2010 Special Issue: Local matrix learning in clustering and applications for manifold visualization

Authors:
Banchar Arnonkijpanich;Alexander Hasenfuss;Barbara Hammer
Affiliations:
Khon Kaen University, Faculty of Science, Department of Mathematics, 40002, Thailand and Centre of Excellence in Mathematics, the Commission on Higher Education, Si Ayutthaya Road, Bangkok 10400, ...;Clausthal University of Technology, Department of Computer Science, Germany;University of Bielefeld, Faculty of Technology, CITEC, Germany
Venue:
Neural Networks
Year:
2010

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Abstract

Electronic data sets are increasing rapidly with respect to both, size of the data sets and data resolution, i.e. dimensionality, such that adequate data inspection and data visualization have become central issues of data mining. In this article, we present an extension of classical clustering schemes by local matrix adaptation, which allows a better representation of data by means of clusters with an arbitrary spherical shape. Unlike previous proposals, the method is derived from a global cost function. The focus of this article is to demonstrate the applicability of this matrix clustering scheme to low-dimensional data embedding for data inspection. The proposed method is based on matrix learning for neural gas and manifold charting. This provides an explicit mapping of a given high-dimensional data space to low dimensionality. We demonstrate the usefulness of this method for data inspection and manifold visualization.