Second Order Subspace Analysis and Simple Decompositions
- Cite this paper as:
- Gutch H.W., Maehara T., Theis F.J. (2010) Second Order Subspace Analysis and Simple Decompositions. In: Vigneron V., Zarzoso V., Moreau E., Gribonval R., Vincent E. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2010. Lecture Notes in Computer Science, vol 6365. Springer, Berlin, Heidelberg
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.
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