Linear data projection using a feedforward neural network

Abstract

Linear data projection methods provide useful tools in exploratory data analysis and pattern recognition. The most widely used methods in this respect are principal components analysis (PCA) and linear discriminant analysis (LDA). These methods are able to condense multidimensional information in two (or three) dimensions, allowing us to analyze the underlying structure of the data by visual inspection. This paper describes an alternative linear data projection method using a feedforward neural network. The method uses category information to obtain a projection maximally separating the predefined classes of data patterns (supervised data projection). The projection is constructed by training a feedforward network consisting of two subnetworks. The first subnetwork receives the training input and performs the actual projection, while the second one performs the desired classification using the output of the first subnetwork. After training the projection, subnetwork provides the 2D (or 3D) projection map, where as the complete network behaves as an ordinary classification network. As an example, the method is applied to a data set consisting of 13 dioxin concentrations for 145 samples of cow's milk, originating from the vicinity of five different sources of dioxin contamination. 2D projection maps were constructed using PCA, LDA and the proposed neural network using different classification subnets and starting values of the network weights. The neural network approach produced a number of significant different mappings, most of them showing an improved class separation as compared to PCA and LDA.