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There has recently been considerable interest in completing a low-rank matrix or tensor given only a small fraction (or few linear combinations) of its entries. Related approaches have found considerable success in the area of recommender…

Machine Learning · Computer Science 2017-02-20 Nikos Kargas , Nicholas D. Sidiropoulos

Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical…

Machine Learning · Computer Science 2020-04-24 Huyan Huang , Yipeng Liu , Ce Zhu

Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…

Machine Learning · Computer Science 2020-02-26 Lukáš Adam , Václav Mácha , Václav Šmídl , Tomáš Pevný

We present new deterministic algorithms for several cases of the maximum rank matrix completion problem (for short matrix completion), i.e. the problem of assigning values to the variables in a given symbolic matrix as to maximize the…

Data Structures and Algorithms · Computer Science 2014-07-11 Gábor Ivanyos , Marek Karpinski , Nitin Saxena

We consider the problem of completing a matrix with categorical-valued entries from partial observations. This is achieved by extending the formulation and theory of one-bit matrix completion. We recover a low-rank matrix $X$ by maximizing…

Numerical Analysis · Computer Science 2015-07-03 Yang Cao , Yao Xie

This paper presents a hierarchical low-rank decomposition algorithm assuming any matrix element can be computed in $O(1)$ time. The proposed algorithm computes rank-revealing decompositions of sub-matrices with a blocked adaptive cross…

Numerical Analysis · Mathematics 2019-09-06 Yang Liu , Wissam Sid-Lakhdar , Elizaveta Rebrova , Pieter Ghysels , Xiaoye Sherry Li

Matrix completion aims to recover an unknown low-rank matrix from a small subset of its entries. In many applications, the rank of the unknown target matrix is known in advance. In this paper, first we revisit a recently proposed rank-based…

Optimization and Control · Mathematics 2024-06-11 Tacildo de Souza Araújo , Douglas S. Gonçalves , Cristiano Torezzan

The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and…

Machine Learning · Computer Science 2009-02-24 Amit Singer , Mihai Cucuringu

In this paper, we propose a novel model to recover a low-rank tensor by simultaneously performing double nuclear norm regularized low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An block successive…

Computer Vision and Pattern Recognition · Computer Science 2020-05-07 Haijin Zeng , Xiaozhen Xie , Jifeng Ning

Factoring a matrix into two low rank matrices is at the heart of many problems. The problem of matrix completion especially uses it to decompose a sparse matrix into two non sparse, low rank matrices which can then be used to predict…

Machine Learning · Computer Science 2018-01-12 Mukul Bhutani , Bamdev Mishra

We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…

Machine Learning · Statistics 2020-03-25 Yunfeng Cai , Ping Li

In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…

Rings and Algebras · Mathematics 2018-06-13 Stephen Linton , Gabriele Nebe , Alice Niemeyer , Richard Parker , Jon Thackray

We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important…

Machine Learning · Statistics 2026-02-05 Dimitris Bertsimas , Nicholas A. G. Johnson

Based on an idea in [4] we propose a new iterative multiplicative filtering algorithm for label assignment matrices which can be used for the supervised partitioning of data. Starting with a row-normalized matrix containing the averaged…

Numerical Analysis · Mathematics 2018-12-10 Ronny Bergmann , Jan Henrik Fitschen , Johannes Persch , Gabriele Steidl

We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…

Statistics Theory · Mathematics 2015-02-03 Olga Klopp

In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…

Numerical Analysis · Computer Science 2018-05-23 Longhao Yuan , Chao Li , Danilo Mandic , Jianting Cao , Qibin Zhao

We present a new, simple and computationally efficient iterative method for low rank matrix completion. Our method is inspired by the class of factorization-type iterative algorithms, but substantially differs from them in the way the…

Optimization and Control · Mathematics 2021-06-30 Jonathan Bauch , Boaz Nadler , Pini Zilber

The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…

Statistics Theory · Mathematics 2014-08-27 Olga Klopp , Jean Lafond , Eric Moulines , Joseph Salmon

The low-tubal-rank tensor model has been recently proposed for real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of its…

Machine Learning · Computer Science 2016-10-12 Xiao-Yang Liu , Shuchin Aeron , Vaneet Aggarwal , Xiaodong Wang

Predicting unobserved entries of a partially observed matrix has found wide applicability in several areas, such as recommender systems, computational biology, and computer vision. Many scalable methods with rigorous theoretical guarantees…

Machine Learning · Statistics 2018-02-15 Vatsal Shah , Nikhil Rao , Weicong Ding