Title: Comparison of graph-based methods for non-linear dimensionality reduction

Authors: Rashmi Gupta; Rajiv Kapoor

Addresses: Ambedkar Institute of Advanced Communication Technologies and Research (Formerly Ambedkar Institute of Technology), Geeta Colony, Govt. of NCT of Delhi, Affiliated to Guru Gobind Singh Indraprastha University, Delhi, India ' Delhi Technological University (Formerly Delhi College of Engineering), Bawana Road, Delhi, India

Abstract: In this paper, four broadly representative graph-based techniques for manifold learning namely Isomap, Maximum Variance Unfolding (MVU), locally linear embedding and Laplacian eigenmaps have been reviewed and compared for non-linear dimensionality reduction. These methods begin by constructing a sparse graph in which the nodes represent input patterns and the edges represent neighbourhood relations. From these graphs, matrices can be constructed whose spectral decompositions reveal the low dimensional structure of the submanifold. All the four techniques are implemented on Swiss roll, helix, twin peak and broken Swiss roll dataset.

Keywords: dimension reduction; feature extraction; manifold learning; Isomap; maximum variance unfolding; local linear embedding; Laplacian eigenmaps; nonlinear dimensionality; sparse graphs.

DOI: 10.1504/IJSISE.2012.047783

International Journal of Signal and Imaging Systems Engineering, 2012 Vol.5 No.2, pp.101 - 109

Received: 30 Jul 2011
Accepted: 12 Jan 2012
Published online: 31 Dec 2014 *

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