DATA REPLICATION IN DENSE MATRIX FACTORIZATION

Gossiping is proposed as the preferred communication primitive for replicating pivot data in dense matrix factorization on message passing multicomputer. Performance gains are demonstrated on a hypercube for LU factorization algorithms based on gossiping as opposed to broadcasting. This finding has consequences for the design of numerical software libraries.

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Session MP8a2: Message passing and matrix factorization algorithms

2017 51st Asilomar Conference on Signals, Systems, and Computers ◽

10.1109/acssc.2017.8335368 ◽

2017 ◽

Keyword(s):

Matrix Factorization ◽

Message Passing ◽

Factorization Algorithms

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Recursive Approach in Sparse Matrix LU Factorization

Scientific Programming ◽

10.1155/2001/569670 ◽

2001 ◽

Vol 9 (1) ◽

pp. 51-60 ◽

Cited By ~ 8

Author(s):

Jack Dongarra ◽

Victor Eijkhout ◽

Piotr Łuszczek

Keyword(s):

Matrix Factorization ◽

Sparse Matrix ◽

Sparse Matrices ◽

Recursive Method ◽

Lu Factorization ◽

Dense Matrix ◽

Matrix Computations ◽

Software Packages ◽

Performance Results ◽

Sparse Matrix Factorization

This paper describes a recursive method for the LU factorization of sparse matrices. The recursive formulation of common linear algebra codes has been proven very successful in dense matrix computations. An extension of the recursive technique for sparse matrices is presented. Performance results given here show that the recursive approach may perform comparable to leading software packages for sparse matrix factorization in terms of execution time, memory usage, and error estimates of the solution.

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Parallel Nonnegative Matrix Factorization via Newton Iteration

Parallel Processing Letters ◽

10.1142/s0129626416500146 ◽

2016 ◽

Vol 26 (03) ◽

pp. 1650014 ◽

Cited By ~ 3

Author(s):

Markus Flatz ◽

Marián Vajteršic

Keyword(s):

Shared Memory ◽

Matrix Factorization ◽

Message Passing ◽

Nonnegative Matrix Factorization ◽

Nonnegative Matrix ◽

Newton Iteration ◽

Parallel Execution ◽

Kkt Conditions ◽

Nonnegative Matrices ◽

First Order

The goal of Nonnegative Matrix Factorization (NMF) is to represent a large nonnegative matrix in an approximate way as a product of two significantly smaller nonnegative matrices. This paper shows in detail how an NMF algorithm based on Newton iteration can be derived using the general Karush-Kuhn-Tucker (KKT) conditions for first-order optimality. This algorithm is suited for parallel execution on systems with shared memory and also with message passing. Both versions were implemented and tested, delivering satisfactory speedup results.

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Communication-Optimal Parallel 2.5D Matrix Multiplication and LU Factorization Algorithms

Euro-Par 2011 Parallel Processing - Lecture Notes in Computer Science ◽

10.1007/978-3-642-23397-5_10 ◽

2011 ◽

pp. 90-109 ◽

Cited By ~ 51

Author(s):

Edgar Solomonik ◽

James Demmel

Keyword(s):

Matrix Multiplication ◽

Lu Factorization ◽

Factorization Algorithms

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Introduction to Matrix Factorization for Recommender Systems

10.31219/osf.io/pnd5w ◽

2021 ◽

Author(s):

Shalin Shah

Keyword(s):

Singular Value Decomposition ◽

Online Education ◽

Recommender Systems ◽

Matrix Factorization ◽

Gradient Descent ◽

Large Scale ◽

Singular Value ◽

Factorization Algorithms ◽

Value Decomposition ◽

Interaction History

Recommender systems aim to personalize the experience of user by suggesting items to the user based on the preferences of a user. The preferences are learned from the user’s interaction history or through explicit ratings that the user has given to the items. The system could be part of a retail website, an online bookstore, a movie rental service or an online education portal and so on. In this paper, I will focus on matrix factorization algorithms as applied to recommender systems and discuss the singular value decomposition, gradient descent-based matrix factorization and parallelizing matrix factorization for large scale applications.

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