Seminar “First-order Perturbation Analysis of Low-rank Tensor Approximations Based on the Truncated HOSVD”
Published at: April 12, 2019 Category: NewsSpeaker: Prof. Dr. Martin Haardt (Ilmenau University of Technology)
When: 04/27/2017, 10:30h
Where: Sala de Seminários do GTEL (Bloco 722 do Campus do Pici)
Abstract:
The truncated version of the higher-order singular value decomposition (HOSVD) has a great significance in multi-dimensional tensor-based signal processing. It allows to extract the principal components from noisy observations in order to find a low-rank approximation of the multi-dimensional data. In a variety of applications, including image processing, object and pattern recognition, high-resolution parameter estimation, control engineering as well as data analysis, the truncated HOSVD is used to “denoise” or “compress” noise-corrupted data.
In this presentation, we address the question of how good this approximation is by analytically quantifying the tensor reconstruction error introduced by the truncated HOSVD. To this end, we present a first-order perturbation analysis of the truncated HOSVD to obtain analytical expressions for the signal subspace error in each dimension as well as the tensor reconstruction error induced by the low-rank approximation of the noise corrupted tensor. The results are asymptotic in the signal-to-noise ratio (SNR) and expressed in terms of the second-order moments of the noise, such that apart from a zero mean, no assumptions on the noise statistics are required. Empirical simulation results verify the obtained analytical expressions.
