Symmetry-Based Automatic Clustering

Abstract

This chapter deals with some automatic clustering techniques, where the number of clusters need not be fixed a priori. First some recently developed genetic algorithm-based automatic clustering techniques are described briefly. Thereafter a recently developed point symmetry-based automatic genetic clustering technique, VGAPS, is described in detail; it uses Sym-index for computing the fitness of the chromosomes. In VGAPS clustering, the assignment of points to different clusters is done based on the point symmetry distance rather than the Euclidean distance when the point is indeed symmetric with respect to a center. Moreover, the use of adaptive mutation and crossover probabilities helps VGAPS clustering to converge faster. The global convergence property of VGAPS-clustering is also established. Experimental results prove the fact that VGAPS clustering is well suited to detect the number of clusters and the proper partitioning from data sets having clusters with widely varying characteristics, irrespective of their convexity, or overlap or size, as long as they possess the property of symmetry. Thereafter a variable string length genetic point symmetry-based fuzzy clustering technique, Fuzzy-VGAPS, is described in this chapter. It utilizes the fuzzy version of Sym-index. Fuzzy-VGAPS can detect clusters of any shape (e.g., hyperspherical, linear, ellipsoidal, ring shaped, etc.) and size (mixture of small and large clusters, i.e., clusters of unequal sizes) as long as they satisfy the property of point symmetry. In a part of the experiment, a real-life application of Fuzzy-VGAPS to automatically segment magnetic resonance brain images with multiple sclerosis lesions is demonstrated.