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In this work we present a new framework for the analysis and design of randomized gossip algorithms for solving the average consensus problem. We show how classical randomized iterative methods for solving linear systems can be interpreted…

Optimization and Control · Mathematics 2019-06-04 Nicolas Loizou , Peter Richtárik

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…

Signal Processing · Electrical Eng. & Systems 2023-07-19 Xiao Fu , Nico Vervliet , Lieven De Lathauwer , Kejun Huang , Nicolas Gillis

A well-known method for completing low-rank matrices based on convex optimization has been established by Cand{\`e}s and Recht. Although theoretically complete, the method may not entirely solve the low-rank matrix completion problem. This…

Methodology · Statistics 2014-07-17 Guangcan Liu , Ping Li

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…

Information Theory · Computer Science 2020-07-15 Xu Zhang , Wei Cui , Yulong Liu

We consider the problem of matrix completion with side information (\textit{inductive matrix completion}). In real-world applications many side-channel features are typically non-informative making feature selection an important part of the…

Machine Learning · Statistics 2018-10-09 Ivan Nazarov , Boris Shirokikh , Maria Burkina , Gennady Fedonin , Maxim Panov

The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…

Systems and Control · Electrical Eng. & Systems 2021-11-10 Mingzhou Yin , Roy S. Smith

Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…

Numerical Analysis · Mathematics 2022-06-08 Rishi Advani , Sean O'Hagan

This paper studies the problem of decomposing a low-rank matrix into a factor with binary entries, either from $\{\pm 1\}$ or from $\{0,1\}$, and an unconstrained factor. The research answers fundamental questions about the existence and…

Data Structures and Algorithms · Computer Science 2019-08-01 Richard Kueng , Joel A. Tropp

We propose a method that meta-learns a knowledge on matrix factorization from various matrices, and uses the knowledge for factorizing unseen matrices. The proposed method uses a neural network that takes a matrix as input, and generates…

Machine Learning · Statistics 2021-06-30 Tomoharu Iwata

We propose to transfer representational knowledge from multiple sources to a target noisy matrix completion task by aggregating singular subspaces information. Under our representational similarity framework, we first integrate linear…

Machine Learning · Statistics 2024-12-10 Yong He , Zeyu Li , Dong Liu , Kangxiang Qin , Jiahui Xie

In this work we describe an efficient implementation of a hierarchy of algorithms for the decomposition of dense matrices over the field with two elements (GF(2)). Matrix decomposition is an essential building block for solving dense…

Mathematical Software · Computer Science 2010-06-10 Martin R. Albrecht , Clément Pernet

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…

Optimization and Control · Mathematics 2011-08-09 Venkat Chandrasekaran , Sujay Sanghavi , Pablo A. Parrilo , Alan S. Willsky

We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…

Machine Learning · Computer Science 2014-05-14 Behnam Neyshabur , Rina Panigrahy

Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as…

Statistics Theory · Mathematics 2016-02-08 Siamak Ravanbakhsh , Barnabas Poczos , Russell Greiner

The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…

Machine Learning · Computer Science 2025-04-23 Samuel Wertz , Arnaud Vandaele , Nicolas Gillis

Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…

Disordered Systems and Neural Networks · Physics 2023-07-12 Francesco Camilli , Marc Mézard

Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…

Machine Learning · Statistics 2022-11-18 Yunxiao Chen , Xiaoou Li

We consider the problem of reconstructing a low-rank matrix from a small subset of its entries. In this paper, we describe the implementation of an efficient algorithm called OptSpace, based on singular value decomposition followed by local…

Numerical Analysis · Computer Science 2013-01-30 Raghunandan H. Keshavan , Sewoong Oh

Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…

Machine Learning · Computer Science 2014-10-24 Jingbo Shang , Tianqi Chen , Hang Li , Zhengdong Lu , Yong Yu

We consider the problem of designing a coding scheme that allows both sparsity and privacy for distributed matrix-vector multiplication. Perfect information-theoretic privacy requires encoding the input sparse matrices into matrices…

Information Theory · Computer Science 2022-03-04 Marvin Xhemrishi , Rawad Bitar , Antonia Wachter-Zeh