Efficient approximations of kernel robust soft LVQ

Abstract

Robust soft learning vector quantization (RSLVQ) constitutes a probabilistic extension of learning vector quantization (LVQ) based on a labeled Gaussian mixture model of the data. Training optimizes the likelihood ratio of the model and recovers a variant similar to LVQ2.1 in the limit of small bandwidth. Recently, RSLVQ has been extended to a kernel version, thus opening the way towards more general data structures characterized in terms of a Gram matrix only. While leading to state of the art results, this extension has the drawback that models are no longer sparse, and quadratic training complexity is encountered. In this contribution, we investigate two approximation schemes which lead to sparse models: k-approximations of the prototypes and the Nyström approximation of the Gram matrix. We investigate the behavior of these approximations in a couple of benchmarks. © 2013 Springer-Verlag.