Manifold-Regularized Selectable Factor Extraction for Semi-supervised Image Classification

Feature selection methods are efficient in modern computer vision applications to reduce the computational cost and the chance of over-fitting. Recently, a novel selectable factor extraction (SFE[3]) framework is proposed to simultaneously perform feature selection and extraction, and is theoretically and practically proved to be effective for high-dimensional data. Although it is advantageous in several aspects, SFE is only designed for either supervised or unsupervised learning, and is not suitable when there are limited labeled samples and a large number of unlabeled samples. To tackle this problem, we propose a novel manifold regularized SFE (MRSFE) framework for semi-supervised image classification. We use a low rank penalized regression model to explore the label information. A low rank matrix of the regression coefficients, together with the `2,1 or `2,0 norm penalty is learned for joint feature selection and extraction. In addition, all the labeled and unlabeled samples are utilized in MRSFE to construct the data adjacency graph to approximate the underlying data manifold, which the data distribution is assumed to be supported on. The graph Laplacian is then incorporated as a regularization term to smooth the coefficients matrix. In this way, the local structures of the whole dataset are preserved, and the data distribution is well exploited. To derive our model, we begin with the reduced rank regression (RRR) model[1]: min B ‖YL−XLB‖F , s.t. rank(B)≤ r. (1)