Label constrained convolutional factor analysis for classification with limited training samples

Abstract This paper mainly addresses the statistical classification robust to small training data size. We develop a label constrained convolutional factor analysis (LCCFA) model, which unifies the factor analysis (FA), convolution operation and supervised learning. In the LCCFA model, each dictionary atom is used as a small-sized convolution kernel with the goal of learning the observations’ basic structures, which have highly shared characteristics among all observed data. This property enables the proposed method to describe data with fewer dictionary atoms than the FA model and reduces the model complexity. Consequently, the classification performance of the LCCFA model can be improved in the case of limited training samples. Meanwhile, the proposed model also projects the weight vectors of dictionary atoms to their class labels to constrain the learning of parameters. The difference in weight vectors from different classes increases due to the label constraint, thereby offering the potential to enhance the inter-class separability of statistical models. Additionally, the efficient parameter estimation is implemented via variational Bayesian (VB) algorithm. Experimental results on several benchmark datasets and measured radar high-resolution range profile (HRRP) data show that our method outperforms other related models in terms of small sample classification.