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

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Izvleček
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.

Jezik:Angleški jezik
Ključne besede:non-negative matrix factorization, fixed point method, block coordinate descent, projected gradient method, adaptive moment estimation method
Vrsta gradiva:Članek v reviji
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:FS - Fakulteta za strojništvo
Status publikacije:Objavljeno
Različica publikacije:Objavljena publikacija
Leto izida:2022
Št. strani:30 str.
Številčenje:Vol. 82
PID:20.500.12556/RUL-141007 Povezava se odpre v novem oknu
UDK:512.622.462
ISSN pri članku:0925-5001
DOI:10.1007/s10898-021-01074-3 Povezava se odpre v novem oknu
COBISS.SI-ID:75116803 Povezava se odpre v novem oknu
Datum objave v RUL:22.09.2022
Število ogledov:551
Število prenosov:77
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Gradivo je del revije

Naslov:Journal of global optimization
Skrajšan naslov:J. glob. optim.
Založnik:Springer Nature
ISSN:0925-5001
COBISS.SI-ID:2822695 Povezava se odpre v novem oknu

Sekundarni jezik

Jezik:Slovenski jezik
Ključne besede:negativna matrična faktorizacija, metoda negibne točke, bločno koordinatni spust, metoda projiciranega gradienta, ADAM

Projekti

Financer:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
Številka projekta:P2-0098
Naslov:Računalniške strukture in sistemi

Financer:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
Številka projekta:J1-8155
Naslov:Zlivanje biomedicinskih podatkov z uporabo nenegativne matrične trifaktorizacije

Financer:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
Številka projekta:PR-07606

Financer:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
Številka projekta:N1-0071
Naslov:Razširitev algoritmov prvega in drugega reda za izbrane razrede optimizacijskih problemov s ciljem rešiti računsko zahtevne industrijske probleme

Financer:EC - European Commission
Program financ.:H2020
Številka projekta:770827
Naslov:Integrated Connectedness for a New Representation of Biology
Akronim:ICON-BIO

Financer:Drugi - Drug financer ali več financerjev
Program financ.:Spain, State Research Agency (AEI)
Številka projekta:10.13039/501100011033

Financer:Drugi - Drug financer ali več financerjev
Program financ.:Spain, State Research Agency (AEI)
Številka projekta:PID2019-105500GB-I00

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