Bayesian distance metric learning for discriminative fuzzy c-means clustering

Abstract A great number of machine learning algorithms strongly depend on the underlying distance metric for representing the important correlations of input data. Distance metric learning is defined as learning an appropriate similarity or distance metric for all input data pairs. Metric learning algorithms are of supervised and unsupervised categories with different deterministic and probabilistic approaches. One of the objectives of unsupervised metric learning is to project data points into a new space in such a way that high clustering accuracy is provided. This is obtainable by maximizing between-clusters separation. There exist some deterministic metric learning methods to serve this purpose. In this article, a probabilistic method for unsupervised distance metric learning is proposed which aims to maximize the separability among different clusters in the projected space. In this proposed method, distance metric learning and fuzzy c-means clustering are jointly formulated in a sense that FCM provides clusters, and distance metric learning algorithm applies the obtained clusters to materialize the maximum separability among all; moreover, Markov Chain Monte Carlo (MCMC) algorithm is applied to infer the latent variables. This proposed method, not only can obtain a low dimensional projection with specified number of dimensions, but also it can learn the proper number of reduced dimensions for each dataset in an automated sense. The experimental results reveal the out-performance of this method on different real-world datasets against its counterparts.