Institute of Informatics
Acta Cybernetica
Past Issues
Volume 18, Number 2, 2007
Independent Subspace Analysis can Cope with the `Curse of Dimensionality'
# Independent Subspace Analysis can Cope with the `Curse of Dimensionality'

**Zoltán Szabó and András Lőrincz**

### Abstract (in LaTeX format)

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 \emph{and then} to a grouping procedure that collects the respective non-independent 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.

**Keywords: ** independent subspace analysis, non-combinatorial solution.

### Full text

Available electronic editions: PDF.

### DOI

DOI is not available for this article.

### BibTeX entry
`
@ARTICLE{Szabo:2007:ActaCybernetica,`

author = {Zolt\'an Szab\'o and Andr\'as L\H{o}rincz},

title = {Independent Subspace Analysis can Cope with the `Curse of Dimensionality'},

journal = {Acta Cybernetica},

year = {2007},

volume = {18},

pages = {213--221},

number = {2},

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 \emph{and then} to a grouping procedure that collects the respective non-independent 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. },

keywords = {independent subspace analysis, non-combinatorial solution}

}