Related papers: Non-Orthogonal Tensor Diagonalization
In addition to the diagonalization of a normal matrix by a unitary similarity transformation, there are two other types of diagonalization procedures that sometimes arise in quantum theory applications -- the singular value decomposition…
In this paper, a numerical method is proposed for canonical polyadic (CP) decomposition of small size tensors. The focus is primarily on decomposition of tensors that correspond to small matrix multiplications. Here, rank of the tensors is…
Tensor decomposition is a fundamental technique widely applied in signal processing, machine learning, and various other fields. However, traditional tensor decomposition methods encounter limitations when jointly analyzing multi-block…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
The ParaTuck-2 decomposition (PT2D) of third-order tensor is a two-layer generalization of the well-known canonical polyadic decomposition (CPD).While being more flexible than the CPD, the PT2D also possesses similar uniqueness…
Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of…
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…
A family of symmetric matrices $A_1,\ldots, A_d$ is SDC (simultaneous diagonalization by congruence, also called non-orthogonal joint diagonalization) if there is an invertible matrix $X$ such that every $X^T A_k X$ is diagonal. In this…
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 a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the…
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…
Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
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…
We study symmetric tensor decompositions, i.e., decompositions of the form $T = \sum_{i=1}^r u_i^{\otimes 3}$ where $T$ is a symmetric tensor of order 3 and $u_i \in \mathbb{C}^n$.In order to obtain efficient decomposition algorithms, it is…
This article provides next step towards solving speed bottleneck of any system that intensively uses convolutions operations (e.g. CNN). Method described in the article is applied on deformable part models (DPM) algorithm. Method described…
We present an algorithm aimed to recognize if a given tensor is a non-identifiable rank-3 tensor.
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex…
In 2011, Kilmer and Martin proposed tensor singular value decomposition (T-SVD) for third order tensors. Since then, T-SVD has applications in low rank tensor approximation, tensor recovery, multi-view clustering, multi-view feature…