Abstract
This paper discusses the matrix estimation for sparse component analysis under the k-SCA condition. Here, to estimate the mixing matrix using hyperplane clustering, we propose a new algorithm based on normal vector for hyperplane. Compared with the Hough SCA algorithm, we give a method to calculate normal vector for hyperplane, and the algorithm has lower complexity and higher precision. Two examples demonstrates its performance.
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References
Cardoso, J.F.: Blind signals separation: Statistical principles. Proc. IEEE 86, 1129–1159 (1998)
Zhang, J., Xie, S., Wang, J.: Multi-input single-output neural network blind separation algorithm based on penalty function. DCDIS-Series B-Applications & Algorithms Suppl. SI, 353–361 (2003)
Xie, S., He, Z., Gao, Y.: Adaptive Theory of Signal Processing. Chinese Science Press, Beijing (2006)
Xie, S., He, Z., Fu, Y.: A note on Stone’s conjecture of blind signal separation. Neural Computation 17, 321–330 (2005)
Cichocki, A., Amari, S.: Adaptive blind signal and image processing: learning algorithms and applications. Wiley, New York (2002)
Bofill, P., Zibulevsky, M.: Underdetermined blind source separation using sparse representations. Signal Processing 81, 2353–2362 (2001)
Li, Y., Amari, S., Cichocki, A., et al.: Underdetermined Blind Source Separation Based on Sparse Representation. IEEE Transactions on Signal Processing 54(2), 423–437 (2006)
He, Z., Xie, S., Fu, Y.: FIR convolutive BSS based on sparse representation. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3497, pp. 532–537. Springer, Heidelberg (2005)
He, Z., Cichocki, A.: K-EVD Clustering and its Applications to Sparse Component Analysis. In: Rosca, J.P., Erdogmus, D., PrÃncipe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, vol. 3889, pp. 90–97. Springer, Heidelberg (2006)
Georgiev, P.G., Theis, F.J., Cichocki, A.: Sparse component analysis and blind source separation of underdetermined mixtures. IEEE Transactions of NeuralNetworks 16(4), 992–996 (2005)
Theis, F.J., Georgiev, P.G., Cichocki, A.: Robust overcomplete matrix recovery for sparse sources using a generalized hough transform. In: Proceedings of 12th European Symposium on Artificial Neural Networks (ESANN 2004), Bruges, Belgium, April 2004, pp. 343–348 (2004)
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Gao, F., Sun, G., Xiao, M., Lv, J. (2010). Matrix Estimation Based on Normal Vector of Hyperplane in Sparse Component Analysis. In: Tan, Y., Shi, Y., Tan, K.C. (eds) Advances in Swarm Intelligence. ICSI 2010. Lecture Notes in Computer Science, vol 6146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13498-2_23
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DOI: https://doi.org/10.1007/978-3-642-13498-2_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13497-5
Online ISBN: 978-3-642-13498-2
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