Related papers: Fundamental Conditions for Low-CP-Rank Tensor Comp…

The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

We study the least-squares (LS) functional of the canonical polyadic (CP) tensor decomposition. Our approach is based on the elimination of one factor matrix which results in a reduced functional. The reduced functional is reformulated into…

Motivated by questions arising in signal processing, computational complexity, and other areas, we study the ranks and border ranks of symmetric tensors using geometric methods. We provide improved lower bounds for the rank of a symmetric…

We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor…

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…

Recent approaches to the tensor completion problem have often overlooked the nonnegative structure of the data. We consider the problem of learning a nonnegative low-rank tensor, and using duality theory, we propose a novel factorization of…

We study the symmetric tensor rank of multiplication over finite field extensions using linearized polynomials. Via field trace, symmetric linearized polynomials are identified with symmetric bilinear forms and symmetric matrices, allowing…

The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required…

We present an orthogonal matrix outer product decomposition for the fourth-order conjugate partial-symmetric (CPS) tensor and show that the greedy successive rank-one approximation (SROA) algorithm can recover this decomposition exactly.…

We consider the problem of finding the smallest or largest entry of a tensor of order N that is specified via its rank decomposition. Stated in a different way, we are given N sets of R-dimensional vectors and we wish to select one vector…

We consider the problem of constructing a canonical polyadic (CP) decomposition for a tensor network, rather than a single tensor. We illustrate how it is possible to reduce the complexity of constructing an approximate CP representation of…

Low-rank matrix completion addresses the problem of completing a matrix from a certain set of generic specified entries. Over the complex numbers a matrix with a given entry pattern can be uniquely completed to a specific rank, called the…

In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties -- the set of tensors with bounded Tucker…

In this paper, we investigate the sample complexity of recovering tensors with low symmetric rank from symmetric rank-one measurements. This setting is particularly motivated by the study of higher-order interactions and the analysis of…

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…

Recent studies have demonstrated the great potential of reduced order modeling for parametric dynamical systems using low-rank tensor decompositions (LRTD). In particular, within the framework of interpolatory tensorial reduced order models…

Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-rank matrix completion (Recht et al., 2010) are extensions of PCA to allow for outliers and missing entries respectively. It is well-known that solving these problems…

Obtaining a reliable estimate of the joint probability mass function (PMF) of a set of random variables from observed data is a significant objective in statistical signal processing and machine learning. Modelling the joint PMF as a tensor…

A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor…