Feature Extraction Based on Discriminative Alternating Regression

Canonical Correlation Analysis (CCA) aims at measuring linear relationships between two sets of variables (views). Recently, CCA has been used for feature extraction in classification problems with multi-view data by means of view fusion. However, the extracted correlated features with CCA may not be discriminative since CCA does not utilize the class labels in its traditional formulation. Besides, the CCA features are computed based on within-set and between-set sample covariance matrices of the views which can be very sensitive to representation-specific details and noisy samples of the two views. In this paper, we propose a method, D-AR (Discriminative Alternating Regression), in which the two above-mentioned problems encountered in the application of CCA for feature extraction are addressed: (1) the class labels are incorporated into the proposed feature fusion framework to explore correlated and also discriminative features, and (2) the use of sensitive sample covariates matrices is avoided while fusing the two views. D-AR is a supervised feature fusion approach based on Multi-layer Perceptron (MLP) implementation of alternating regression. From the neurobiological perspective, the architecture of D-AR is similar to the model of a single neuron in the cerebral cortex which has a function of discovering and representing one of the hidden factors in its sensory environment. The MLP trained on each view aims to predict the class labels and also the hidden factors which are responsible for the correlation. We show that the features found by D-AR on training sets accomplishes significantly higher classification accuracies on test set of an experimental dataset.