Independent subspace analysis can cope with the 'curse of dimensionality'

Authors:
Zoltán Szabó;András Lörincz
Affiliations:
Department of Information Systems, Eütvüs Loránd University, Pázmány Péter sétány, Budapest, Hungary;Department of Information Systems, Eütvüs Loránd University, Pázmány Péter sétány, Budapest, Hungary
Venue:
Acta Cybernetica
Year:
2007

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Abstract

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 the ISA task can be reduced to the independent component analysis (ICA) task that assumes one-dimensional components and then to a grouping procedure that collects the respective nonindependent elements into independent groups. We show that non-combinatorial grouping is feasible by means of the non-linear f-correlation matrices between the estimated components.