PCA_Visual.py

import pandas as pd
import numpy as np
import seaborn as sns
from sklearn import datasets
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
import matplotlib.pyplot as plt
from matplotlib.colors import cnames
from itertools import cycle
from bokeh.plotting import output_notebook, output_file, figure, show, ColumnDataSource
from bokeh.models import HoverTool
import warnings
warnings.filterwarnings(action='ignore')
output_notebook()


def get_float_list(range_max:int, div:int=100) -> list:
    """ To get 0 -> 1, range_max must be same order of mag as div """
    return [float(x)/div for x in range(int(range_max))]


def get_colorcycle(colordict:dict):
    """ Subset cnames with a string match and get a color cycle for plotting """
    return cycle(list(colordict.keys()))


def get_colordict(filter_:str='dark') -> dict:
    """ return dictionary of colornames by filter """
    return dict((k, v) for k, v in cnames.items() if filter_ in k)


def pca_report_interactive(X, scale_X:bool=True, save_plot:bool=False):
    """
    X:          input data matrix
    scale_X:    determine whether to rescale X (StandardScaler) [default: True, X is not prescaled
    save_plot:  save plot to file (html) and not show
    """

    # calculate mean and var
    X_mean, X_var = X.mean(), X.var()
    print('\n*--- PCA Report ---*\n')
    print(f'X mean:\t\t{X_mean:.3f}\nX variance:\t{X_var:.3f}')

    if scale_X:
        # rescale and run PCA
        print("\n...Rescaling data...\n")
        scaler = StandardScaler()
        X_scaled = scaler.fit_transform(X)
        X_s_mean, X_s_var = X_scaled.mean(), X_scaled.var()
        print(f'X_scaled mean:\t\t{np.round(X_s_mean):.3f}')
        print(f'X_scaled variance:\t{np.round(X_s_var):.3f}\n')
        pca_ = PCA().fit(X_scaled)
        X_pca = PCA().fit_transform(X)
    else:
        # run PCA directly
        print("...Assuming data is properly scaled...")
        pca_ = PCA().fit(X)
        X_pca = PCA().fit_transform(X)
            
    # Get cumulative explained variance for each dimension
    pca_evr = pca_.explained_variance_ratio_
    cumsum_ = np.cumsum(pca_evr)
    
    # Get dimensions where var >= 95% and values for variance at 2D, 3D
    dim_95 = np.argmax(cumsum_ >= 0.95) + 1
    twoD = np.round(cumsum_[1], decimals=3)*100 
    threeD = np.round(cumsum_[2], decimals=3)*100
    instances_, dims_ =  X.shape
    
    # check shape of X
    if dims_ > instances_:
        print("WARNING: number of features greater than number of instances.")
        dimensions = list(range(1, instances_+1))
    else:
        dimensions = list(range(1, dims_+1))
    
    # Print report
    print("\n -- Summary --")
    print(f"You can reduce from {dims_} to {dim_95} dimensions while retaining 95% of variance.")
    print(f"2 principal components explain {twoD:.2f}% of variance.")
    print(f"3 principal components explain {threeD:.2f}% of variance.")
    
    """ - Plotting - """
    # Create custom HoverTool -- we'll name each ROC curve 'ROC' so we only see info on hover there
    hover_ = HoverTool(names=['PCA'], tooltips=[("dimensions", "@x_dim"), 
                                                ("cumulative variance", "@y_cumvar"),
                                                ("explained variance", "@y_var")])
    p_tools = [hover_, 'crosshair', 'zoom_in', 'zoom_out', 'save', 'reset', 'tap', 'box_zoom']

    # insert 0 at beginning for cleaner plotting
    cumsum_plot = np.insert(cumsum_, 0, 0) 
    pca_evr_plot = np.insert(pca_evr, 0, 0)
    dimensions_plot = np.insert(dimensions, 0, 0)

