Second Order Subspace Analysis and Simple Decompositions
The recovery of the mixture of an N-dimensional signal generated by N independent processes is a well studied problem (see e.g. [1,10]) and robust algorithms that solve this problem by Joint Diagonalization exist. While there is a lot of empirical evidence suggesting that these algorithms are also capable of solving the case where the source signals have block structure (apart from a final permutation recovery step), this claim could not be shown yet - even more, it previously was not known if this model separable at all. We present a precise definition of the subspace model, introducing the notion of simple components, show that the decomposition into simple components is unique and present an algorithm handling the decomposition task.
Unable to display preview. Download preview PDF.
- 6.Maehara, T., Murota, K.: Error-controlling algorithm for simultaneous block-diagonalization and its application to independent component analysis. JSIAM Letters (submitted)Google Scholar
- 7.Maehara, T., Murota, K.: Algorithm for error-controlled simultaneous block-diagonalization of matrices. Technical Report METR-2009-53 (December 2009)Google Scholar
- 9.Theis, F.J.: Towards a general independent subspace analysis. In: Proc. NIPS, pp. 1361–1368 (January 2006)Google Scholar
- 10.Tong, L., Soon, V.C., Huang, Y.-F., Liu, R.: AMUSE: a new blind identification algorithm. In: IEEE International Symposium on Circuits and Systems, vol. 3, pp. 1784–1787 (1990)Google Scholar