Sparse kernel feature analysis using FastMap and its variants

In this paper, we propose a novel learning framework to reformulate a kernel-based classifier in terms of three modular components: kernel-function determination to incorporate domain knowledge, sparse data representation using FastMap and its variants, and supervised classification performed by using primal form analyzers such as linear SVM. The first important property of this approach is the reusability of the modules: Each module can be easily replaced by its counterparts for a specific learning purpose, e.g., the sparse representation of the data can not only support classification tasks but also be applied in function regression or unsupervised data analysis. Another contribution of the proposed approach is that it enables easy adaption of available primal-form algorithms for nonlinear kernel-based learning. Finally, numerical experiments show that FastMap and SupFM can yield efficient sparse representations with nonlinear kernels. The representation realized better sparsity while maintaining a generalization ability that is comparable to that of the regular SVM classifier.