Hierarchical Sparse Dictionary Learning

Sparse coding plays a key role in high dimensional data analysis. One critical challenge of sparse coding is to design a dictionary that is both adaptive to the training data and generalizable to unseen data of same type. In this paper, we propose a novel dictionary learning method to build an adaptive dictionary regularized by an a-priori over-completed dictionary. This leads to a sparse structure of the learned dictionary over the a-priori dictionary, and a sparse structure of the data over the learned dictionary. We apply the hierarchical sparse dictionary learning approach on both synthetic data and real-world high-dimensional time series data. The experimental results demonstrate that the hierarchical sparse dictionary learning approach reduces overfitting and enhances the generalizability of the learned dictionary. Moreover, the learned dictionary is optimized to adapt to the given data and result in a more compact dictionary and a more robust sparse representation. The experimental results on real datasets demonstrate that the proposed approach can successfully characterize the heterogeneity of the given data, and leads to a better and more robust dictionary.