Related papers: Optimization via Separated Representations and the…

Decoupling multivariate polynomials is useful for obtaining an insight into the workings of a nonlinear mapping, performing parameter reduction, or approximating nonlinear functions. Several different tensor-based approaches have been…

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…

Symmetric tensor decomposition is an important problem with applications in several areas for example signal processing, statistics, data analysis and computational neuroscience. It is equivalent to Waring's problem for homogeneous…

In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…

In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…

Tucker decomposition is a popular technique for many data analysis and machine learning applications. Finding a Tucker decomposition is a nonconvex optimization problem. As the scale of the problems increases, local search algorithms such…

The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…

In this paper we give a new and simple algorithm to put any multivariate polynomial into a normal determinant form in which each entry has the form , and in each column the same variable appears. We also apply the algorithm to obtain a…

Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…

Convolutional neural networks excel in image recognition tasks, but this comes at the cost of high computational and memory complexity. To tackle this problem, [1] developed a tensor factorization framework to compress fully-connected…

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…

This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…

In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…

The (efficient and parsimonious) decomposition of higher-order tensors is a fundamental problem with numerous applications in a variety of fields. Several methods have been proposed in the literature to that end, with the Tucker and PARAFAC…

We provide a novel analysis of low-rank tensor completion based on hypergraph expanders. As a proxy for rank, we minimize the max-quasinorm of the tensor, which generalizes the max-norm for matrices. Our analysis is deterministic and shows…