Independent Subspace Analysis Using Three Scatter Matrices
AbstractIn independent subspace analysis (ISA) one assumes that the components of the observed random vector are linear combinations of the components of a latent random vector with independent subvectors. The problem is then to find an estimate of a transformation matrix to recover the independent subvectors. Regular independent component analysis (ICA) is a special case. In this paper we show how three scatter matrices with the so called block independence property can be used in independent subspace analysis. The procedure is illustrated with a small example.
Cardoso, J.-F. (1998). Multidimensional independent component analysis. In Proceedings of ICASSP 1998 (p. 1941-1944). Seattle.
Gutch, H. W., and Theis, F. J. (2007). Independent subsapce analysis is unique, given irreducibility. In M. E. Davies, C. C. James, S. A. Abdallah, and M. D. Plumbley (Eds.), Independent Component Analysis and Signal Separation (p. 49-56). Heidelberg: Springer.
Gutch, H. W., and Theis, F. J. (2010). Uniqueness of linear factorizations into independent subspaces. (submitted)
Hyvärinen, A., Karhunen, J., and Oja, E. (2001). Independent Component Analysis. New York: Wiley & Sons.
Hyvärinen, A., and Köster, U. (2006). FastISA: A fast fixed-point algorithm for independent subspace analysis. In Proceedings of the European Symposium on Artificial Neural Networks. Bruges, Belgium.
Nordhausen, K., Oja, H., and Ollila, E. (2008). Robust independent component analysis based on two scatter matrices. Austrian Journal of Statistics, 37, 91-100.
Oja, H., Sirkiä, S., and Eriksson, J. (2006). Scatter matrices and independent component analysis. Austrian Journal of Statistics, 35, 175-189.
Ollila, E., Oja, H., and Koivunen, V. (2008). Complex-valued ICA based on a pair of generalized covariance matrices. Computational Statistics & Data Analysis, 52, 3789-3805.
Poczos, B., and Lörincz, A. (2005). Independent subspace analysis using k-nearest neighborhood distances. In Proceedings of ICANN 2005, Vol. 3696 of LNCS (p. 163-168). Warsaw: Springer.
Szabo, Z., and Lörincz, A. (2001). Real and complex independent subspace analysis by generalized variance. In ICA Research Network International Workshop (ICARN 2006) (p. 85-88).
Theis, F. (2004). Uniqueness of complex and multidimensional independent component analysis. Signal Processing, 84, 951-956.
Theis, F. (2007). Towards a general independent subspace analysis. In B. Schölkopf, J. Platt, and T. Hoffman (Eds.), Proceedings of NIPS 2006 (p. 1361-1368). Cambridge, MA: MIT Press.
Tyler, D. E., Critchley, F., Dümbgen, L., and Oja, H. (2009). Invariant coordinate selection. Journal of Royal Statistical Society, Series B, 71, 549-592.
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