Robust kernel Isomap

Isomap is one of widely-used low-dimensional embedding methods, where geodesic distances on a weighted graph are incorporated with the classical scaling (metric multidimensional scaling). In this paper we pay our attention to two critical issues that were not considered in Isomap, such as: (1) generalization property (projection property); (2) topological stability. Then we present a robust kernel Isomap method, armed with such two properties. We present a method which relates the Isomap to Mercer kernel machines, so that the generalization property naturally emerges, through kernel principal component analysis. For topological stability, we investigate the network flow in a graph, providing a method for eliminating critical outliers. The useful behavior of the robust kernel Isomap is confirmed through numerical experiments with several data sets. Key words: Isomap, Kernel PCA, Manifold learning, Multidimensional scaling (MDS), Nonlinear dimensionality reduction.

• Type: Journal
• Year: 2007
• Where: PR
• Authors: Heeyoul Choi, Seungjin Choi
• Keywords: Generalization Property, PR 2007, Robust Kernel Isomap, Topological Stability