Factorization of Nonnegative Matrices by the Use of Elementary Operation

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

A method based on elementary column and row operations of the factorization of nonnegative matrices is proposed. It is shown that the nonnegative matrix R×( ? ) has positive full column rank if and only if it can be transformed to a matrix with cyclicstructure. A procedure for computation of nonnegative matrices ? R ×, ? R × ( ? rank (,)) satisfying = is proposed.

Słowa kluczowe

EN

factorization; nonnegative matrix; positive rank; procedure; computation

PL

faktoryzacja; nieujemna macierz; procedura; obliczanie

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2012
• Tom: Vol. 6, no. 4
• Strony: 15--18
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Białystok University of Technology, ul. Wiejska 45D, 15-351 Białystok, Poland,

Bibliografia

• 1. Cichocki A., Zdunek R., (2006), Multilayer Nonnegative Matrix Factorization, Electronics Letters, Vol. 42, No. 16, 947-948.
• 2. Cohen J.E., Rothblum U.G. (1993), Nonnegative ranks, decompositions, and factorizations of nonnegative matrices, Linear Algebra Appl., 190, 149–168.
• 3. de Almeida A. (2011), About Nonnegative Matrix Factorization: on the posrank approximation, Proceedings of International Conference on Adaptive and Natural Computing Algorithms, ICANNGA'11, Ljubljana, Slovenia.
• 4. Donoho D., Stodden V. (2004), When does nonnegative matrix factorization give a correct decomposition into parts?, S. Thrun et al. (eds.) Proceedings of Advances in Neural Information Processing, NIPS 2003, Vol. 16, MIT Press Cambridge.
• 5. Kaczorek T. (1993), Linear Control Systems, Vol. 1, J. Wiley, New York.
• 6. Kaczorek T. (2001), Positive 1D and 2D systems, Springer Verlag, London.
• 7. Lee D.D., Seung H.S. (2001), Algorithms for nonnegative matrix factorization, Advances in Neural Information Processing, Vol. 13, MIT Press Cambridge.
• 8. Lin C. (2007), Projected gradient methods for nonnegative matrix factorization, Neural Computing, Vol. 19, 2756-2779.
• 9. Merzyakov J.I. (1963), On the existence of positive solutions of a system of linear equations, Uspekhi Matematicheskikh Nauk, Vol. 18, No. 3, 179–186 (in Russian).