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

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.