Element-centric similarity

element-centric-similarity.py

import numpy as np 
from scipy import sparse 

#
# Evaluation
#
def calc_esim(y, ypred, normalize=False):
    """
    Element centric similarity.
    
    y: numpy array of the true group memberships
    ypred: numpy array of the detected group memberships
    normalize: normalize = False gives the element-centric similarity. With normalize=True, the similarity is shifted to be zero for random partition on average and rescaled such that the maximum value is 1.
    
    """
    ylab, y = np.unique(y, return_inverse=True)
    ypredlab, ypred = np.unique(ypred, return_inverse=True)

    Ka, Kb = len(ylab), len(ypredlab)

    K = np.maximum(Ka, Kb)
    N = len(y)
    UA = sparse.csr_matrix((np.ones_like(y), (np.arange(y.size), y)), shape=(N, K))
    UB = sparse.csr_matrix(
        (np.ones_like(ypred), (np.arange(ypred.size), ypred)), shape=(N, K)
    )

    nA = np.array(UA.sum(axis=0)).reshape(-1)
    nB = np.array(UB.sum(axis=0)).reshape(-1)

    nAB = (UA.T @ UB).toarray()
    nAB_rand = np.outer(nA, nB) / N

    # Calc element-centric similarity
    Q = np.maximum(nA[:, None] @ np.ones((1, K)), np.ones((K, 1)) @ nB[None, :])
    Q = 1 / np.maximum(Q, 1)
    S = np.sum(np.multiply(Q, (nAB**2))) / N

    if normalize == False:
        return S
  
    # Calc the expected element-centric similarity for random partitions
    Q = np.maximum(nA[:, None] @ np.ones((1, K)), np.ones((K, 1)) @ nB[None, :])
    Q = 1 / np.maximum(Q, 1)
    Srand = np.sum(np.multiply(Q, (nAB_rand**2))) / N
    Scorrected = (S - Srand) / (1 - Srand)
    return Scorrected