A review of sparsity-based clustering methods

In case of high dimensionality, a class of data clustering methods has been proposed as a solution that includes suitable subspace search to find inherent clusters. Sparsity-based clustering approaches include a twist in subspace approach as they incorporate a dimensionality expansion through the usage of an overcomplete dictionary representation. Thus, these approaches provide a broader search space to utilize subspace clustering at large. However, sparsity constraint alone does not enforce structured clusters. Through certain stricter constraints, data grouping is possible, which translates to a type of clustering depending on the types of constraints. The dual of the sparsity constraint, namely the dictionary, is another aspect of the whole sparsity-based clustering methods. Unlike off-the-shelf or fixed-waveform dictionaries, adaptive dictionaries can additionally be utilized to shape the state-model entity into a more adaptive form. Chained with structured sparsity, adaptive dictionaries force the state-model into well-formed clusters. Subspaces designated with structured sparsity can then be dissolved through recursion to acquire deep sparse structures that correspond to a taxonomy. As a final note, such procedure can further be extended to include various other machine learning perspectives.