    """
    ColumnDataSource
    - a special type in Bokeh that allows you to store data for plotting
    - store data as dict (key:list)
    - to plot two keys against one another, make sure they're the same length!
    - below:
        x_dim    # of dimensions (length = # of dimensions)
        y_cumvar # cumulative variance (length = # of dimensions)
        var_95   # y = 0.95 (length = # of dimensions)
        zero_one # list of 0 to 1
        twoD     # x = 2 
        threeD   # x = 3 
    """ 
    
    # get sources
    source_PCA = ColumnDataSource(data=dict(x_dim = dimensions_plot,y_cumvar = cumsum_plot, y_var = pca_evr_plot))    
    source_var95 = ColumnDataSource(data=dict(var95_x = [dim_95]*96, var95_y = get_float_list(96)))
    source_twoD = ColumnDataSource(data=dict(twoD_x = [2]*(int(twoD)+1), twoD_y = get_float_list(twoD+1)))
    source_threeD = ColumnDataSource(data=dict(threeD_x = [3]*(int(threeD)+1), threeD_y = get_float_list(threeD+1)))

    """ PLOT """
    # set up figure and add axis labels
    p = figure(title='PCA Analysis', tools=p_tools)
    p.xaxis.axis_label = f'N of {dims_} Principal Components' 
    p.yaxis.axis_label = 'Variance Explained (per PC & Cumulative)'
    
    # add reference lines: y=0.95, x=2, x=3
    p.line('twoD_x', 'twoD_y', line_width=0.5, line_dash='dotted', color='#435363', source=source_twoD) # x=2
    p.line('threeD_x', 'threeD_y', line_width=0.5, line_dash='dotted', color='#435363', source=source_threeD) # x=3
    p.line('var95_x', 'var95_y', line_width=2, line_dash='dotted', color='#435363', source=source_var95) # var = 0.95

    # add bar plot for variance per dimension
    p.vbar(x='x_dim', top='y_var', width=.5, bottom=0, color='#D9F2EF', source=source_PCA, name='PCA')
    
    # add cumulative variance (scatter + line)
    p.line('x_dim', 'y_cumvar', line_width=1, color='#F79737', source=source_PCA)
    p.circle('x_dim', 'y_cumvar', size=7, color='#FF4C00', source=source_PCA, name='PCA')

    # change gridlines
    p.ygrid.grid_line_alpha = 0.25
    p.xgrid.grid_line_alpha = 0.25

    # change axis bounds and grid
    p.xaxis.bounds = (0, dims_)
    p.yaxis.bounds = (0, 1)
    p.grid.bounds = (0, dims_)

    # save and show p
    if save_plot:
        output_file('PCA_analysis.html')
    show(p)
        
    # output PCA info as a dataframe
    df_PCA = pd.DataFrame({'dimension': dimensions, 'variance_cumulative': cumsum_, 'variance': pca_evr}).set_index(['dimension'])
        
    return df_PCA, X_pca, pca_evr


def pca_feature_correlation(X, X_pca, explained_var, features:list=None, fig_dpi:int=150, save_plot:bool=False):
    """
    1. Get dot product of X and X_pca
    2. Run normalizations of X*X_pca
    3. Retrieve df/matrices

    X:               data (numpy matrix)
    X_pca:           PCA
    explained_var:   explained variance matrix
    features:        list of feature names
    fig_dpi:         dpi to use for heatmaps
    save_plot:       save plot to file (html) and not show
    """
    
    # Add zeroes for data where features > instances
    outer_diff = X.T.shape[0] - X_pca.shape[1]
    if outer_diff > 0: # outer dims must match to get sq matrix
        Z = np.zeros([X_pca.shape[0], outer_diff])
        X_pca = np.c_[X_pca, Z]
        explained_var = np.append(explained_var, np.zeros(outer_diff))
    
    # Get correlation between original features (X) and PCs (X_pca)
    dot_matrix = np.dot(X.T, X_pca)
    print(f"X*X_pca: {X.T.shape} * {X_pca.shape} = {dot_matrix.shape}")
    
    # Correlation matrix -> df
    df_dotproduct = pd.DataFrame(dot_matrix)
    df_dotproduct.columns = [''.join(['PC', f'{i+1}']) for i in range(dot_matrix.shape[0])]
    if any(features): df_dotproduct.index = features    
    
