Kernel ridge regression for out-of-sample mapping in supervised manifold learning

Abstract

Manifold learning methods for unsupervised nonlinear dimensionality reduction have proven effective in the visualization of high dimensional data sets. When dealing with classification tasks, supervised extensions of manifold learning techniques, in which class labels are used to improve the embedding of the training points, require an appropriate method for out-of-sample mapping.In this paper we propose multi-output kernel ridge regression (KRR) for out-of-sample mapping in supervised manifold learning, in place of general regression neural networks (GRNN) that have been adopted by previous studies on the subject. Specifically, we consider a supervised agglomerative variant of Isomap and compare the performance of classification methods when the out-of-sample embedding is based on KRR and GRNN, respectively. Extensive computational experiments, using support vector machines and k-nearest neighbors as base classifiers, provide statistical evidence that out-of-sample mapping based on KRR consistently dominates its GRNN counterpart, and that supervised agglomerative Isomap with KRR achieves a higher accuracy than direct classification methods on most data sets.