Improved Structured Dictionary Learning via Correlation and Class Based Block Formation

In recent years, the creation of the block-structured dictionary has attracted a lot of interest. It involves a two-step process: block formation and dictionary update. Both the steps are important in producing an effective dictionary. The existing works mostly assume that the block structure is known a priori while learning the dictionary. For finding the unknown block structure of a given dictionary, the sparse agglomerative clustering (SAC) is most commonly used. It groups atoms based on their consistency in sparse coding of the data over the given dictionary. This paper explores two innovations toward improving the reconstruction, as well as the classification ability achieved with the block-structured dictionary. First, we propose a novel block structuring approach that makes use of the correlation among dictionary atoms. Unlike the SAC approach, which groups diverse atoms, in the proposed approach the blocks are formed by grouping the top most correlated atoms of the dictionary. The proposed block clustering approach is noted to yield significant reduction in redundancy. It also provides a direct control on the block size when compared with the existing SAC-based block structuring. Second, we present a novel dictionary learning rule, which includes the class-specific reconstruction error as a regularization to further enhance the classification ability of the block dictionary. The impact of the proposed innovations on the reconstruction ability has been demonstrated on synthetic data while that on the classification ability has been assessed on both speaker verification and face recognition tasks.