Tensor dictionary learning with sparse TUCKER decomposition

Dictionary learning algorithms are typically derived for dealing with one or two dimensional signals using vector-matrix operations. Little attention has been paid to the problem of dictionary learning over high dimensional tensor data. We propose a new algorithm for dictionary learning based on tensor factorization using a TUCKER model. In this algorithm, sparseness constraints are applied to the core tensor, of which the n-mode factors are learned from the input data in an alternate minimization manner using gradient descent. Simulations are provided to show the convergence and the reconstruction performance of the proposed algorithm. We also apply our algorithm to the speaker identification problem and compare the discriminative ability of the dictionaries learned with those of TUCKER and K-SVD algorithms. The results show that the classification performance of the dictionaries learned by our proposed algorithm is considerably better as compared to the two state of the art algorithms.