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Four algorithms to solve symmetric multi-type non-negative matrix tri-factorization problem
ID Hribar, Rok (Author), ID Hrga, Timotej (Author), ID Papa, Gregor (Author), ID Petelin, Gašper (Author), ID Povh, Janez (Author), ID Pržulj, Nataša (Author), ID Vukašinović, Vida (Author)

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Abstract
In this paper, we consider the symmetric multi-type non-negative matrix tri-factorization problem (SNMTF), which attempts to factorize several symmetric non-negative matrices simultaneously. This can be considered as a generalization of the classical non-negative matrix tri-factorization problem and includes a non-convex objective function which is a multivariate sixth degree polynomial and a has convex feasibility set. It has a special importance in data science, since it serves as a mathematical model for the fusion of different data sources in data clustering. We develop four methods to solve the SNMTF. They are based on four theoretical approaches known from the literature: the fixed point method (FPM), the block-coordinate descent with projected gradient (BCD), the gradient method with exact line search (GMELS) and the adaptive moment estimation method (ADAM). For each of these methods we offer a software implementation: for the former two methods we use Matlab and for the latter Python with the TensorFlow library. We test these methods on three data-sets: the synthetic data-set we generated, while the others represent real-life similarities between different objects. Extensive numerical results show that with sufficient computing time all four methods perform satisfactorily and ADAM most often yields the best mean square error (MSE). However, if the computation time is limited, FPM gives the best MSE because it shows the fastest convergence at the beginning. All data-sets and codes are publicly available on our GitLab profile.

Language:English
Keywords:non-negative matrix factorization, fixed point method, block coordinate descent, projected gradient method, adaptive moment estimation method
Work type:Article
Typology:1.01 - Original Scientific Article
Organization:FS - Faculty of Mechanical Engineering
Publication status:Published
Publication version:Version of Record
Year:2022
Number of pages:30 str.
Numbering:Vol. 82
PID:20.500.12556/RUL-141007 This link opens in a new window
UDC:512.622.462
ISSN on article:0925-5001
DOI:10.1007/s10898-021-01074-3 This link opens in a new window
COBISS.SI-ID:75116803 This link opens in a new window
Publication date in RUL:22.09.2022
Views:857
Downloads:91
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Record is a part of a journal

Title:Journal of global optimization
Shortened title:J. glob. optim.
Publisher:Springer Nature
ISSN:0925-5001
COBISS.SI-ID:2822695 This link opens in a new window

Secondary language

Language:Slovenian
Keywords:negativna matrična faktorizacija, metoda negibne točke, bločno koordinatni spust, metoda projiciranega gradienta, ADAM

Projects

Funder:ARRS - Slovenian Research Agency
Project number:P2-0098
Name:Računalniške strukture in sistemi

Funder:ARRS - Slovenian Research Agency
Project number:J1-8155
Name:Zlivanje biomedicinskih podatkov z uporabo nenegativne matrične trifaktorizacije

Funder:ARRS - Slovenian Research Agency
Project number:PR-07606

Funder:ARRS - Slovenian Research Agency
Project number:N1-0071
Name:Razširitev algoritmov prvega in drugega reda za izbrane razrede optimizacijskih problemov s ciljem rešiti računsko zahtevne industrijske probleme

Funder:EC - European Commission
Funding programme:H2020
Project number:770827
Name:Integrated Connectedness for a New Representation of Biology
Acronym:ICON-BIO

Funder:Other - Other funder or multiple funders
Funding programme:Spain, State Research Agency (AEI)
Project number:10.13039/501100011033

Funder:Other - Other funder or multiple funders
Funding programme:Spain, State Research Agency (AEI)
Project number:PID2019-105500GB-I00

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