similarity_functions.py

# Note, this code is adapted from https://github.com/Slowika/Bag-of-Recipes
import numpy as np


def jaccard(X):
    """ Function to compute Jaccard similarity between two sets of elements.
        In this case, we have a list of recipes that contain each ingredient in the pair
        ingredients we are evaluating.

        Inputs:
            X: dataframe of recipes x ingredients
    """

    # Find the intersection of each ingredient pair (co-occurrences).
    inters = X.T.dot(X)

    # Find the union of each ingredient pair (number of recipes with either a or b or both).
    union = np.add.outer(np.diag(inters), np.diag(inters)) - inters

    # Check if any unions are zero.
    if np.any(union == 0):
        asims = np.zeros(X.shape[1])
        print("Some ingredients were not present in any recipe.")

    # Calculate Jaccard similarities.
    jacs = inters / union

    return np.array(jacs)


def asymmetric_cosine(X, alpha=0.2):
    """ Function to compute asymmetric cosine similarity between two sets of elements
        In this case, we have a list of recipes that contain each ingredient in the pair
        ingredients we are evaluating.

        Inputs:
            X:     dataframe of recipes x ingredients
            alpha: tuning parameter, different weights to set sizes for the elements in the pair
    """

    # Find the intersection of each ingredient pair (co-occurrences).
    inters = X.T.dot(X)

    # Find the denominator (|U(i)|^alpha * |U(j)|^(1-alpha).
    denom = np.outer(np.diag(inters)**alpha, np.diag(inters)**(1 - alpha))

    # Check if any unions are zero.
    if np.any(denom == 0):
        asims = np.zeros(X.shape[1])
        print("Some ingredients were not present in any recipe.")

    # Calculate asymmetric cosine similarities.
    asims = inters / denom

    return np.array(asims)


def pmi(X):
    """Calculate Pointwise Mutual Information (PMI) between all columns in a binary dataframe.
    
       Inputs:
           X: dataframe of recipes x ingredients
    """

    cooc = X.T.dot(X) / X.shape[0]  # Get co-occurrence matrix.
    pmi = cooc / np.outer(np.diag(cooc), np.diag(cooc).T)  # Calculate PMIs.
    pmi.values[[range(pmi.shape[0])] * 2] = 0  # Set self-PMI to zero.

    return np.array(pmi)