th>Brittle</th>\n",
       "      <th>TOC</th>\n",
       "      <th>VR</th>\n",
       "      <th>Prod</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.966707</td>\n",
       "      <td>-0.816627</td>\n",
       "      <td>-0.308666</td>\n",
       "      <td>2.703111</td>\n",
       "      <td>0.305481</td>\n",
       "      <td>1.123308</td>\n",
       "      <td>-1.771156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.870846</td>\n",
       "      <td>-0.383621</td>\n",
       "      <td>0.449229</td>\n",
       "      <td>-0.203734</td>\n",
       "      <td>-0.275431</td>\n",
       "      <td>-0.348756</td>\n",
       "      <td>-0.401986</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.321971</td>\n",
       "      <td>-1.077879</td>\n",
       "      <td>1.746017</td>\n",
       "      <td>2.051587</td>\n",
       "      <td>-0.275431</td>\n",
       "      <td>2.324341</td>\n",
       "      <td>-0.837169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.735470</td>\n",
       "      <td>1.339654</td>\n",
       "      <td>-0.559592</td>\n",
       "      <td>-0.592008</td>\n",
       "      <td>0.114185</td>\n",
       "      <td>-0.348756</td>\n",
       "      <td>0.829950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.702820</td>\n",
       "      <td>0.295415</td>\n",
       "      <td>0.362601</td>\n",
       "      <td>-5.199338</td>\n",
       "      <td>1.036433</td>\n",
       "      <td>-0.269066</td>\n",
       "      <td>-0.532220</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Por      Perm        AI   Brittle       TOC        VR      Prod\n",
       "0 -0.966707 -0.816627 -0.308666  2.703111  0.305481  1.123308 -1.771156\n",
       "1 -0.870846 -0.383621  0.449229 -0.203734 -0.275431 -0.348756 -0.401986\n",
       "2 -0.321971 -1.077879  1.746017  2.051587 -0.275431  2.324341 -0.837169\n",
       "3  0.735470  1.339654 -0.559592 -0.592008  0.114185 -0.348756  0.829950\n",
       "4  0.702820  0.295415  0.362601 -5.199338  1.036433 -0.269066 -0.532220"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import QuantileTransformer\n",
    "nscore = QuantileTransformer(n_quantiles=100, random_state=73, output_distribution = 'normal') \n",
    "nsfeatures = nscore.fit_transform(df)                                                             # standardize all the values extracted from the DataFrame \n",
    "df_ns = pd.DataFrame()                                      # instantiate a new DataFrame\n",
    "df_ns = pd.DataFrame(nsfeatures, index=df.index, columns=df.columns) # copy the standardized values into the new DataFrame\n",
    "df_ns.head() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the Gaussian transformed feature histograms.\n",
    "\n",
    "* we should see a nice bell shape centered on 0.0 with a range of about -4 to 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "histograms(df_ns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, let's check out the reverse transform.  We just reverse the previous quantile transform\n",
    "\n",
    "\\begin{equation}\n",
    "x = F_x^{-1}(G_y(y))\n",
    "\\end{equation}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Por</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "      <th>Brittle</th>\n",
       "      <th>TOC</th>\n",
       "      <th>VR</th>\n",
       "      <th>Prod</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12.08</td>\n",
       "      <td>2.92</td>\n",
       "      <td>2.80</td>\n",
       "      <td>81.40</td>\n",
       "      <td>1.16</td>\n",
       "      <td>2.31</td>\n",
       "      <td>1695.360819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12.38</td>\n",
       "      <td>3.53</td>\n",
       "      <td>3.22</td>\n",
       "      <td>46.17</td>\n",
       "      <td>0.89</td>\n",
       "      <td>1.88</td>\n",
       "      <td>3007.096063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>14.02</td>\n",
       "      <td>2.59</td>\n",
       "      <td>4.01</td>\n",
       "      <td>72.80</td>\n",
       "      <td>0.89</td>\n",
       "      <td>2.72</td>\n",
       "      <td>2531.938259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>17.67</td>\n",
       "      <td>6.75</td>\n",
       "      <td>2.63</td>\n",
       "      <td>39.81</td>\n",
       "      <td>1.08</td>\n",
       "      <td>1.88</td>\n",
       "      <td>5288.514854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.52</td>\n",
       "      <td>4.57</td>\n",
       "      <td>3.18</td>\n",
       "      <td>10.94</td>\n",
       "      <td>1.51</td>\n",
       "      <td>1.90</td>\n",
       "      <td>2859.469624</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Por  Perm    AI  Brittle   TOC    VR         Prod\n",
       "0  12.08  2.92  2.80    81.40  1.16  2.31  1695.360819\n",
       "1  12.38  3.53  3.22    46.17  0.89  1.88  3007.096063\n",
       "2  14.02  2.59  4.01    72.80  0.89  2.72  2531.938259\n",
       "3  17.67  6.75  2.63    39.81  1.08  1.88  5288.514854\n",
       "4  17.52  4.57  3.18    10.94  1.51  1.90  2859.469624"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rfeatures = nscore.inverse_transform(df_ns.values)\n",
    "df_reverse = pd.DataFrame()                                     # instantiate a new DataFrame\n",
    "df_reverse = pd.DataFrame(rfeatures, index=df.index, columns=df.columns) # copy the standardized values into the new DataFrame\n",
    "df_reverse.head() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also perform a uniform transform. Let's show the quntile transformation to a uniform distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Por</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "      <th>Brittle</th>\n",
       "      <th>TOC</th>\n",
       "      <th>VR</th>\n",
       "      <th>Prod</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.166845</td>\n",
       "      <td>0.207071</td>\n",
       "      <td>0.378788</td>\n",
       "      <td>0.996565</td>\n",
       "      <td>0.620000</td>\n",
       "      <td>0.869347</td>\n",
       "      <td>0.038267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.191919</td>\n",
