Related papers: An efficient algorithm computing composition facto…
This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…
We present an efficient algorithm for learning mixed membership models when the number of variables $p$ is much larger than the number of hidden components $k$. This algorithm reduces the computational complexity of state-of-the-art tensor…
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…
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 decomposition is a fundamental method used in various areas to deal with high-dimensional data. \emph{Tensor power method} (TPM) is one of the widely-used techniques in the decomposition of tensors. This paper presents a novel tensor…
We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals…
Decomposing tensors into orthogonal factors is a well-known task in statistics, machine learning, and signal processing. We study orthogonal outer product decompositions where the factors in the summands in the decomposition are required to…
We present new efficient (O(N log N)) methods for computing three quantities crucial to electronic structure calculations: the ionic potential, the electron-ion contribution to the Born-Oppenheimer forces, and the electron-ion contribution…
The tensor-train (TT) decomposition is widely used to compress large tensors into a more compact form by exploiting their inherent data structures. A fundamental approach for constructing the TT format is the well-known TT-SVD method, which…
Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
Participation factors (PFs) quantify the interaction between system modes and state variables, and they play a crucial role in various applications such as modal analysis, model reduction, and control design. With increasing system…
A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast…
Efficient and fast computation of a tensor singular value decomposition (t-SVD) with a few passes over the underlying data tensor is crucial because of its many potential applications. The current/existing subspace randomized algorithms…
Consider a data set collected by (individuals-features) pairs in different times. It can be represented as a tensor of three dimensions (Individuals, features and times). The tensor biclustering problem computes a subset of individuals and…
This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…
We determine the composition factors of the tensor product $S(E)\otimes S(E)$ of two copies of the symmetric algebra of the natural module $E$ of a general linear group over an algebraically closed field of positive characteristic. Our main…
Modular composition is the problem of computing the composition of two univariate polynomials modulo a third one. For a long time, the fastest algebraic algorithm for this problem was that of Brent and Kung (1978). Recently, we improved…
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…
We provide an effective algorithm for determining whether an element of the outer automorphism group of a free group is fully irreducible. Our method produces a finite list which can be checked for periodic proper free factors.