Kernel and graph: Two approaches for nonlinear competitive learning clusterin

Abstract

Competitive learning has attracted a significant amount of attention in the past decades in the field of data clustering. In this paper, we will present two works done by our group which address the nonlinearly separable problem suffered by the classical competitive learning clustering algorithms. They are kernel competitive learning (KCL) and graph-based multi-prototype competitive learning (GMPCL), respectively. In KCL, data points are first mapped from the input data space into a high-dimensional kernel space where the nonlinearly separable pattern becomes linear one. Then the classical competitive learning is performed in this kernel space to generate a cluster structure. To realize on-line learning in the kernel space without knowing the explicit kernel mapping, we propose a prototype descriptor, each row of which represents a prototype by the inner products between the prototype and data points as well as the squared length of the prototype. In GMPCL, a graph-based method is employed to produce an initial, coarse clustering. After that, a multi-prototype competitive learning is introduced to refine the coarse clustering and discover clusters of an arbitrary shape. In the multi-prototype competitive learning, to generate cluster boundaries of arbitrary shapes, each cluster is represented by multiple prototypes, whose subregions of the Voronoi diagram together approximately characterize one cluster of an arbitrary shape. Moreover, we introduce some extensions of these two approaches with experiments demonstrating their effectiveness.