PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Spherical embeddings for non-Euclidean dissimilarities
Richard Wilson, Edwin Hancock, Elzbieta Pekalska and Robert Duin
In: CVPR 2010, June 13-18, San Francisco, USA.

Abstract

Many computer vision and pattern recognition problems may be posed by defining a way of measuring dissimilarities between patterns. For many types of data, these dissimilarities are not Euclidean, and may not be metric. In this paper, we provide a means of embedding such data. We aim to embed the data on a hypersphere whose radius of curvature is determined by the dissimilarity data. The hypersphere can be either of positive curvature (elliptic) or of negative curvature (hyperbolic). We give an efficient method for solving the elliptic and hyperbolic embedding problems on symmetric dissimilarity data. This method gives the radius of curvature and a method for approximating the objects as points on a hyperspherical manifold. We apply our method to a variety of data including shape-similarities, graph-similarity and gesture-similarity data. In each case the embedding maintains the local structure of the data while placing the points in a metric space.

EPrint Type:Conference or Workshop Item (Poster)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Machine Vision
Learning/Statistics & Optimisation
ID Code:7388
Deposited By:Edwin Hancock
Deposited On:17 March 2011