Semi-Supervised Sparse Coding

Given a data sample with its feature vector, SC tries to learn a codebook with some codeworks, and approximate the data sample as the linear combination of the codewords. SC assume that only a few codewords in the codebook are enough to represent the data sample, thus the combination coefficients should be sparse, i.e. most of the coefficients are zeros, leaving only a few of them non-zeros. The linear combination coefficients of the data sample could be its new representation. Because they are sparse, the coefficient vector is often referred to as the sparse code. To solve the sparse code, one usually minimizes the approximation error with regard to the codebook and the sparse code, and at the same time seeks the sparsity of the sparse code. Although SC has been used in many pattern recognition applications, such as palmprint recognition [24], dynamic texture recognition [25], human action recognition [26], [27], [28], speech recognition [29], digit recognition [30], image annotation [31], [32], [33], and face recognition [34], in most cases, SC is used as an unsupervised learning method. When SC is performed to the training data set, it is assumed that the class labels of the training samples are unavailable. Then after the sparse codes are learned, they will be used to learn a classifier. Thus the class labels are ignored during the sparse coding procedure.