Related papers: A nearly optimal algorithm to decompose binary for…
We prove a generalization to Jennrich's uniqueness theorem for tensor decompositions in the undercomplete setting. Our uniqueness theorem is based on an alternative definition of the standard tensor decomposition, which we call…
We consider the problem of decomposing higher-order moment tensors, i.e., the sum of symmetric outer products of data vectors. Such a decomposition can be used to estimate the means in a Gaussian mixture model and for other applications in…
In this work, we consider the optimization formulation for symmetric tensor decomposition recently introduced in the Subspace Power Method (SPM) of Kileel and Pereira. Unlike popular alternative functionals for tensor decomposition, the SPM…
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…
A new implementation of the canonical polyadic decomposition (CPD) is presented. It features lower computational complexity and memory usage than the available state of art implementations available. The CPD of tensors is a challenging…
A new algorithm of the canonical polyadic decomposition (CPD) presented here. It features lower computational complexity and memory usage than the available state of the art implementations. We begin with some examples of CPD applications…
We bound the tensor ranks of elementary symmetric polynomials, and we give explicit decompositions into powers of linear forms. The bound is attained when the degree is odd.
We give algorithms to compute decompositions of a given polynomial, or more generally mixed tensor, as sum of rank one tensors, and to establish whether such a decomposition is unique. In particular, we present methods to compute the…
Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…
We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
In this paper we consider a Metzner-Kapturowski-like decoding algorithm for high-order interleaved sum-rank-metric codes, offering a novel perspective on the decoding process through the concept of an error code. The error code, defined as…
Decompositions of higher-order tensors into sums of simple terms are ubiquitous. We show that in order to verify that two tensors are generated by the same (possibly scaled) terms it is not necessary to compute the individual…
In this work, we study the tensor ring decomposition and its associated numerical algorithms. We establish a sharp transition of algorithmic difficulty of the optimization problem as the bond dimension increases: On one hand, we show the…
The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two…
The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a…
A real binary tensor consists of $2^d$ real entries arranged into hypercube format $2^{\times d}$. For $d=2$, a real binary tensor is a $2\times 2$ matrix with two singular values. Their product is the determinant. We generalize this…
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…
Symmetry properties of r-times covariant tensors T can be described by certain linear subspaces W of the group ring K[S_r] of a symmetric group S_r. If for a class of tensors T such a W is known, the elements of the orthogonal subspace…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…