On Pattern Classification with Sammon's Nonlinear Mapping--an Experimental Study ~ Chromosomes Classification Feature Extraction Multilayer Perceptron Neural Networks Sammon's Mapping

Abstraet-Sammon's mapping is conventionally used for exploratory data projection, and as such is usually inapplicable for classification. In this paper we apply a neural network (NN) implementation of Sammon's mapping to classification by extracting an arbitrary number of projections. The projection map and classification accuracy of the mapping are compared with those of the auto-associative NN (AANN), multilayer perceptron (MLP) and principal component (PC) feature extractor for chromosome data. We demonstrate that chromosome classification based on Sammon's (unsupervised) mapping is superior to the classification based on the AANN and PC feature extractor and highly comparable with that based on the (supervised) MLP. Feature extraction is the process of mapping original features (measurements) into fewer features, which preserve the main information of the data structure. A large variety of feature extraction paradigms appear in the literature, (1-4/ some of them are based on NNs.(5 10/The NN-based feature extraction paradigms provide adaptivity to a changing environment and the possibility of relatively easy hardware implementation. They can even overcome the drawbacks of classical algorithms (7' lo) or enhance the classification per-formanceF' 11) In all the methods, a mapping ftrans-forms a pattern y of a d-dimensional input space to a pattern x of an m-dimensional projected space, m < d, i.e., x = f(y), (1) such that a criterion J is optimized. The mapping fis determined from among all the transformations g, as one that satisfies, (2) J {f(y)} = max J {g (Y) }. (2) g The mappings differ by the functional forms of g and by the criteria they have to optimize. Feature extraction methods can be grouped into four categories (71 based on a priori knowledge used for the computation of J: supervised versus unsupervised, and by the functional form of g: linear versus nonlin-ear. In cases where the target classes of the patterns are unknown, unsupervised methods are the only way to perform feature extraction, whereas in other cases, supervised paradigms are preferable. Linear methods are simpler and are often based on an analytical solution but they are inferior to nonlinear methods when the classification task requires complex separation hypersurfaces. Discriminant analysis is a well-known procedure for linearly projecting labeled data (3l in which the ratio of the determinants of the between-class scatter matrix (B) and the within-class scatter matrix (W) is maximized. Data is projected onto the space spanned by the eigenvectors corresponding to the largest (nonzero) eigenvalues of …