Non-negativity and locality constrained Laplacian sparse coding for image classification

The traditional sparse coding (SC) method has achieved good results in image classification. However, one of its serious weaknesses is that it ignores the relationship between features thus losing spatial information. Moreover, in combinatorial optimisation problems, operations of addition and subtraction are involved, and the use of subtraction may cause features to be cancelled. In this paper, we propose a method called non-negativity and locality constrained Laplacian sparse coding (NLLSC) for image classification. Firstly, non-negative matrix factorisation (NMF) is used in the Laplacian sparse coding (LSC), which is applied to constrain the negativity of both codebook and code coefficient. Secondly, we introduce K-nearest neighbouring codewords for local features because locality is more important than sparseness. Finally, non-negativity and locality constrained operators are introduced to obtain a novel sparse coding for local features, and then in the pooling step, we use spatial pyramid division (SPD) and max pooling (MP) to represent the final images. As for image classification, multi-class linear SVM is adopted. Experiments on several standard image datasets have shown better performance than previous algorithms.