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On Connection between the Convolutive and Ordinary Nonnegative Matrix Factorizations

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Latent Variable Analysis and Signal Separation (LVA/ICA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7191))

Abstract

A connection between the convolutive nonnegative matrix factorization (NMF) and the conventional NMF has been established. As a result, we can convey arbitrary alternating update rules for NMF to update rules for CNMF. In order to illustrate the novel derivation method, a multiplicative algorithm and a new ALS algorithm for CNMF are derived. The experiments confirm validity and high performance of our method and of the proposed algorithm.

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References

  1. Schmidt, M.N., Mørup, M.: Nonnegative Matrix Factor 2-D Deconvolution for Blind Single Channel Source Separation. In: Rosca, J.P., Erdogmus, D., Principe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, vol. 3889, pp. 700–707. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  2. Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. Wiley, Chichester (2009)

    Book  Google Scholar 

  3. O’Grady, P.D., Pearlmutter, B.A.: Discovering speech phones using convolutive non-negative matrix factorization with a sparseness constraint. Neurocomput. 72, 88–101 (2008)

    Article  Google Scholar 

  4. Smaragdis, P.: Convolutive speech bases and their application to supervised speech separation. IEEE Transactions on Audio, Speech and Language Processing 15(1), 1–12 (2007)

    Article  Google Scholar 

  5. Ozerov, A., Févotte, C.: Multichannel nonnegative matrix factorization in convolutive mixtures with application to blind audio source separation. In: ICASSP 2009, USA, pp. 3137–3140 (2009)

    Google Scholar 

  6. Wang, W., Cichocki, A., Chambers, J.A.: A multiplicative algorithm for convolutive non-negative matrix factorization based on squared Euclidean distance. IEEE Transactions on Signal Processing 57(7), 2858–2864 (2009)

    Article  MathSciNet  Google Scholar 

  7. Lee, D.D., Seung, H.S.: Algorithms for Nonnegative Matrix Factorization, vol. 13. MIT Press (2001)

    Google Scholar 

  8. Berry, M., Browne, M., Langville, A., Pauca, P., Plemmons, R.: Algorithms and applications for approximate nonnegative matrix factorization. Computational Statistics and Data Analysis 52(1), 155–173 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Smaragdis, P.: Non-Negative Matrix Factor Deconvolution; Extraction of Multiple Sound Sources from Monophonic Inputs. In: Puntonet, C.G., Prieto, A.G. (eds.) ICA 2004. LNCS, vol. 3195, pp. 494–499. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  10. Ellis, D.: Spectrograms: Constant-q (log-frequency) and conventional (linear) (May 2004), http://labrosa.ee.columbia.edu/matlab/sgram/

  11. FitzGerald, D., Cranitch, M., Coyle, E.: Extended Nonnegative Tensor Factorisation Models for Musical Sound Source Separation. In: Computational Intelligence and Neuroscience, vol. 2008, Article ID 872425, 15 pages (2008), doi:10.1155/2008/872425

    Google Scholar 

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Fabian Theis Andrzej Cichocki Arie Yeredor Michael Zibulevsky

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© 2012 Springer-Verlag Berlin Heidelberg

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Phan, A.H., Cichocki, A., Tichavský, P., Koldovský, Z. (2012). On Connection between the Convolutive and Ordinary Nonnegative Matrix Factorizations. In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2012. Lecture Notes in Computer Science, vol 7191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28551-6_36

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  • DOI: https://doi.org/10.1007/978-3-642-28551-6_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28550-9

  • Online ISBN: 978-3-642-28551-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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