Related papers: Tensor principal component analysis via sum-of-squ…
In this paper, we provide the first convergence guarantee for the factorization approach. Specifically, to avoid the scaling ambiguity and to facilitate theoretical analysis, we optimize over the so-called left-orthogonal TT format which…
Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and to characterize the sparse structures of noise. Current approaches…
Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…
Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…
We consider the problem of structured tensor denoising in the presence of unknown permutations. Such data problems arise commonly in recommendation system, neuroimaging, community detection, and multiway comparison applications. Here, we…
In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial and noisy observations for third-order tensors. Because of sparsity and nonnegativity, the underlying tensor is decomposed into the…
In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…
Harmonic retrieval (HR) has a wide range of applications in the scenes where signals are modelled as a summation of sinusoids. Past works have developed a number of approaches to recover the original signals. Most of them rely on classical…
We introduce the tensor numerical method for solution of the $d$-dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $n^{\otimes d}$ tensor-product Cartesian grids. The approach…
We study the problem of tensor robust principal component analysis (TRPCA), which aims to separate an underlying low-multilinear-rank tensor and a sparse outlier tensor from their sum. In this work, we propose a fast non-convex algorithm,…
Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode…
Large-dimensional factor model has drawn much attention in the big-data era, in order to reduce the dimensionality and extract underlying features using a few latent common factors. Conventional methods for estimating the factor model…
We are interested in the numerical solution of the tensor least squares problem \[ \min_{\mathcal{X}} \| \mathcal{F} - \sum_{i =1}^{\ell} \mathcal{X} \times_1 A_1^{(i)} \times_2 A_2^{(i)} \cdots \times_d A_d^{(i)} \|_F, \] where…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
We present a novel analysis of the dynamics of tensor power iterations in the overcomplete regime where the tensor CP rank is larger than the input dimension. Finding the CP decomposition of an overcomplete tensor is NP-hard in general. We…
We present an algorithm for low rank decomposition of tensors of any symmetry type, from fully asymmetric to fully symmetric. It recovers the decomposition one summand at a time via the higher-order power method. This approach is known to…
We consider the problem of recovering a low-rank tensor from its noisy observation. Previous work has shown a recovery guarantee with signal to noise ratio $O(n^{\lceil K/2 \rceil /2})$ for recovering a $K$th order rank one tensor of size…
The oriented singular value decomposition (O-SVD) proposed by Zeng and Ng provides a hybrid approach to the t-product based third-order tensor singular value decomposition with the transform matrix being a factor matrix of the higher order…
Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…
The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses…