The Singular Value Decomposition (SVD) may be extended to tensors at least in two very different ways. One is the High-Order SVD (HOSVD), and the other is the Canonical Decomposition (CanD). Only the latter is closely related to the tensor rank. Important basic questions are raised in this short paper, such as the maximal achievable rank of a tensor of given dimensions, or the computation of a ...

A novel tensor decomposition called pattern or P-decomposition is proposed to make it possible to identify replicating structures in complex data, such as textures and patterns in music spectrograms. In order to establish a computational framework for this paradigm, we adopt a multiway (tensor) approach. To this end, a novel tensor product is introduced, and the analysis of its properties shows...

We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued, pairwise orthogonal vectors. Such decompositions do not generally exist, but we show that some symmetric tensor decomposition problems can be converted to orthogonal problems following the whitening procedure proposed by Anandkumar et al. (2012). If an orthogonal decomposition of a...

In this paper, we deal with the problem of spherical interpolation of discretely given data of tensorial type. To this end, spherical tensor elds are investigated and a decomposition formula is described. It is pointed out that the decomposition formula is of importance for the spectral analysis of the gra-vitational tensor in (spaceborne) gradiometry. Tensor spherical harmonics are introduced ...

We analyze the statistical performance of a recently proposed convex tensor decomposition algorithm. Conventionally tensor decomposition has been formulated as non-convex optimization problems, which hindered the analysis of their performance. We show under some conditions that the mean squared error of the convex method scales linearly with the quantity we call the normalized rank of the true ...

We study separability properties of solutions of elliptic equations with piecewise constant coefficients in R d , d ≥ 2. Besides that, we develop efficient tensor-structured preconditioner for the diffusion equation with variable coefficients. It is based only on rank structured decomposition of the tensor of reciprocal coefficient and on the decomposition of the inverse of the Laplacian operat...

This paper proposes a simplified Tucker decomposition of a tensor model for gait recognition from dense local spatiotemporal (S/T) features extracted from gait video sequences. Unlike silhouettes, local S/T features have displayed state-of-art performances on challenging action recognition testbeds, and have the potential to push gait ID towards real-world deployment. We adopt a Fisher represen...

OF THE DISSERTATIONDiscovery of Latent Factors in High-dimensional Data Using Tensor MethodsByFurong HuangDoctor of Philosophy in Electrical and Computer EngineeringUniversity of California, Irvine, 2016Assistant Professor Animashree Anandkumar, Chair Unsupervised learning aims at the discovery of hidden structure that drives the observationsin the real world. It is ...

To solve some problems which JPEG compression obtains results of poor reconstruction quality and high computational complexity for image containing more high frequency information, a novel tensor approximation algorithm based on high order singular value decomposition has been proposed. The new algorithm respects each image both gray image and color image as a high order tensor. It transforms t...

The t-SVD based Tensor Robust Principal Component Analysis (TRPCA) decomposes low rank multi-linear signal corrupted by gross errors into low multi-rank and sparse component by simultaneously minimizing tensor nuclear norm and l1 norm. But if the multi-rank of the signal is considerably large and/or large amount of noise is present, the performance of TRPCA deteriorates. To overcome this proble...