# -*- 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, 2024
"""
This module contains the main function for Multi-View Evidential C-Medoid clustering (MECMdd) with adaptive weightings with Relevance Weight for each dissimilarity matrix
estimated Locally (MECMdd-RWL), i.e for each cluster, using weight Sum (MECMdd-RWL-S) constraint or weight Product (MECMdd-RWL-P) constraint.
Armel Soubeiga, Violaine Antoine and Sylvain Moreno. "Multi-View Relational Evidential C-Medoid Clustering with Adaptive Weighted"
2024 IEEE 11th International Conference on Data Science and Advanced Analytics (DSAA)
"""
#---------------------- Packges------------------------------------------------
from evclust.utils import makeF, extractMass
import numpy as np
#---------------------- MECMdd-RWL------------------------------------------------
[docs]
def mecmdd_rwl(Xlist, c, type='full', alpha=1, beta=1.5, delta=9, epsi=1e-4,
disp=True, gamma=0.5, eta=1, weight='sum', s=None):
"""
Multi-View Evidential C-Medoid clustering (MECMdd) with adaptive weightings with Relevance Weight for each dissimilarity matrix
estimated Locally (MECMdd-RWL), i.e for each cluster, using weight Sum (MECMdd-RWL-S) constraint or weight Product (MECMdd-RWL-P) constraint.
Parameters:
-----------
Xlist (list of np.array):
A list of square symmetric dissimilarity matrices.
c (int):
Number of clusters to create.
type (str):
Type of structure ('full' by default).
alpha (float):
Weighting parameter for cardinalities.
beta (float):
uncertainty exponent for membership degrees.
delta (float or None):
Precision parameter (used to calculate delta2). If None, distribution of matrix are considere.
epsi (float):
Convergence threshold.
disp (bool):
Whether to display the objective function value during iteration.
gamma (float):
Coefficient to adjust the imprecise contribution.
eta (float):
Coefficient for outlier identification.
weight (str):
Type of constraint function using to learn weight ('sum' or 'prod').
s (float or None):
Additional weight parameter.
Returns:
--------
The credal partition (an object of class "credpart").
Example:
--------
.. highlight:: python
.. code-block:: python
from evclust.mecmdd_rwl import mecmdd_rwl
matrix1 = np.random.rand(5, 5)
matrix1 = (matrix1 + matrix1.T) / 2
matrix2 = np.random.rand(5, 5)
matrix2 = (matrix2 + matrix2.T) / 2
Xlist = [matrix1, matrix2]
clus = mecmdd_rwl(Xlist, c=2, type='simple', alpha=1, beta=1.5, delta=9, epsi=1e-4,
disp=True, gamma=0.5, eta=1, weight='prod', s=None)
clus['param']['lambda'] # View weight
References:
-----------
Armel Soubeiga, Violaine Antoine and Sylvain Moreno. "Multi-View Relational Evidential C-Medoid Clustering with Adaptive Weighted"
2024 IEEE 11th International Conference on Data Science and Advanced Analytics (DSAA).
.. seealso::
:func:`~extractMass`, :func:`~makeF`,
:func:`~lambdaInit_local`
.. note::
Keywords : Evidential clustering, credal partition, relational multi-view, belief function
MECMdd-RWL is able to address the uncertainty and imprecision of multi-view relational data clustering, and provides a credible partition, which extends fuzzy, possibilistic and rough partitions.
It can automatically lern the importance of each views by estimated a weight locally for each cluster in a collaborative learning framework.
"""
if not Xlist or not isinstance(Xlist, list) or len(Xlist) <= 1:
raise ValueError("The data set (Xlist) must be given, must not be empty, must be a list, and must contain more than one matrix")
tailles = [x.shape for x in Xlist]
if not all(t == tailles[0] for t in tailles):
raise ValueError("All matrices in Xlist must have the same size")
# Determine s based on weight type
if weight == 'prod':
s = 1
elif weight == 'sum':
if s is None:
s = 2
# Delta calculation
pmatrix = len(Xlist)
if delta is None:
delta2 = sum(np.quantile(mat[np.triu_indices_from(mat, k=1)], 0.95) for mat in Xlist)
elif isinstance(delta, (int, float)):
delta2 = sum([delta ** 2] * pmatrix)
elif len(delta) == pmatrix:
delta2 = sum([d ** 2 for d in delta])
else:
raise ValueError("Delta must be None, a scalar, or a list of length equal to the number of matrices.")
