  The clustering methods have been used in a variety of fields such as image
processing, data mining, pattern recognition, and statistical analysis.
Generally, the clustering algorithms consider all variables equally relevant or
not correlated for the clustering task. Nevertheless, in real situations, some
variables can be correlated or may be more or less relevant or even irrelevant
for this task. This paper proposes partitioning fuzzy clustering algorithms
based on Euclidean, City-block and Mahalanobis distances and entropy
regularization. These methods are an iterative three steps algorithms which
provide a fuzzy partition, a representative for each fuzzy cluster, and the
relevance weight of the variables or their correlation by minimizing a suitable
objective function. Several experiments on synthetic and real datasets,
including its application to noisy image texture segmentation, demonstrate the
usefulness of these adaptive clustering methods.
