Abstract
In this paper a generalization of Post Nonlinear Independent Component Analysis (PNL-ICA) to Post Nonlinear Independent Subspace Analysis (PNL-ISA) is presented. In this framework sources to be identified can be multidimensional as well. For this generalization we prove a separability theorem: the ambiguities of this problem are essentially the same as for the linear Independent Subspace Analysis (ISA). By applying this result we derive an algorithm using the mirror structure of the mixing system. Numerical simulations are presented to illustrate the efficiency of the algorithm.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cichocki, A., Amari, S.: Adaptive blind signal and image processing. John Wiley & Sons, West Sussex, England (2002)
Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. John Wiley & Sons, West Sussex, England (2001)
Taleb, A., Jutten, C.: Source separation in post-nonlinear mixtures. IEEE Transactions on Signal Processing 10(47), 2807–2820 (1999)
Jutten, C., Karhunen, J.: Advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear systems. International Journal of Neural Systems 14(5), 267–292 (2004)
Cardoso, J.: Multidimensional independent component analysis. In: Proc. of ICASSP 1998, vol. 4, pp. 1941–1944 (1998)
Akaho, S., Kiuchi, Y., Umeyama, S.: MICA: Multimodal independent component analysis. In: Proc. of IJCNN 1999, vol. 2, pp. 927–932 (1999)
Hyvärinen, A., Hoyer, P.O.: Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces. Neural Computation 12, 1705–1720 (2000)
Hyvärinen, A., Köster, U.: FastISA: A fast fixed-point algorithm for independent subspace analysis. In: Proc. of ESANN, pp. 371–376 (2006)
Vollgraf, R., Obermayer, K.: Multi-dimensional ICA to separate correlated sources. In: Proc. of NIPS 2001, vol. 14, pp. 993–1000 (2001)
Bach, F.R., Jordan, M.I.: Beyond independent components: Trees and clusters. Journal of Machine Learning Research 4, 1205–1233 (2003)
Póczos, B., Lőrincz, A.: Independent subspace analysis using k-nearest neighborhood distances. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds.) ICANN 2005. LNCS, vol. 3697, pp. 163–168. Springer, Heidelberg (2005)
Póczos, B., Lőrincz, A.: Independent subspace analysis using geodesic spanning trees. In: Proc. of ICML 2005, vol. 119, pp. 673–680 (2005)
Theis, F.J.: Blind signal separation into groups of dependent signals using joint block diagonalization. In: Proc. of ISCAS 2005, vol. 6, pp. 5878–5881 (2005)
Szabó, Z., Lőrincz, A.: Real and complex independent subspace analysis by generalized variance. In: Proc. of ICARN, pp. 85–88 (2006)
Nolte, G., Meinecke, F.C., Ziehe, A., Müller, K.-R.: Identifying interactions in mixed and noisy complex systems. Physical Review E 73(051913) (2006)
Theis, F.J.: Towards a general independent subspace analysis. In: Proc. of NIPS, vol. 19 (2006)
Comon, P.: Independent component analysis, a new concept? Signal Processing 36, 287–314 (1994)
Achard, S., Jutten, C.: Identifiability of post nonlinear mixtures. IEEE Signal Processing Letters 12(5), 423–426 (2005)
Theis, F.J.: Uniqueness of complex and multidimensional independent component analysis. Signal Processing 84(5), 951–956 (2004)
Theis, F.J.: A new concept for separability problems in source separation. Neural Computation 16, 1827–1850 (2004)
Theis, F.J.: Multidimensional independent component analysis using characteristic functions. In: Proc. of EUSIPCO (2005)
Petrov, V.: Central limit theorem for m-dependent variables. In: Proc. of the All-Union Conf. on Probability Theory and Mathematical Statistics, pp. 38–44 (1958)
Ziehe, A., Kawanabe, M., Harmeling, S., Müller, K.-R.: Blind separation of post-nonlinear mixtures using linearizing transformations and temporal decorrelation. Journal of Machine Learning Research 4(7-8), 1319–1338 (2004)
Solé-Casals, J., Jutten, C., Pham, D.: Fast approximation of nonlinearities for improving inversion algorithms of PNL mixtures and wiener systems. Signal Processing 85, 1780–1786 (2005)
Amari, S., Cichocki, A., Yang, H.H.: A new learning algorithm for blind signal separation. Advances in Neural Information Processing Systems 8, 757–763 (1996)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Szabó, Z., Póczos, B., Szirtes, G., Lőrincz, A. (2007). Post Nonlinear Independent Subspace Analysis. In: de Sá, J.M., Alexandre, L.A., Duch, W., Mandic, D. (eds) Artificial Neural Networks – ICANN 2007. ICANN 2007. Lecture Notes in Computer Science, vol 4668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74690-4_69
Download citation
DOI: https://doi.org/10.1007/978-3-540-74690-4_69
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74689-8
Online ISBN: 978-3-540-74690-4
eBook Packages: Computer ScienceComputer Science (R0)