Abstract
Independent component analysis (ICA) is a widely applicable and effective approach in blind source separation (BSS) for basic ICA model, but with limitations that sources should be statistically independent, while more common situation is BSS for non-negative linear (NNL) model where observations are linear combinations of non-negative sources with non-negative coefficients and sources may be statistically dependent. By recognizing the fact that BSS for basic ICA model corresponds to matrix factorization problem, in this paper, a novel idea of BSS for NNL model is proposed that the BSS for NNL corresponds to a non-negative matrix factorization problem and the non-negative matrix factorization (NMF) technique is utilized. For better expression of the patterns of the sources, the NMF is further extended to pattern expression NMF (PE-NMF) and its algorithm is presented. Finally, the experimental results are presented which show the effectiveness and efficiency of the PE-NMF to BSS for a variety of applications which follow NNL model.
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References
Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. John Wiley, New York (2001)
Hoyer, P.O., Hyvärinen, A.: Independent Component Analysis Applied to Feature Extrac-tion from Colour and Stereo Images. Network: Computation in Neural Systems 11(3), 191–210 (2000)
Haykin, S.: Neural networks: A Comprehensive Foundation, 2nd edn. Prentice-Hall. Inc., Englewood Cliffs (1999)
Zhang, J.Y., Wei, L., Wang, Y.: Computational Decomposition of Molecular Signatures based on Blind Source Separation of Non-negative Dependent Sources with NMF. In: 2003 IEEE International Workshop on Neural Networks for Signal Processing, Toulouse, France, September 17-19 (2003)
Guillamet, D., Vitria, J.: Classifying Faces with Non-negative Matrix Factorization. In: Escrig, M.T., Toledo, F.J., Golobardes, E. (eds.) CCIA 2002. LNCS (LNAI), vol. 2504, pp. 24–31. Springer, Heidelberg (2002)
Guillamet, D., Vitria, J.: Application of Non-negative Matrix Factorization to Dynamic Positron Emission Tomography. In: Proceedings of the International Conference on Inde-pendent Component Analysis and Signal Separation (ICA 2001), San Diego, California, December 9-13, pp. 629–632 (2001)
Guillamet, D., Vitria, J.: Unsupervised Learning of Part-based Representations. In: Proceedings of the 9th International Conference on Computer Analysis of Images and Patterns, September 5-7, pp. 700–708 (2001)
Hesse, C.W., James, C.J.: The FastICA Algorithm with Spatial Con-straints. IEEE Signal Processing Letters 12(11), 792–795 (2005)
Lee, D., Seung, H.S.: Learning the Parts of Objects by Non-negative Matrix Factorization. Nature 401, 788–791 (1999)
Lee, D., Seung, H.S.: Algorithms for Non-negative Matrix Factorization. Advances in Neural Information Processing Systems 13, 556–562 (2001)
Novak, M., Mammone, R.: Use of Non-negative Matrix Factorization for Language Model Adaptation in A Lecture Transcription Task. In: Proceedings of the 2001 IEEE Conference on Acoustics, Speech and Signal Processing, Salt Lake City, UT, May 2001, vol. 1, pp. 541–544 (2001)
Guillamet, D., Bressan, M., Vitria, J.: Weighted Non-negative Matrix Factorization for Local Representations. In: Proc. of Computer Vision and Pattern Recognition (2001)
Foldiak, P.: Forming Sparse Representations by Local Anti-Hebbian Learning. Biological Cybernetics 64(2), 165–170 (1990)
Khan, J., et al.: Classification and Diagnostic Prediction of Cancers Using Gene Expression Profiling and Artificial Neural Networks. Nature Medicine 7(6), 673–679 (2001)
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© 2006 Springer-Verlag Berlin Heidelberg
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Zhang, J., Hongyi, Z., Wei, L., Wang, Y.J. (2006). Blind Source Separation with Pattern Expression NMF. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_171
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DOI: https://doi.org/10.1007/11759966_171
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