# Generate focal set matrix F and initialize parameters
F = makeF(c=c, type=type)
nF = F.shape[0]
card = np.sum(F[1:], axis=1)
n = Xlist[0].shape[0]
medoids = np.random.choice(n, c, replace=False)
prototype = np.zeros(nF-1, dtype=int)
lambda_ = lambdaInit_local(weight, pmatrix, nF-1)
pasfini = True
Jold = float('inf')
iter = 0
while pasfini:
iter += 1
# Update singleton and imprecise (medoid)
for j in range(nF-1):
fj = F[j+1]
medoidsj = medoids[fj != 0]
l_i = np.zeros(n)
if np.sum(fj) == 1:
prototype[j] = medoidsj[0]
else:
for i in range(n):
var_ij = (1/card[j]) * np.sum([(np.sum([Xlist[l][i, medoidsj[k]] for l in range(pmatrix)]) -
(1/card[j]) * np.sum([np.sum([Xlist[l][i, medoidsj[kk]] for l in range(pmatrix)]) for kk in range(len(medoidsj))]))**2 for k in range(len(medoidsj))])
l_i[i] = var_ij + eta * (1/card[j]) * np.sum([np.sum([Xlist[l][i, medoidsj[kk]] for l in range(pmatrix)]) for kk in range(len(medoidsj))])
prototype[j] = np.argmin(l_i)
# Calculation of distances to centers
D = [np.zeros((n, nF-1)) for _ in range(pmatrix)]
for l in range(pmatrix):
for j in range(nF-1):
fj = F[j+1]
medoidsj = medoids[fj != 0]
if np.sum(fj) == 1:
D[l][:, j] = Xlist[l][:, prototype[j]]
elif np.sum(fj) > 1:
D[l][:, j] = (Xlist[l][:, prototype[j]] + (gamma / card[j]) * np.sum(Xlist[l][:, medoidsj], axis=1)) / (1 + gamma)
# Calculation of masses
m = np.zeros((n, nF-1))
for j in range(nF-1):
fj = F[j+1]
medoidsj = medoids[fj != 0]
for i in range(n):
num = (card[j]**alpha * np.sum([D[l][i, j] * (lambda_[j, l])**s for l in range(pmatrix)]))**(-1/(beta-1))
den = (np.sum([(card[k]**alpha * np.sum([D[l][i, k] * (lambda_[k, l])**s for l in range(pmatrix)]))**(-1/(beta-1)) for k in range(nF-1)]) + delta2**(-1/(beta-1)))
m[i, j] = num / den
if np.isnan(m[i, j]) or np.isinf(m[i, j]):
m[i, j] = 1
# Weight
if weight == 'sum':
for j in range(nF-1):
for l in range(pmatrix):
num = np.sum([s * (card[j]**alpha) * m[i, j]**beta * D[l][i, j] for i in range(n)])**(-1/(s-1))
den = np.sum([np.sum([s * (card[j]**alpha) * m[i, j]**beta * D[h][i, j] for i in range(n)])**(-1/(s-1)) for h in range(pmatrix)])
lambda_[j, l] = num / den
if weight == 'prod':
for j in range(nF-1):
for l in range(pmatrix):
num = np.prod([np.sum([(card[j]**alpha) * m[i, j]**beta * D[h][i, j] for i in range(n)])**(1/pmatrix) for h in range(pmatrix)], axis=0)
den = np.sum([(card[j]**alpha) * m[i, j]**beta * D[l][i, j] for i in range(n)])
lambda_[j, l] = num / den
# Medoids
V = np.zeros((n, nF-1))
for k in range(nF-1):
fk = F[k+1]
if np.sum(fk) == 1:
mk_beta = m[:, k]**beta
for i in range(n):
V[i, k] = np.sum([np.sum([Xlist[l][i, :] * (lambda_[k, l])**s for l in range(pmatrix)]) * mk_beta[i]])
V_filtered = V[:, np.sum(V, axis=0) > 0]
medoids = np.array([np.argmin(V_filtered[:, i]) for i in range(V_filtered.shape[1])])
mvide = 1 - np.sum(m, axis=1)
J = np.sum([np.sum([card[j]**alpha * m[i, j]**beta * np.sum([Xlist[l][i, prototype[j]] * (lambda_[j, l])**s for l in range(pmatrix)]) for j in range(nF-1)]) for i in range(n)]) + delta2 * np.sum(mvide**beta)
if disp:
print(iter, J)
pasfini = abs(J - Jold) > epsi
Jold = J
g = medoids
m = np.hstack((1 - np.sum(m, axis=1).reshape(-1, 1), m))
clus = extractMass(m, F, g=g, method="mecmdd", crit=J,
param={'alpha': alpha, 'beta': beta, 'delta': delta, 'lambda': lambda_})
return clus
#---------------------- Utils of MECMdd-RWL------------------------------------------------
[docs]
def lambdaInit_local(weight, p, c):
"""
Initialize lambda matrix.
"""
lambda_ = np.zeros((c, p))
for j in range(c):
if weight == 'sum':
lambda_[j, :] = np.full(p, 1/p)
elif weight == 'prod':
lambda_[j, :] = np.ones(p)
else:
raise ValueError("Weight must be 'sum' or 'prod'.")
return lambda_