    # Normalize & Sort
    df_n, df_na, df_nabv = normalize_dataframe(df_dotproduct, explained_var, plot_opt=True, save_plot=save_plot)
    
    return df_dotproduct, df_n, df_na, df_nabv


def normalize_dataframe(df, explained_var=None, fig_dpi:int=150, plot_opt:bool=True, save_plot:bool=False):
    """
    1. Get z-normalized df (normalized to µ=0, σ=1)
    2. Get absolute value of z-normalized df
    3. If explained_variance matrix provided, dot it w/ (2)
    """
    # Normalize, Reindex, & Sort
    df_norm = (df.copy()-df.mean())/df.std()
    df_norm = df_norm.sort_values(list(df_norm.columns), ascending=False)
    
    # Absolute value of normalized (& sort)
    df_abs = df_norm.copy().abs().set_index(df_norm.index)
    df_abs = df_abs.sort_values(by=list(df_abs.columns), ascending=False)
    
    # Plot
    if plot_opt:
        # Z-normalized corr matrix
        plt.figure(dpi=fig_dpi)
        ax_normal = sns.heatmap(df_norm, cmap="RdBu")
        ax_normal.set_title("Z-Normalized Data")
        if save_plot:
            plt.savefig('Z_normalized_corr_matrix.png')
        else:
            plt.show()

        # |Z-normalized corr matrix|  
        plt.figure(dpi=fig_dpi)
        ax_abs = sns.heatmap(df_abs, cmap="Purples")
        ax_abs.set_title("|Z-Normalized|")
        if save_plot:
            plt.savefig('Z_normalized_corr_matrix_Abs.png')
        else:
            plt.show()
        
    # Re-normalize by explained var (& sort)
    if explained_var.any():
        df_byvar = df_abs.copy()*explained_var
        df_byvar = df_byvar.sort_values(by=list(df_norm.columns), ascending=False)
        if plot_opt:
            plt.figure(dpi=fig_dpi)
            ax_relative = sns.heatmap(df_byvar, cmap="Purples")
            ax_relative.set_title("|Z-Normalized|*Explained_Variance")
            if save_plot:
                plt.savefig('Normalized_corr_matrix.png')
            else:
                plt.show()
    else:
        df_byvar = None
    return df_norm, df_abs, df_byvar


def pca_rank_features(df_nabv, verbose:bool=True):
    """
    Given a dataframe df_nabv with dimensions [f, p], where:
        f = features (sorted)
        p = principal components
        df_nabv.values are |Z-normalized X|*pca_.explained_variance_ratio_
        
    1. Create column of sum of each row, sort by it 'score_'
    3. Set index as 'rank'
    """
    df_rank = df_nabv.copy().assign(score_ = df_nabv.sum(axis=1)).sort_values('score_', ascending=False)
    df_rank['feature_'] = df_rank.index
    df_rank.index = range(1, len(df_rank)+1)
    df_rank.drop(df_nabv.columns, axis=1, inplace=True)
    df_rank.index.rename('rank', inplace=True)
    if verbose: print(df_rank)
    return df_rank


def pca_full_report(X, features_:list=None, fig_dpi:int=150, save_plot:bool=False):
    """
    Run complete PCA workflow:
        1. pca_report_interactive()
        2. pca_feature_correlation()
        3. pca_rank_features()
        
    X:            data (numpy array)
    features_:    list of feature names
    fig_dpi:      image resolution
    
    """
    # Retrieve the interactive report
    df_pca, X_pca, pca_evr = pca_report_interactive(X, save_plot=save_plot)
    # Get feature-PC correlation matrices
    df_corr, df_n, df_na, df_nabv = pca_feature_correlation(X, X_pca, pca_evr, features_, fig_dpi, save_plot) 
    # Get rank for each feature
    df_rank = pca_rank_features(df_nabv)
    return (df_pca, X_pca, pca_evr, df_corr, df_n, df_na, df_nabv, df_rank)