Abstract
In the paper, we present a new approach to multi-way Blind Source Separation (BSS) and corresponding 3D tensor factorization that has many potential applications in neuroscience and multi-sensory or multidimensional data analysis, and neural sparse coding. We propose to use a set of local cost functions with flexible penalty and regularization terms whose simultaneous or sequential (one by one) minimization via a projected gradient technique leads to simple Hebbian-like local algorithms that work well not only for an over-determined case but also (under some weak conditions) for an under-determined case (i.e., a system which has less sensors than sources). The experimental results confirm the validity and high performance of the developed algorithms, especially with usage of the multi-layer hierarchical approach.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Smilde, A., Bro, R., Geladi, P.: Multi-way Analysis: Applications in the Chemical Sciences. John Wiley and Sons, New York (2004)
Hazan, T., Polak, S., Shashua, A.: Sparse image coding using a 3D non-negative tensor factorization. In: International Conference of Computer Vision (ICCV), pp. 50–57 (2005)
Heiler, M., Schnoerr, C.: Controlling sparseness in non-negative tensor factorization. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3951, pp. 56–67. Springer, Heidelberg (2006)
Miwakeichi, F., Martnez-Montes, E., Valds-Sosa, P., Nishiyama, N., Mizuhara, H., Yamaguchi, Y.: Decomposing EEG data into space−time−frequency components using parallel factor analysi. NeuroImage 22, 1035–1045 (2004)
Mørup, M., Hansen, L.K., Herrmann, C.S., Parnas, J., Arnfred, S.M.: Parallel factor analysis as an exploratory tool for wavelet transformed event-related EEG. NeuroImage 29, 938–947 (2006)
Lee, D.D., Seung, H.S.: Learning the parts of objects by nonnegative matrix factorization. Nature 401, 788–791 (1999)
Cichocki, A., Amari, S.: Adaptive Blind Signal and Image Processing (New revised and improved edition). John Wiley, New York (2003)
Dhillon, I., Sra, S.: Generalized nonnegative matrix approximations with Bregman divergences. In: Neural Information Proc. Systems, Vancouver, Canada, pp. 283–290 (2005)
Berry, M., Browne, M., Langville, A., Pauca, P., Plemmons, R.: Algorithms and applications for approximate nonnegative matrix factorization. Computational Statistics and Data Analysis (in press, 2006)
Bobin, J., Starck, J.L., Fadili, J., Moudden, Y., Donoho, D.L.: Morphological component analysis: An adaptive thresholding strategy. IEEE Transactions on Image Processing (in print, 2007)
Elad, M.: Why simple shrinkage is still relevant for redundant representations? IEEE Trans. On Information Theory 52, 5559–5569 (2006)
Kovac, A.: Smooth functions and local extreme values. Computational Statistics and Data Analysis 51, 5155–5171 (2007)
Tao, T., Vidakovic, B.: Almost everywhere behavior of general wavelet shrinkage operators. Applied and Computational Harmonic Analysis 9, 72–82 (2000)
Daubechies, I., Defrrise, M., Mol, C.D.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Pure and Applied Mathematics 57, 1413–1457 (2004)
Cichocki, A., Zdunek, R.: Multilayer nonnegative matrix factorization. Electronics Letters 42, 947–948 (2006)
Cichocki, A., Zdunek, R.: NTFLAB for Signal Processing. Technical report, Laboratory for Advanced Brain Signal Processing, BSI, RIKEN, Saitama, Japan (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cichocki, A., Phan, A.H., Zdunek, R., Zhang, LQ. (2008). Flexible Component Analysis for Sparse, Smooth, Nonnegative Coding or Representation. In: Ishikawa, M., Doya, K., Miyamoto, H., Yamakawa, T. (eds) Neural Information Processing. ICONIP 2007. Lecture Notes in Computer Science, vol 4984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69158-7_84
Download citation
DOI: https://doi.org/10.1007/978-3-540-69158-7_84
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69154-9
Online ISBN: 978-3-540-69158-7
eBook Packages: Computer ScienceComputer Science (R0)