Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Second Order Subspace Analysis and Simple Decompositions

Harold W. Gutch, Takanori Maehara, and Fabian J. Theis (2010)

In: Latent Variable Analysis and Signal Separation, edited by Vincent Vigneron and Vicente Zarzoso and Eric Moreau and Rémi Gribonval and Emmanuel Vincent. Springer, pages 370--377.  ( BibTeX export )

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.