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Erschienen in:
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2017 | OriginalPaper | Buchkapitel

Fast Nonnegative Matrix Factorization and Completion Using Nesterov Iterations

verfasst von : Clément Dorffer, Matthieu Puigt, Gilles Delmaire, Gilles Roussel

Erschienen in: Latent Variable Analysis and Signal Separation

Verlag: Springer International Publishing

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Abstract

In this paper, we aim to extend Nonnegative Matrix Factorization with Nesterov iterations (Ne-NMF)—well-suited to large-scale problems—to the situation when some entries are missing in the observed matrix. In particular, we investigate the Weighted and Expectation-Maximization strategies which both provide a way to process missing data. We derive their associated extensions named W-NeNMF and EM-W-NeNMF, respectively. The proposed approaches are then tested on simulated nonnegative low-rank matrix completion problems where the EM-W-NeNMF is shown to outperform state-of-the-art methods and the W-NeNMF technique.

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Vorheriges Kapitel Modeling Parallel Wiener-Hammerstein Systems Using Tensor Decomposition of Volterra Kernels
Nächstes Kapitel Blind Source Separation of Single Channel Mixture Using Tensorization and Tensor Diagonalization
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Fußnoten
1
See for example the CPU-time consumptions of [27] at https://​github.​com/​andrewssobral/​lrslibrary.
 
2
As explained above, the standard approach was shown to be slow to converge in [32], because many MUs were applied at each M-step. To prevent such an issue, at each M-stage, we here run one NMF update per matrix factor, i.e., one MU.
 
3
In some preliminary tests, we noticed that the EM-W-ANLS method [16] provided a performance similar to EM-WNMF [32]. We thus do not include it in these tests.
 
