Related papers: Solving Tensor Low Cycle Rank Approximation
Tensor train decomposition is a powerful tool for dealing with high-dimensional, large-scale tensor data, which is not suffering from the curse of dimensionality. To accelerate the calculation of the auxiliary unfolding matrix, some…
In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…
A common approach for compressing large-scale data is through matrix sketching. In this work, we consider the problem of recovering low-rank matrices from two noisy linear sketches using the double sketching scheme discussed in Fazel et al.…
In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing.…
This work presents a low-rank tensor model for multi-dimensional Markov chains. A common approach to simplify the dynamical behavior of a Markov chain is to impose low-rankness on the transition probability matrix. Inspired by the success…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…
Ranking is a key aspect of many applications, such as information retrieval, question answering, ad placement and recommender systems. Learning to rank has the goal of estimating a ranking model automatically from training data. In…
In this work we present recent results on application of low-rank tensor decompositions to modelling of aggregation kinetics taking into account multi-particle collisions (for three and more particles). Such kinetics can be described by…
Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…
In the literature, tensors have been effectively used for capturing the context information in language models. However, the existing methods usually adopt relatively-low order tensors, which have limited expressive power in modeling…
Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…
We propose a novel tensor network language model based on the simplest tensor network (i.e., tensor trains), called `Tensor Train Language Model' (TTLM). TTLM represents sentences in an exponential space constructed by the tensor product of…
In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…
Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…
Tensor Attention, a multi-view attention that is able to capture high-order correlations among multiple modalities, can overcome the representational limitations of classical matrix attention. However, the $O(n^3)$ time complexity of tensor…
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…
In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…
Constrained least squares problems arise in many applications. Their memory and computation costs are expensive in practice involving high-dimensional input data. We employ the so-called "sketching" strategy to project the least squares…
This work proposes a low complexity nonlinearity model and develops adaptive algorithms over it. The model is based on the decomposable---or rank-one, in tensor language---Volterra kernels. It may also be described as a product of FIR…