Nonnegative Shifted Tensor Factorization in time frequency domain

In this paper, we proposed a Nonnegative Shifted Tensor Factorization (NSTF) model considering multiple component delays by time frequency analysis. Explicit mathematical representation for the delays is presented to recover the patterns from the original data. In order to explore multilinear shifted component in different modes, we use fast fourier transform (FFT) to transform the non-integer delays into frequency domain by gradients search. The ALS algorithm for NSTF is developed by alternating least square procedure to estimate the nonnegative factor matrices in each mode and enforce the sparsity of model. Simulation results indicate that ALS-NSTF algorithm can extract the shift-invariance sparse features and improve the recognition performance of robust speaker identification and structural magnetic resonance imaging (sMRI) diagnosis for Alzheimer´s Disease.