Related papers: Fast and Guaranteed Tensor Decomposition via Sketc…

The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…

We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low…

Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…

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…

In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a…

In this paper, we propose a general framework for solving high-dimensional partial differential equations with tensor networks. Our approach uses Monte-Carlo simulations to update the solution and re-estimates the new solution from samples…

We consider the problem of constructing a canonical polyadic (CP) decomposition for a tensor network, rather than a single tensor. We illustrate how it is possible to reduce the complexity of constructing an approximate CP representation of…

Channel pruning and tensor decomposition have received extensive attention in convolutional neural network compression. However, these two techniques are traditionally deployed in an isolated manner, leading to significant accuracy drop…

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…

A new paradigm for large-scale spectrum occupancy learning based on long short-term memory (LSTM) recurrent neural networks is proposed. Studies have shown that spectrum usage is a highly correlated time series. Moreover, there is a…

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…

Alternating least squares is the most widely used algorithm for CP tensor decomposition. However, alternating least squares may exhibit slow or no convergence, especially when high accuracy is required. An alternative approach is to regard…

We show how to develop sampling-based alternating least squares (ALS) algorithms for decomposition of tensors into any tensor network (TN) format. Provided the TN format satisfies certain mild assumptions, resulting algorithms will have…

In this paper, we suggest a new method for a given tensor to find CP decompositions using a less number of rank $1$ tensors. The main ingredient is the Least Absolute Shrinkage and Selection Operator (LASSO) by considering the decomposition…

In this paper, we develop a novel procedure for low-rank tensor regression, namely \emph{\underline{I}mportance \underline{S}ketching \underline{L}ow-rank \underline{E}stimation for \underline{T}ensors} (ISLET). The central idea behind…

Mining massive spatio-temporal data can help a variety of real-world applications such as city capacity planning, event management, and social network analysis. The tensor representation can be used to capture the correlation between space…

The tensor rank decomposition, also known as canonical polyadic(CP) or simply tensor decomposition, has a long history in multilinear algebra. However, computing a rank decomposition becomes particularly challenging when the rank lies…

With the continuous increase in the number and resolution of video surveillance cameras, the burden of transmitting and storing surveillance video is growing. Traditional communication methods based on Shannon's theory are facing…

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…

We propose two provably accurate methods for low CP-rank tensor completion - one using adaptive sampling and one using nonadaptive sampling. Both of our algorithms combine matrix completion techniques for a small number of slices along with…