Abstract
Independent Subspace Analysis (ISA) is an extension of Independent Component Analysis (ICA) that aims to linearly transform a random vector such as to render groups of its components mutually independent. A recently proposed fixed-point algorithm is able to locally perform ISA if the sizes of the subspaces are known, however global convergence is a serious problem as the proposed cost function has additional local minima. We introduce an extension to this algorithm, based on the idea that the algorithm converges to a solution, in which subspaces that are members of the global minimum occur with a higher frequency. We show that this overcomes the algorithm’s limitations. Moreover, this idea allows a blind approach, where no a priori knowledge of subspace sizes is required.
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References
Comon, P.: Independent component analysis - a new concept? Signal Processing 36, 287–314 (1994)
Cardoso, J.: Multidimensional independent component analysis. In: Proc. of ICASSP 1998, Seattle (1998)
Hyvärinen, A., Hoyer, P.: Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces. Neural Computation 12(7), 1705–1720 (2000)
Theis, F.: Towards a general independent subspace analysis. In: Proc. NIPS 2006 (2007)
Hyvärinen, A., Köster, U.: Fastisa: A fast fixed-point algorithm for independent subspace analysis. In: ESANN, pp. 371–376 (2006)
Gutch, H., Theis, F.J.: Independent subspace analysis is unique, given irreducibility. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, vol. 4666, pp. 49–56. Springer, Heidelberg (2007)
Edelman, A., Arias, T., Smith, S.: The geometry of algorithms with orthogonality constraints. SIAM Journal on Matrix Analysis and Applications 20(2), 303–353 (1999)
Gruber, P., Theis, F.: Grassmann clustering. In: Proc. EUSIPCO 2006, Florence, Italy (2006)
Sarlette, A., Sepulchre, R.: Consensus optimization on manifolds (to appear, 2008)
Vitányi, P., Li, M.: Minimum description length induction, bayesianism, and kolmogorov complexity. IEEE Transactions on Information Theory 46, 446–464 (2000)
Vetter, R., Vesin, J.M., Celka, P., Renevey, P., Krauss, J.: Automatic nonlinear noise reduction using local principal component analysis and MDL parameter selection. In: Proceedings of the IASTED International Conference on Signal Processing Pattern Recognition and Applications (SPPRA 2002), Crete, pp. 290–294 (2002)
Gruber, P., Stadlthanner, K., Böhm, M., Theis, F.J., Lang, E.W., Tomé, A.M., Teixeira, A.R., Puntonet, C.G., Saéz, J.M.G.: Denoising using local projective subspace methods. Neurocomputing (2006)
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Gruber, P., Gutch, H.W., Theis, F.J. (2009). Hierarchical Extraction of Independent Subspaces of Unknown Dimensions. In: Adali, T., Jutten, C., Romano, J.M.T., Barros, A.K. (eds) Independent Component Analysis and Signal Separation. ICA 2009. Lecture Notes in Computer Science, vol 5441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00599-2_33
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DOI: https://doi.org/10.1007/978-3-642-00599-2_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00598-5
Online ISBN: 978-3-642-00599-2
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