A Computational Framework for Nonlinear Dimensionality Reduction and Clustering

Abstract

We introduce the Exploration Machine (Exploratory Observation Machine, XOM) as a novel versatile instrument for scientific data analysis and knowledge discovery. XOM systematically inverts structural and functional components of topology-preserving mappings. In contrast to conventional approaches known from the literature, this novel computational framework for self-organization does not require to incorporate additional graphical display or coloring techniques, or to modify topology-preserving mapping algorithms by additional regularization in order to recover the underlying cluster structure of inhomogeneously distributed input data. Thus, XOM can be seen as an approach to bridge the gap between nonlinear embedding and classical topology-preserving feature mapping. At the same time, XOM results in tremendous computational savings when compared to conventional topology-preserving mapping, thus allowing for direct structure-preserving visualization of large data collections without prior data reduction.