Multiple Manifolds Learning Framework Based on Hierarchical Mixture Density Model

Authors:
Xiaoxia Wang;Peter Tiňo;Mark A. Fardal
Affiliations:
School of Computer Science, University of Birmingham, UK and Dept. of Astronomy, University of Massachusetts, USA;School of Computer Science, University of Birmingham, UK and Dept. of Astronomy, University of Massachusetts, USA;School of Computer Science, University of Birmingham, UK and Dept. of Astronomy, University of Massachusetts, USA
Venue:
ECML PKDD '08 Proceedings of the European conference on Machine Learning and Knowledge Discovery in Databases - Part II
Year:
2008

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Abstract

Several manifold learning techniques have been developed to learn, given a data, a single lower dimensional manifold providing a compact representation of the original data. However, for complex data sets containing multiple manifolds of possibly of different dimensionalities, it is unlikely that the existing manifold learning approaches can discover all the interesting lower-dimensional structures. We therefore introduce a hierarchical manifolds learning framework to discover a variety of the underlying low dimensional structures. The framework is based on hierarchical mixture latent variable model, in which each submodel is a latent variable model capturing a single manifold. We propose a novel multiple manifold approximation strategy used for the initialization of our hierarchical model. The technique is first verified on artificial data with mixed 1 ï戮驴, 2 ï戮驴 and 3 ï戮驴dimensional structures. It is then used to automatically detect lower-dimensional structures in disrupted satellite galaxies.