Literatur
1.
Candès, E.J., Plan, Y.: Matrix completion with noise. Proc. IEEE 98(6), 925–936 (2010)CrossRef
2.
3.
Choo, J., Lee, C., Reddy, C.K., Park, H.: Weakly supervised nonnegative matrix factorization for user-driven clustering. Data Min. Knowl. Disc. 29(6), 1598–1621 (2015)MathSciNetCrossRef
4.
Chreiky, R., Delmaire, G., Puigt, M., Roussel, G., Courcot, D., Abche, A.: Split gradient method for informed non-negative matrix factorization. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds.) Proceedings of LVA/ICA, pp. 376–383 (2015)
5.
Dorffer, C., Puigt, M., Delmaire, G., Roussel, G.: Blind calibration of mobile sensors using informed nonnegative matrix factorization. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds.) Proceedings of LVA/ICA, pp. 497–505 (2015)
6.
Dorffer, C., Puigt, M., Delmaire, G., Roussel, G.: Blind mobile sensor calibration using an informed nonnegative matrix factorization with a relaxed rendezvous model. In: Proceedings of ICASSP, pp. 2941–2945 (2016)
7.
Dorffer, C., Puigt, M., Delmaire, G., Roussel, G.: Nonlinear mobile sensor calibration using informed semi-nonnegative matrix factorization with a Vandermonde factor. In: Proceedings of SAM (2016)
8.
Fazel, M.: Matrix rank minimization with applications. Ph.D. thesis, Stanford University (2002)
9.
Guan, N., Tao, D., Luo, Z., Yuan, B.: NeNMF: an optimal gradient method for nonnegative matrix factorization. IEEE Trans. Signal Proc. 60(6), 2882–2898 (2012)MathSciNetCrossRef
10.
Guillamet, D., Vitrià, J., Schiele, B.: Introducing a weighted non-negative matrix factorization for image classification. Pattern Recogn. Lett. 24(14), 2447–2454 (2003)CrossRefMATH
11.
Haldar, J.P., Hernando, D.: Rank-constrained solutions to linear matrix equations using powerfactorization. IEEE Signal Process. Lett. 16(7), 584–587 (2009)CrossRef
12.
Hamon, R., Emiya, V., Févotte, C.: Convex nonnegative matrix factorization with missing data. In: Procceedings of MLSP (2016)
13.
Ho, N.D.: Nonnegative matrix factorizations algorithms and applications. Ph.D. thesis, Université Catholique de Louvain (2008)
14.
Hoyer, P.O.: Non-negative matrix factorization with sparseness constraints. J. Mach. Learn. Res. 5, 1457–1469 (2004)MathSciNetMATH
15.
Kim, H., Park, H.: Nonnegative matrix factorization based on alternating nonnegativity constrained least squares and active set method. SIAM J. Matrix Anal. Appl. 30(2), 713–730 (2008)MathSciNetCrossRefMATH
16.
Kim, Y.D., Choi, S.: Weighted nonnegative matrix factorization. In: Proceedings of ICASSP, pp. 1541–1544, April 2009
17.
Kumar, R., Da Silva, C., Akalin, O., Aravkin, A.Y., Mansour, H., Recht, B., Herrmann, F.J.: Efficient matrix completion for seismic data reconstruction. Geophysics 80(5), V97–V114 (2015)CrossRef
18.
Lantéri, H., Theys, C., Richard, C., Févotte, C.: Split gradient method for nonnegative matrix factorization. In: Proceedings of EUSIPCO (2010)
19.
Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: NIPS, pp. 556–562 (2001)
20.
Limem, A., Delmaire, G., Puigt, M., Roussel, G., Courcot, D.: Non-negative matrix factorization under equality constraints–a study of industrial source identification. Appl. Numer. Math. 85, 1–15 (2014)MathSciNetCrossRefMATH
21.
Limem, A., Puigt, M., Delmaire, G., Roussel, G., Courcot, D.: Bound constrained weighted NMF for industrial source apportionment. In: Proceedings of MLSP (2014)
22.
23.
Liu, C., Yang, H.C., Fan, J., He, L.W., Wang, Y.M.: Distributed nonnegative matrix factorization for web-scale dyadic data analysis on MapReduce. In: Proceedings of WWW Conference, April 2010
24.
Mairal, J., Bach, F., Ponce, J., Sapiro, G.: Online learning for matrix factorization and sparse coding. J. Mach. Learn. Res. 11, 19–60 (2010)MathSciNetMATH
25.
Nesterov, Y.: A method of solving a convex programming problem with convergence rate O(1/k2). Sov. Math. Doklady 27, 372–376 (1983)MATH
26.
Savvaki, S., Tsagkatakis, G., Panousopoulou, A., Tsakalides, P.: Application of matrix completion on water treatment data. In: Proceedings of CySWater, pp. 3:1–3:6 (2015)
27.
Sobral, A., Bouwmans, T., Zahzah, E.: LRSLibrary: low-rank and sparse tools for background modeling and subtraction in videos. In: Robust Low-Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing. CRC Press, Taylor and Francis Group
28.
Srebro, N., Jaakkola, T.: Weighted low-rank approximations. In: Proceedings of ICML (2003)
29.
Tepper, M., Sapiro, G.: Compressed nonnegative matrix factorization is fast and accurate. IEEE Trans. Signal Process. 64(9), 2269–2283 (2016)MathSciNetCrossRef
30.
Wang, Y.X., Zhang, Y.J.: Nonnegative matrix factorization: a comprehensive review. IEEE Trans. Knowl. Data Eng. 25(6), 1336–1353 (2013)CrossRef
31.
Wen, Z., Yin, W., Zhang, Y.: Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm. Math. Program. Comput. 4(4), 333–361 (2012)MathSciNetCrossRefMATH
32.
Zhang, S., Wang, W., Ford, J., Makedon, F.: Learning from incomplete ratings using non-negative matrix factorization, chap. 58, pp. 549–553 (2006)
33.
Zhou, G., Cichocki, A., Xie, S.: Fast nonnegative matrix/tensor factorization based on low-rank approximation. IEEE Trans. Signal Process. 60(6), 2928–2940 (2012)MathSciNetCrossRef
Metadaten
Titel
Fast Nonnegative Matrix Factorization and Completion Using Nesterov Iterations
verfasst von
Clément Dorffer
Matthieu Puigt
Gilles Delmaire
Gilles Roussel
Copyright-Jahr
2017
Buch
Latent Variable Analysis and Signal Separation

Print ISBN: 978-3-319-53546-3

Electronic ISBN: 978-3-319-53547-0

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-53547-0_3