Related papers: Tensor Completion by Multi-Rank via Unitary Transf…
There has been an increased interest in multimodal language processing including multimodal dialog, question answering, sentiment analysis, and speech recognition. However, naturally occurring multimodal data is often imperfect as a result…
Using the matrix product state (MPS) representation of tensor train decompositions, in this paper we propose a tensor completion algorithm which alternates over the matrices (tensors) in the MPS representation. This development is motivated…
Low-rank tensors appear to be prosperous in many applications. However, the sets of bounded-rank tensors are non-smooth and non-convex algebraic varieties, rendering the low-rank optimization problems to be challenging. To this end, we…
We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different…
Tensor data, or multi-dimensional arrays, is a data format popular in multiple fields such as social network analysis, recommender systems, and brain imaging. It is not uncommon to observe tensor data containing missing values, and tensor…
We consider the multi-view data completion problem, i.e., to complete a matrix $\mathbf{U}=[\mathbf{U}_1|\mathbf{U}_2]$ where the ranks of $\mathbf{U},\mathbf{U}_1$, and $\mathbf{U}_2$ are given. In particular, we investigate the…
The rotation of multi-dimensional arrays, or tensors, is a fundamental operation in computer science with applications ranging from data processing to scientific computing. While various methods exist, achieving this rotation in-place…
Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…
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…
We obtain the first polynomial-time algorithm for exact tensor completion that improves over the bound implied by reduction to matrix completion. The algorithm recovers an unknown 3-tensor with $r$ incoherent, orthogonal components in…
In this paper, we show that the low rank matrix completion problem can be reduced to the problem of finding the rank of a certain tensor.
We study tensor completion in the agnostic setting. In the classical tensor completion problem, we receive $n$ entries of an unknown rank-$r$ tensor and wish to exactly complete the remaining entries. In agnostic tensor completion, we make…
In this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called alternating singular value decomposition. This method is based on the computation of maximal singular values and the…
We analyze rates of approximation by quantized, tensor-structured representations of functions with isolated point singularities in ${\mathbb R}^3$. We consider functions in countably normed Sobolev spaces with radial weights and analytic-…
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…
In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as…
In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently…
This paper presents a multi-dimensional computational method to predict the spatial variation data inside and across multiple dies of a wafer. This technique is based on tensor computation. A tensor is a high-dimensional generalization of a…
Effective non-parametric density estimation is a key challenge in high-dimensional multivariate data analysis. In this paper,we propose a novel approach that builds upon tensor factorization tools. Any multivariate density can be…
In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…