A New Robust Deep Canonical Correlation Analysis Algorithm for Small Sample Problems

Abstract

As a nonlinear feature learning method, deep canonical correlation analysis (DCCA) has got a great success in computer vision. Compared with kernel methods, deep neural networks can more easily process large amounts of training data and do not require referring to the training set at test time. However, in the real world, due to the noise disturbance and the limited number of training samples, within-set and between-set sample covariance matrices cannot usually be estimated accurately, which causes that the gradient direction deviates from the true one when training DCCA. It incorporates fractional-order within-set and between-set scatter matrices to reduce the deviations of sample covariance matrices for gradient direction correction. In addition, to make full use of convolutional network's feature extraction ability and fractional model in modifying neural network gradient directions, we further propose two novel convolutional network-based FDCCA methods, named convolutional neural network-based FDCCA (CNN-FDCCA) and two-convolutional neural networks based FDCCA (2CNNs-FDCCA), respectively. The experimental results on MNIST and RAVDNESS datasets show that FDCCA has better recognition rates than existing methods. The experiments on ATT dataset show that CNN-FDCCA and 2CNNs-FDCCA have great robustness in processing images.