Discriminative Feature Extraction by a Neural Implementation of Canonical Correlation Analysis

The canonical correlation analysis (CCA) aims at measuring linear relationships between two sets of variables (views) that can be used for feature extraction in classification problems with multiview data. However, the correlated features extracted by the CCA may not be class discriminative, since CCA does not utilize the class labels in its traditional formulation. Although there is a method called discriminative CCA (DCCA) that aims to increase the discriminative ability of CCA inspired from the linear discriminant analysis (LDA), it has been shown that the extracted features with this method are identical to those by the LDA with respect to an orthogonal transformation. Therefore, DCCA is simply equivalent to applying single-view (regular) LDA to each one of the views separately. Besides, DCCA and the other similar DCCA approaches have generalization problems due to the sample covariance matrices used in their computation, which are sensitive to outliers and noisy samples. In this paper, we propose a method, called discriminative alternating regression (D-AR), to explore correlated and also discriminative features. D-AR utilizes two (alternating) multilayer perceptrons, each with a linear hidden layer, learning to predict both the class labels and the outputs of each other. We show that the features found by D-AR on training sets significantly accomplish higher classification accuracies on test sets of facial expression recognition, object recognition, and image retrieval experimental data sets.

I. Introduction

Dimensionality reduction is a crucial step in machine learning problems, especially when the number of samples is small when compared with data dimensionality. Extracting important features from data reduces dimensionality while preserving salient information that can help in learning predictive models with high generalization. With the assumption that such important factors are redundantly represented in multiple ways/views in the observed data, the canonical correlation analysis (CCA) can effectively be used to extract dependence (mutual information) between two given views [1]–[5]. Here, the term view is used to refer each related set of features about the same underlying phenomenon.