Separation Theorem for Independent Subspace Analysis with Sufficient Conditions

Separation Theorem for K-Independent Subspace Analysis with Sufficient Conditions

Abstract. Here, a Separation Theorem about K-Independent Subspace Analysis (K ∈ {R,C} real or complex), a generalization of K-Independent Component Analysis (K-ICA) is proven. According to the theorem, K-ISA estimation can be executed in two steps under certain conditions. In the first step, 1-dimensional K-ICA estimation is executed. In the second step, optimal permutation of the K-ICA element...

Separation Theorem for Independent Subspace Analysis

Here, a separation theorem about Independent Subspace Analysis (ISA), a generalization of Independent Component Analysis (ICA) is proven. According to the theorem, ISA estimation can be executed in two steps under certain conditions. In the first step, 1-dimensional ICA estimation is executed. In the second step, optimal permutation of the ICA elements is searched for. We shall show that ellipt...

Sufficient Conditions for Density in Extended Lipschitz Algebras

Independent Subspace Analysis can Cope with the 'Curse of Dimensionality'

We search for hidden independent components, in particular we consider the independent subspace analysis (ISA) task. Earlier ISA procedures assume that the dimensions of the components are known. Here we show a method that enables the non-combinatorial estimation of the components. We make use of a decomposition principle called the ISA separation theorem. According to this separation theorem t...

Complete Blind Subspace Deconvolution

Cocktail-party Problems (increasing generality): • Independent component analysis (ICA) [1, 2]: onedimensional sound sources. • Independent subspace analysis (ISA) [3]: independent groups of people. • Blind source deconvolution (BSD) [4]: one-dimensional sound sources and echoic room. • Blind subspace deconvolution (BSSD) [5]: independent source groups and echoes. Separation Theorem: • ISA ([3]...