Designing Structured Sparse Dictionaries for Sparse Representation Modeling

Linear approaches to the problem of unsupervised data dimensionality reduction consist in finding a suitable set of factors, which is usually called dictionary, on the basis of which data can be represented as a linear combination of the dictionary elements. In recent years there have been relevant efforts for searching data representation which are based on sparse dictionary elements or a sparse linear combination of the dictionary elements. Here we investigate the possibility to combine the advantages of both sparse dictionary elements and sparse linear combination. Notably, we also impose a structure on the dictionary elements. We compare our algorithm with two other different approaches presented in literature which impose either sparse structured dictionary elements or sparse linear combination. These (preliminary) results suggests that our approach presents some promising advantages, in particular a greater possibility of interpreting the data representation.