       "      <td>0.350630</td>\n",
       "      <td>0.673367</td>\n",
       "      <td>0.419281</td>\n",
       "      <td>0.391493</td>\n",
       "      <td>0.363636</td>\n",
       "      <td>0.343847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.373737</td>\n",
       "      <td>0.140544</td>\n",
       "      <td>0.959596</td>\n",
       "      <td>0.979895</td>\n",
       "      <td>0.391493</td>\n",
       "      <td>0.989946</td>\n",
       "      <td>0.201249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.768973</td>\n",
       "      <td>0.909821</td>\n",
       "      <td>0.287879</td>\n",
       "      <td>0.276923</td>\n",
       "      <td>0.545455</td>\n",
       "      <td>0.363636</td>\n",
       "      <td>0.796716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.758916</td>\n",
       "      <td>0.616162</td>\n",
       "      <td>0.641549</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.850000</td>\n",
       "      <td>0.393939</td>\n",
       "      <td>0.297287</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Por      Perm        AI   Brittle       TOC        VR      Prod\n",
       "0  0.166845  0.207071  0.378788  0.996565  0.620000  0.869347  0.038267\n",
       "1  0.191919  0.350630  0.673367  0.419281  0.391493  0.363636  0.343847\n",
       "2  0.373737  0.140544  0.959596  0.979895  0.391493  0.989946  0.201249\n",
       "3  0.768973  0.909821  0.287879  0.276923  0.545455  0.363636  0.796716\n",
       "4  0.758916  0.616162  0.641549  0.000000  0.850000  0.393939  0.297287"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import QuantileTransformer\n",
    "uniform = QuantileTransformer(n_quantiles=100, random_state=73, output_distribution = 'uniform') \n",
    "unifeatures = uniform.fit_transform(df)                                                             # standardize all the values extracted from the DataFrame \n",
    "df_uni = pd.DataFrame()                                      # instantiate a new DataFrame\n",
    "df_uni = pd.DataFrame(unifeatures, index=df.index, columns=df.columns) # copy the standardized values into the new DataFrame\n",
    "df_uni.head() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the uniform transformed feature histograms.\n",
    "\n",
    "* we should see a uniform frequencies (with some noise due to limited sampling) $\\in [0,1]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "histograms(df_uni)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have features with uniform distributions $[0,1]$.\n",
    "\n",
    "### Custom Transformers\n",
    "\n",
    "We can also create our own custom transform.  We can specify our own transform within a scikit learn preprocessing function\n",
    "\n",
    "* this allows us to have a convenient method for forward and reverse transforms of our features as we have seen above\n",
    "\n",
    "Let's demonstrate with the natural log for the foward transform and the exponential for the reverse transform.\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "y = log(x)\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "x = exp(y)\n",
    "\\end{equation}\n",
    "\n",
    "```python\n",
    "custom_transformer = FunctionTransformer(func = np.log, inverse_func = np.exp)\n",
    "```\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LogPerm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.071584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.261298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.951658</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.909543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.519513</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    LogPerm\n",
       "0  1.071584\n",
       "1  1.261298\n",
       "2  0.951658\n",
       "3  1.909543\n",
       "4  1.519513"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import FunctionTransformer\n",
    "custom_transformer = FunctionTransformer(func = np.log, inverse_func = np.exp, check_inverse = True, validate=True)\n",
    "custom_features = custom_transformer.fit_transform(df['Perm'].values.reshape(-1, 1))                                                             # standardize all the values extracted from the DataFrame \n",
    "df_custom = pd.DataFrame(custom_features, columns = ['LogPerm'])                 # instantiate a new DataFrame\n",
    "df_custom.head() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's demonstrate that our custom transform is reversible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Perm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.57</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Perm\n",
       "0  2.92\n",
       "1  3.53\n",
       "2  2.59\n",
       "3  6.75\n",
       "4  4.57"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rfeatures = custom_transformer.inverse_transform(df_custom.values)\n",
    "df_reverse = pd.DataFrame(rfeatures, index=df_custom.index, columns=['Perm']) # copy the standardized values into the new DataFrame\n",
    "df_reverse.head() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the back-transformed permeability values to the original dataset.  The reverse transform that we speficied with our custom transformation works!\n",
    "\n",
    "#### Comments\n",
    "\n",
    "This was a basic demonstration of feature transformations. This might not seem very interesting at this time, but these transformations are important building blocks of workflow construction for data analytics and machine learning! \n",
    "\n",
    "I have other demonstrations on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, trend modeling and many other workflows available at https://github.com/GeostatsGuy/PythonNumericalDemos and https://github.com/GeostatsGuy/GeostatsPy. \n",
    "  \n",
    "I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "#### The Author:\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
  },
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   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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