Related papers: Convex Coupled Matrix and Tensor Completion

Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the unfoldings of the…

Over the past decade, various matrix completion algorithms have been developed. Thresholded singular value decomposition (SVD) is a popular technique in implementing many of them. A sizable number of studies have shown its theoretical and…

Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex…

We study a noisy tensor completion problem of broad practical interest, namely, the reconstruction of a low-rank tensor from highly incomplete and randomly corrupted observations of its entries. While a variety of prior work has been…

In the low-rank matrix completion (LRMC) problem, the low-rank assumption means that the columns (or rows) of the matrix to be completed are points on a low-dimensional linear algebraic variety. This paper extends this thinking to cases…

In this paper, we propose a novel method for matrix completion under general non-uniform missing structures. By controlling an upper bound of a novel balancing error, we construct weights that can actively adjust for the non-uniformity in…

We propose a new tensor completion method based on tensor trains. The to-be-completed tensor is modeled as a low-rank tensor train, where we use the known tensor entries and their coordinates to update the tensor train. A novel tensor train…

In this paper, we study the popularly dubbed matrix completion problem, where the task is to "fill in" the unobserved entries of a matrix from a small subset of observed entries, under the assumption that the underlying matrix is of…

Tensor completion is a challenging problem with various applications. Many related models based on the low-rank prior of the tensor have been proposed. However, the low-rank prior may not be enough to recover the original tensor from the…

Despite the recent development in machine learning, most learning systems are still under the concept of "black box", where the performance cannot be understood and derived. With the rise of safety and privacy concerns in public, designing…

We study extensions of compressive sensing and low rank matrix recovery to the recovery of low rank tensors from incomplete linear information. While the reconstruction of low rank matrices via nuclear norm minimization is rather…

The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…

We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…

Tensor completion recovers a multi-dimensional array from a limited number of measurements. Using the recently proposed tensor ring (TR) decomposition, in this paper we show that a d-order tensor of dimensional size n and TR rank r can be…

This paper presents novel algorithms which exploit the intrinsic algebraic and combinatorial structure of the matrix completion task for estimating missing en- tries in the general low rank setting. For positive data, we achieve results…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

We present a novel method for matrix completion, specifically designed for matrices where one dimension is significantly larger than the other. Our Columns Selected Matrix Completion (CSMC) method combines Column Subset Selection with…

This paper studies the problem of completing a low-rank matrix from a few of its random entries with the aid of prior information. We suggest a strategy to incorporate prior information into the standard matrix completion procedure by…

In this paper, we propose a coupled tensor norm regularization that could enable the model output feature and the data input to lie in a low-dimensional manifold, which helps us to reduce overfitting. We show this regularization term is…

In this paper we provide a latent-variable formulation and solution to the recommender system (RS) problem in terms of a fundamental property that any reasonable solution should be expected to satisfy. Specifically, we examine a novel…