Tensor dictionary learning with sparse TUCKER decomposition

Abstract

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.

Discriminativetensor dictionaries and sparsity for speaker identification

“…To investigate the classification performance of our proposed algorithm, GT-D, over other tensor decomposition methods, we apply our GT-D on a speaker identification problem and compare the results with baseline TUCKER decomposition algorithms such as standard TUCKER method TALS [3], and the state-of-the-art GT-G [10], HALS [6], TCCD [11] and APG [12] methods. We use all of these algorithm with their default parameters.…”

“…For each classification application, the test feature matrix Y test is projected on to each class-specific classifier tensor obtained by (10) to get the coefficients by using the least squares method. The resulting coefficients are used to reconstruct the test feature matrixŶ test i with the help of each D (1) i .…”

Learning Fast Dictionaries for Sparse Representations Using Low-Rank Tensor Decompositions

“…2-KS dictionaries). The model was extended to the 3rd-order (3-KS dictionaries) [12,19] and even for an arbitrary tensor order [4,7] based on the Tucker decomposition, a model coined as Tucker Dictionary Learning. However, none of these works include a sum of Kronecker terms.…”

Tensor-Based Dictionary Learning for Spectral CT Reconstruction

“…These two decompositions can be viewed as generalizations of singular value decomposition (SVD) [33]. With a tensor decomposition method, the conventional dictionary learning (denoted as vectorized dictionary learning, abbreviated as VDL) can be extended into tensor-based dictionary learning (TDL) [34]–[36], which ought to be more powerful in capturing structures and more sparsely representing a multidimensional array. In 2015, we proposed an adaptive tensor-based spatio-temporal dictionary learning method for 4D CT reconstruction [37].…”