Abstract
We treat the problem of searching for hidden multi-dimensional independent auto-regressive processes. First, we transform the problem to Independent Subspace Analysis (ISA). Our main contribution concerns ISA. We show that under certain conditions, ISA is equivalent to a combinatorial optimization problem. For the solution of this optimization we apply the cross-entropy method. Numerical simulations indicate that the cross-entropy method can provide considerable improvements over other state-of-the-art methods.
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
Choi, S., Cichocki, A., Park, H.M., Lee, S.Y.: Blind Source Separation and Independent Component Analysis. Neural Inf. Proc. Lett. and Reviews (2005)
Cardoso, J.: Multidimensional Independent Component Analysis. In: ICASSP 1998, Seattle, WA (1998)
Akaho, S., Kiuchi, Y., Umeyama, S.: MICA: Multimodal Independent Component Analysis. In: IJCNN, pp. 927–932 (1999)
Póczos, B., Takács, B., Lőrincz, A.: Independent Subspace Analysis on Innovations. In: Gama, J., Camacho, R., Brazdil, P.B., Jorge, A.M., Torgo, L. (eds.) ECML 2005. LNCS (LNAI), vol. 3720, pp. 698–706. Springer, Heidelberg (2005)
Hyvärinen, A.: Independent Component Analysis for Time-dependent Stochastic Processes. In: ICANN 1998, pp. 541–546 (1998)
Vollgraf, R., Obermayer, K.: Multi-Dimensional ICA to Separate Correlated Sources. In: NIPS, vol. 14, pp. 993–1000 (2001)
Bach, F.R., Jordan, M.I.: Finding Clusters in Independent Component Analysis. In: ICA 2003, pp. 891–896 (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: ICML, pp. 673–680 (2005)
Theis, F.J.: Blind Signal Separation into Groups of Dependent Signals Using Joint Block Diagonalization. In: Proc. ISCAS 2005, Kobe, Japan, pp. 5878–5881 (2005)
Van Hulle, M.M.: Edgeworth Approximation of Multivariate Differential Entropy. Neural Comput. 17, 1903–1910 (2005)
Cheung, Y., Xu, L.: Dual Multivariate Auto-Regressive Modeling in State Space for Temporal Signal Separation. IEEE Tr. on Syst. Man Cyb. B 33, 386–398 (2003)
Theis, F.J.: Uniqueness of Complex andMultidimensional Independent Component Analysis. Signal Proc. 84, 951–956 (2004)
Szabó, Z., Póczos, B., Lőrincz, A.: Separation Theorem for Independent Subspace Analysis. Technical report, Eötvös Loránd University, Budapest (2005), http://people.inf.elte.hu/lorincz/Files/TR-ELU-NIPG-31-10-2005.pdf
Yukich, J.E.: Probability Theory of Classical Euclidean Optimization Problems. Lecture Notes in Math., vol. 1675. Springer, Berlin (1998)
Costa, J.A., Hero, A.O.: Manifold Learning Using k-Nearest Neighbor Graphs. In: ICASSP, Montreal, Canada (2004)
Rubinstein, R.Y., Kroese, D.P.: The Cross-Entropy Method. Springer, Heidelberg (2004)
Ekman, P.: Emotion in the Human Face. Cambridge Univ. Press, New York (1982)
Póczos, B., Lőrincz, A.: Non-combinatorial Estimation of Independent Autoregressive Sources (2005) (submitted)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Szabó, Z., Póczos, B., Lőrincz, A. (2006). Cross-Entropy Optimization for Independent Process Analysis. In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2006. Lecture Notes in Computer Science, vol 3889. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11679363_113
Download citation
DOI: https://doi.org/10.1007/11679363_113
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32630-4
Online ISBN: 978-3-540-32631-1
eBook Packages: Computer ScienceComputer Science (R0)