Dictionary learning for fast classification based on soft-thresholding

Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations is a major obstacle that limits the applicability of these methods in large-scale problems, or in scenarios where computational power is restricted. We consider in this paper a simple yet efficient alternative to sparse coding for feature extraction. We study a classification scheme built by applying the soft-thresholding nonlinear mapping in a dictionary, followed by a linear classifier. A novel supervised dictionary learning algorithm tailored for this low complexity classification architecture is proposed. The dictionary learning problem, which jointly estimates the dictionary and linear classifier, is cast as a difference of convex (DC) program, and solved efficiently with an iterative DC solver. We conduct extensive experiments on several datasets, and show that our simple soft-thresholding based classifier competes with state-of-the-art sparse coding classifiers, when the dictionary is learned appropriately. Our classification scheme moreover achieves significant gains in terms of computational time at the testing stage, compared to other classifiers. The proposed scheme shows the potential of the soft-thresholding mapping for classification, and paves the way towards the development of very efficient classification methods for vision problems.