Passage method for nonlinear dimensionality reduction of data on multi-cluster manifolds

Abstract

Nonlinear dimensionality reduction of data lying on multi-cluster manifolds is a crucial issue in manifold learning research. An effective method, called the passage method, is proposed in this paper to alleviate the disconnectivity, short-circuit, and roughness problems ordinarily encountered by the existing methods. The specific characteristic of the proposed method is that it constructs a globally connected neighborhood graph superimposed on the data set through technically building the smooth passages between separate clusters, instead of supplementing some rough inter-cluster connections like some existing methods. The neighborhood graph so constructed is naturally configured as a smooth manifold, and hence complies with the effectiveness condition underlying manifold learning. This theoretical argument is supported by a series of experiments performed on the synthetic and real data sets residing on multi-cluster manifolds.