Dimensionality Reduction by Learning an Invariant Mapping

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Abstract:

Dimensionality reduction involves mapping a set of high dimensional input points onto a low dimensional manifold so that 'similar" points in input space are mapped to nea...Show More

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Abstract:

Dimensionality reduction involves mapping a set of high dimensional input points onto a low dimensional manifold so that 'similar" points in input space are mapped to nearby points on the manifold. We present a method - called Dimensionality Reduction by Learning an Invariant Mapping (DrLIM) - for learning a globally coherent nonlinear function that maps the data evenly to the output manifold. The learning relies solely on neighborhood relationships and does not require any distancemeasure in the input space. The method can learn mappings that are invariant to certain transformations of the inputs, as is demonstrated with a number of experiments. Comparisons are made to other techniques, in particular LLE.

Date of Conference: 17-22 June 2006

Date Added to IEEE Xplore: 09 October 2006

Conference Location: New York, NY, USA

1 Introduction

Modem applications have steadily expanded their use of complex, high dimensional data. The massive, high dimensional image datasets generated by biology, earth science, astronomy, robotics, modern manufacturing, and other domains of science and industry demand new techniques for analysis, feature extraction, dimensionality reduction, and visualization.