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.
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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)
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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
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DOI: https://doi.org/10.1007/11679363_113
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32630-4
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