Accelerating Kernel Neural Gas

Frank-Michael Schleif, Andrej Gisbrecht, Barbara Hammer

Abstract: Clustering approaches constitute important methods for unsupervised data analysis. Traditionally, many clustering models focus on spherical or ellipsoidal clusters in Euclidean space. Kernel methods extend these approaches to more complex cluster forms, and they have been recently integrated into several clustering techniques. While leading to very flexible representations, kernel clustering has the drawback of high memory and time complexity due to its dependency on the full Gram matrix and its implicit representation of clusters in terms of feature vectors. In this contribution, we accelerate the kernelized Neural Gas algorithm by incorporating a Nyström approximation scheme and active learning, and we arrive at sparse solutions by integration of a sparsity constraint. We provide experimental results which show that these accelerations do not lead to a deterioration in accuracy while improving time and memory complexity.