Multilinear tensor rank estimation via Sparse Tucker Decomposition

When we apply techniques of Tucker based tensor decomposition to approximate a given tensor data as a low-rank model, appropriate multi-linear tensor rank is often unknown. In such cases, we have to tune this multi-linear tensor rank from a number of combinations. In this paper, we propose a new algorithm for sparse Tucker decomposition which estimates appropriate multilinear tensor rank of the given data. In this method, we imposed orthogonal constraint into the basis matrices and sparse constraint into the core tensor, and try to prune wasted components by maximizing the sparsity of the core tensor under the condition of error bound. Thus, we call this method as the "Pruning Sparse Tucker Decomposition" (PSTD). The PSTD is very useful for estimating the appropriate multilinear tensor rank of the Tucker based sparse representation such as compression. We demonstrate several experiments of the proposed method to show its advantages.