evclust.ecm

evclust.ecm#

This module contains the main function for ecm :

M.-H. Masson and T. Denoeux. ECM: An evidential version of the fuzzy c-means algorithm. Pattern Recognition, Vol. 41, Issue 4, pages 1384–1397, 2008.

Module Contents#

evclust.ecm.ecm(x, c, g0=None, type='full', pairs=None, Omega=True, ntrials=1, alpha=1, beta=2, delta=10, epsi=0.001, init='kmeans', disp=True)[source]#

Evidential c-means algorithm. ecm Computes a credal partition from a matrix of attribute data using the Evidential c-means (ECM) algorithm.

ECM is an evidential version algorithm of the Hard c-Means (HCM) and Fuzzy c-Means (FCM) algorithms. As in HCM and FCM, each cluster is represented by a prototype. However, in ECM, some sets of clusters are also represented by a prototype, which is defined as the center of mass of the prototypes in each individual cluster. The algorithm iteratively optimizes a cost function, with respect to the prototypes and to the credal partition. By default, each mass function in the credal partition has 2^c focal sets, where c is the supplied number of clusters. We can also limit the number of focal sets to subsets of clusters with cardinalities 0, 1 and c (recommended if c>=10), or to all or some selected pairs of clusters. If initial prototypes g0 are provided, the number of trials is automatically set to 1.

Parameters:#

x (DataFrame):

input matrix of size n x d, where n is the number of objects and d is the number of attributes.

c (int):

Number of clusters.

g0:

Initial prototypes, matrix of size c x d. If not supplied, the prototypes are initialized randomly.

type (str):

Type of focal sets (“simple”: empty set, singletons and Omega; “full”: all 2^c subsets of Omega;: “pairs”: empty set, singletons, Omega, and all or selected pairs).

pairs:

Set of pairs to be included in the focal sets; if None, all pairs are included. Used only if type=”pairs”.

Omega:

Logical. If True (default), the whole frame is included (for types ‘simple’ and ‘pairs’).

ntrials (int):

Number of runs of the optimization algorithm (set to 1 if g0 is supplied).

alpha (float):

Exponent of the cardinality in the cost function.

beta (float):

Exponent of masses in the cost function.

delta (float):

Distance to the empty set.

epsi (float):

Minimum amount of improvement.

init (str):

Initialization: “kmeans” (default) or “rand” (random).

disp (bool):

If True (default), intermediate results are displayed.

Returns:#

The credal partition (an object of class “credpart”).

Example:#

# Import test data
from evclust.datasets import load_iris
df = load_iris()
df=df.drop(['species'], axis = 1)

# Evidential clustering with c=3
from evclust.ecm import ecm
model = ecm(x=df, c=3,beta = 1.1,  alpha=0.1, delta=9)

# Read the output
from evclust.utils import ev_summary, ev_pcaplot
ev_summary(model)
ev_pcaplot(data=df, x=model, normalize=False)

References:#

M.-H. Masson and T. Denoeux. ECM: An evidential version of the fuzzy c-means algorithm. Pattern Recognition, Vol. 41, Issue 4, pages 1384–1397, 2008.