Source code for evclust.metrics

# -*- coding: utf-8 -*-
# This file as well as the whole evclust package are licenced under the MIT licence (see the LICENCE.txt)
# Armel SOUBEIGA (armelsoubeiga.github.io), France, 2023

"""
This module contains the metrics functions using to evaluate credal results
"""

#---------------------- Packges------------------------------------------------
import numpy as np
from scipy.spatial.distance import pdist, squareform




#---------------------- credalRI--------------------------------------------------



def build_matrices(F):
    nbFoc = F.shape[0]
    C = np.zeros((nbFoc, nbFoc))  # matrice pour les degrés de conflit
    for i in range(nbFoc):
        for j in range(nbFoc):
            C[i, j] = 1 - np.max(np.minimum(F[i, :], F[j, :]))

    if np.max(F[0, :]) > 0:
        E = np.zeros((nbFoc, nbFoc))
    else:
        E = np.zeros((nbFoc-1, nbFoc-1))
        E = np.hstack((np.ones((nbFoc-1, 1)), E))
        E = np.vstack((np.ones((1, nbFoc)), E))

    singleton = (np.sum(F, axis=1) == 1)  # matrice pour calculer m_ij(S)
    S = np.diag(singleton)
    
    return {'C': C, 'E': E, 'S': S}





def pairwise_mass(clus):
    """
    Computes relational representations for credal partition such as generated by a credal method.
    """
    n = clus['mass'].shape[0]
    M = clus['mass']
    mat = build_matrices(clus['F'])

    # Calcul des distances en utilisant les matrices E, S et C
    Me = pdist(M @ mat['E'] @ M.T, 'euclidean')
    M1 = pdist(M @ mat['S'] @ M.T, 'euclidean')
    M0 = pdist(M @ (mat['C'] - mat['E']) @ M.T, 'euclidean')

    return {'Me': squareform(Me), 'M1': squareform(M1), 'M0': squareform(M0)}




def credalRI(clus1, clus2):
    """
    Computes generalizations of the Rand index to compare credal partitions.
    
    Parameters :
    ------------
    clus1: 
        Relational representation of the first credal partition such as generated by a credal method.
    clus2: 
        Relational representation of the second credal partition such as generated by a credal method.
    
    Returns :
    ---------
    RI (float): 
        Credal Rand indices.

    References:
    -----------
        In Denoeux et al. (2018), two generalizations of the Rand index for comparing credal partitions
        are defined: one is based on distances between mass function, the other one is based on distances.
    """
    
    P1 = pairwise_mass(clus1)
    P2 = pairwise_mass(clus2)

    RI = 1 - np.mean(P1['Me'] + P2['Me'] - P1['Me'] * P2['Me'] + P1['M1'] * P2['M0'] + P1['M0'] * P2['M1'])

    return RI





#---------------------- nonspecificity--------------------------------------------------


def nonspecificity(mass, F):
    """
    Compute the nonspecificity of a credal partition.

    Parameters
    -----------
    mass ( ndarray (n, F size)):
            The credal partition.
    F (array): 
        The array of length of focalsets.

    Returns
    -------
    NS (float):
        The nonspecificity of the credal partition.
    """
    focalsets = [tuple(index + 1 for index in row.nonzero()[0]) for row in F]
    n_samples = mass.shape[0]
    len_fs = [len(fs) for fs in focalsets if fs != tuple()]
    len_fs = np.array(len_fs)
    NS = np.sum(len_fs * mass[:, 1:]) + np.sum(
        mass[:, 0] * np.log2(max(len_fs)))
    NS /= n_samples * np.log2(max(len_fs))
    return NS