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Many computer vision and pattern recognition problems may be posed as the analysis of a set of dissimilarities between objects. For many types of data, these dissimilarities are not euclidean (i.e., they do not represent the distances between points in a euclidean space), and therefore cannot be isometrically embedded in a euclidean space. Examples include shape-dissimilarities, graph distances and mesh geodesic distances. In this paper, we provide a means of embedding such non-euclidean data onto surfaces of constant curvature. We aim to embed the data on a space whose radius of curvature is determined by the dissimilarity data. The space can be either of positive curvature (spherical) or of negative curvature (hyperbolic). We give an efficient method for solving the spherical and hyperbolic embedding problems on symmetric dissimilarity data. Our approach gives the radius of curvature and a method for approximating the objects as points on a hyperspherical manifold without optimisation. For objects which do not reside exactly on the manifold, we develop a optimisation-based procedure for approximate embedding on a hyperspherical manifold. We use the exponential map between the manifold and its local tangent space to solve the optimisation problem locally in the euclidean tangent space. This process is efficient enough to allow us to embed data sets of several thousand objects. We apply our method to a variety of data including time warping functions, 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. [ABSTRACT FROM AUTHOR]

We propose an eigenvector-based heteroscedastic linear dimension reduction (LOR) technique for multiclass data. The technique is based on a heteroscedastic two-class technique which utilizes the so-called Chemoff criterion, and successfully extends the well-known linear discriminant analysis (LDA). The latter, which is based on the Fisher criterion, is incapable of dealing with heteroscedastic data in a proper way. For the two-class case, the between-class scatter is generalized so to capture differences in (co)variances. It is shown that the classical notion of between-class scatter can be associated with Euclidean distances between class means. From this viewpoint, the between-class scatter is generalized by employing the Chemoff distance measure, leading to our proposed heteroscedastic measure. Finally, using the results from the two-class case, a multiclass extension of the Chemoff criterion is proposed. This criterion combines separation information present in the class mean as well as the class covariance matrices. Extensive experiments and a comparison with similar dimension reduction techniques are presented. [ABSTRACT FROM AUTHOR]

Presents a study which summarized and compared some of the methods used in various stages of a pattern recognition system. Information on pattern recognition; Template matching method used; Statistical approach; Neural networks model; Curse of dimensionality and peaking phenomena.

Provides information on the development of a theoretical framework for combining classifiers which use distinct pattern representations. Comparison of the different classifier combinations schemes; Investigation of the sensitivity analysis of the schemes; Results of the analysis.