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In intelligent transportation systems, traffic data imputation, estimating the missing value from partially observed data is an inevitable and challenging task. Previous studies have not fully considered traffic data's multidimensionality…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…
Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It is generalization of approximate…
We study the problem of learning mixtures of linear dynamical systems (MLDS) from input-output data. The mixture setting allows us to leverage observations from related dynamical systems to improve the estimation of individual models.…
Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a…
The need to know a few singular triplets associated with the largest singular values of third-order tensors arises in data compression and extraction. This paper describes a new method for their computation using the t-product. Methods for…
In this paper, we study the control of a class of time-invariant linear ensemble systems whose natural dynamics are linear in the system parameter. This class of ensemble control systems arises from practical engineering and physical…
The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
This paper presents a new way of describing cross fields based on fourth order tensors. We prove that the new formulation is forming a linear space in $\mathbb{R}^9$. The algebraic structure of the tensors and their projections on…
This paper studies the issues about tensors. Three typical kinds of tensor decomposition are mentioned. Among these decompositions, the t-SVD is proposed in this decade. Different definitions of rank derive from tensor decompositions. Based…
Tensor operations play an essential role in various fields of science and engineering, including multiway data analysis. In this study, we establish a few basic properties of the range and null space of a tensor using block circulant…
This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…
During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey…
In this work, we propose and study a new approach to formulate the optimal control problem of second-order differential equations, with a particular interest in those derived from force-controlled Lagrangian systems. The formulation results…
Tensor-valued data are becoming increasingly available in economics and this calls for suitable econometric tools. We propose a new dynamic linear model for tensor-valued response variables and covariates that encompasses some well-known…
Approximating higher-order tensors by the Tucker format has been applied in many fields such as psychometrics, chemometrics, signal processing, pattern classification, and so on. In this paper, we propose some new Tucker-like approximations…
Developed in a series of seminal papers in the early 2010s, the tubal tensor framework provides a clean and effective algebraic setting for tensor computations, supporting matrix-mimetic features such as a tensor Singular Value…
We prove the existence of an open set of $n_1\times n_2 \times n_3$ tensors of rank $r$ on which a popular and efficient class of algorithms for computing tensor rank decompositions based on a reduction to a linear matrix pencil, typically…