Abstract
In usual ICA methods, sources are typically estimated by maximizing a measure of their statistical independence. This paper explains how to perform non-linear ICA by preprocessing the mixtures with recent non-linear dimensionality reduction techniques. These techniques are intended to produce a low-dimensional representation of the data (the mixtures), which is isometric to their initial high-dimensional distribution. A detailed study of the mixture model that makes the separation possible precedes a practical example.
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References
Bernstein, M., de Silva, V., Langford, J.C., Tenenbaum, J.B.: Graph approximations to geodesics on embedded manifolds. Technical report, Stanford University, Stanford (December 2000)
Comon, P.: Independent Component Analysis – A new concept? Signal Processing 36, 287–314 (1994)
Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley- Interscience, Chichester (2001)
Lee, J.A., Lendasse, A., Verleysen, M.: Curvilinear Distances Analysis versus Isomap. In: Verleysen, M. (ed.) Proceedings of ESANN 2002, pp. 13–20. D-Facto public., Bruges (2002)
Lee, J.A., Verleysen, M.: Curvilinear distance analysis versus isomap. Neurocomputing (2004) (accepted)
Taleb, A., Jutten, C.: Source separation in postnonlinear mixtures. IEEE Transactions on Signal Processing 47(10), 2807–2820 (1999)
Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)
Yang, H.H., Amari, S., Cichocki, A.: Information-theoretic approach to blind separation of sources in non-linear mixtures. Signal Processing 64(3), 291–300 (1998)
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© 2004 Springer-Verlag Berlin Heidelberg
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Lee, J.A., Jutten, C., Verleysen, M. (2004). Non-linear ICA by Using Isometric Dimensionality Reduction. In: Puntonet, C.G., Prieto, A. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2004. Lecture Notes in Computer Science, vol 3195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30110-3_90
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DOI: https://doi.org/10.1007/978-3-540-30110-3_90
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