Previous |  Up |  Next

Article

Title: Multi-agent solver for non-negative matrix factorization based on optimization (English)
Author: Tu, Zhipeng
Author: Li, Weijian
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 57
Issue: 1
Year: 2021
Pages: 60-77
Summary lang: English
.
Category: math
.
Summary: This paper investigates a distributed solver for non-negative matrix factorization (NMF) over a multi-agent network. After reformulating the problem into the standard distributed optimization form, we design our distributed algorithm (DisNMF) based on the primal-dual method and in the form of multiplicative update rule. With the help of auxiliary functions, we provide monotonic convergence analysis. Furthermore, we show by computational complexity analysis and numerical examples that our distributed NMF algorithm performs well in comparison with the centralized NMF algorithm. (English)
Keyword: distributed optimization
Keyword: non-negative matrix factorization
Keyword: multiplicative update rules
Keyword: multi-agent network
MSC: 15A23
MSC: 68W15
idZBL: Zbl 07396256
idMR: MR4231857
DOI: 10.14736/kyb-2021-1-0060
.
Date available: 2021-07-30T12:49:42Z
Last updated: 2021-11-01
Stable URL: http://hdl.handle.net/10338.dmlcz/149027
.
Reference: [1] Bertsekas, D. P., Tsitsiklis, J. W.: Parallel and Distributed Computation: Numerical Methods..Prentice hall Englewood Cliffs, NJ 1989. MR 0896902,
Reference: [2] Cai, D., He, X., Han, J., Huang, T. S.: Graph regularized nonnegative matrix factorization for data representation..IEEE Trans. Pattern Analysis Machine Intell. 33 (2010), 1548-1560.
Reference: [3] Deng, W., Zeng, X., Hong, Y.: Distributed computation for solving the sylvester equation based on optimization..IEEE Control Systems Lett. 4 (2019), 414-419. MR 4211320,
Reference: [4] Godsil, Ch., Royle, G. F.: Algebraic graph theory..Springer Science Business Media 207 (2013). MR 1829620
Reference: [5] He, X., Kan, M.-Y., Xie, P., Chen, X.: Comment-based multi-view clustering of web 2.0 items..In: Proc. 23rd International Conference on World wide web, 2014, pp. 771-782.
Reference: [6] Horst, R., Tuy, H.: Global Optimization..Springer-Verlag, Berlin 1996. MR 1102239,
Reference: [7] Huang, K., Sidiropoulos, N. D., Swami, A.: Non-negative matrix factorization revisited: Uniqueness and algorithm for symmetric decomposition..IEEE Trans. Signal Process. 62 (2013), 211-224. MR 3187989,
Reference: [8] Jain, P., Kar, P.: Non-convex optimization for machine learning..arXiv preprint arXiv:1712.07897, 2017.
Reference: [9] Kim, H., Park, H.: Nonnegative matrix factorization based on alternating non-negativity constrained least squares and active set method..SIAM J. Matrix Analysis Appl. 30 (2008), 713-730. MR 2421467,
Reference: [10] Lee, D. L., Seung, H. S.: Learning the parts of objects by non-negative matrix factorization..Nature 401 (1999), 788-791.
Reference: [11] Lee, D. S., Seung, H. S.: Algorithms for non-negative matrix factorization..Adv. Neural Inform. Process. Systems xx (2001), 556-562.
Reference: [12] Li, W., Zeng, X., Hong, Y., Ji, H.: Distributed Design for nuclear norm minimization of linear matrix equation with constraints..IEEE Trans. Automat. Control(2020). MR 4210456,
Reference: [13] Lin, Ch.-J.: Projected gradient methods for nonnegative matrix factorization..Neural Comput. 19 (2007), 2756-2779. MR 2348161,
Reference: [14] Liu, Ch., Yang, H.-Ch., Fan, J., He, L.-W., Wang, Y.-M.: Distributed nonnegative matrix factorization for web-scale dyadic data analysis on mapreduce..In: Proc. 19th International Conference on World wide web (2010), pp. 681-690.
Reference: [15] Liu, J., Wang, Ch., Gao, J., Han, J.: Multi-view clustering via joint nonnegative matrix factorization..In: Proc. 2013 SIAM International Conference on Data Mining, SIAM 2013, pp. 252-260.
Reference: [16] Nedic, A., A, Ozdaglar, Parrilo, P. A.: Constrained consensus and optimization in multi-agent networks..IEEE Trans. Automat. Control 55 (2010), 922-938. MR 2654432,
Reference: [17] Peterka, V.: Bayesian system identification..In: Trends and Progress in System Identification (P. Eykhoff, ed.), Pergamon Press, Oxford 1981, pp. 239-304. Zbl 0451.93059, MR 0607193,
Reference: [18] Qiu, Z., Liu, S., Xie, L.: Distributed constrained optimal consensus of multi-agent systems..Automatica 68 (2016), 209-215. MR 3483686,
Reference: [19] Ram, S. S., Nedić, A., Veeravalli, V. V.: Distributed stochastic subgradient projection algorithms for convex optimization..J. Optim. Theory Appl. 147 (2010), 516-545. MR 2733992,
Reference: [20] Shi, G., Anderson, B. D. O., Helmke, U.: Network flows that solve linear equations..IEEE Trans. Automat. Control 62 (2017), 2659-2674. MR 3660554,
Reference: [21] Wen, Z., Yin, W., Zhang, Y.: Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm..Math. Programm. Comput. 4 (2012), 333-361. MR 3006618,
Reference: [22] Xu, F., He, G.: New algorithms for nonnegative matrix completion..Pacific J. Optim. 11 (2015), 459-469. MR 3384550
Reference: [23] Yang, S., Liu, Q., Wang, J.: A multi-agent system with a proportional-integral protocol for distributed constrained optimization..IEEE Trans. Automat. Control 62 (2016), 3461-3467. MR 3669466,
Reference: [24] Yi, P., Hong, Y., Liu, F.: Distributed gradient algorithm for constrained optimization with application to load sharing in power systems..Systems Control Lett. 83 (2015), 45-52. Zbl 1327.93033, MR 3373270,
Reference: [25] Yin, J., Gao, L., Zhang, Z. M.: Scalable nonnegative matrix factorization with block-wise updates..In: Joint European Conference on Machine Learning and Knowledge Discovery in Databases, Springer-Heidelberg, Berlin 2014, pp. 337-352.
Reference: [26] Yuan, D., Ho, D. W. C., Xu, S.: Regularized primal-dual subgradient method for distributed constrained optimization..IEEE Trans. Cybernet. 46 (2015), 2109-2118.
Reference: [27] Zeng, X., Cao, K.: Computation of linear algebraic equations with solvability verification over multi-agent networks..Kybernetika 53 (2017), 803-819. MR 3750104,
Reference: [28] Zeng, X., Yi, P., Hong, Y.: Distributed continuous-time algorithm for constrained convex optimizations via nonsmooth analysis approach..IEEE Trans. Automat. Control 62 (2016), 5227-5233. MR 3708893,
Reference: [29] Zeng, X., Liang, S., Hong, Y., Chen, J.: Distributed computation of linear matrix equations: An optimization perspective..IEEE Trans. Automat. Control 64 (2019), 1858-1873. MR 3951032,
.

Files

Files Size Format View
Kybernetika_57-2021-1_5.pdf 1.781Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo