Szabo, Z;
Póczos, B;
Lőrincz, A;
(2012)
Separation theorem for independent subspace analysis and its consequences.
Pattern Recognition
, 45
(4)
1782 - 1791.
10.1016/j.patcog.2011.09.007.
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Abstract
Independent component analysis (ICA) – the theory of mixed, independent, non-Gaussian sources – has a central role in signal processing, computer vision and pattern recognition. One of the most fundamental conjectures of this research field is that independent subspace analysis (ISA) – the extension of the ICA problem, where groups of sources are independent – can be solved by traditional ICA followed by grouping the ICA components. The conjecture, called ISA separation principle, (i) has been rigorously proven for some distribution types recently, (ii) forms the basis of the state-of-the-art ISA solvers, (iii) enables one to estimate the unknown number and the dimensions of the sources efficiently, and (iv) can be extended to generalizations of the ISA task, such as different linear-, controlled-, post nonlinear-, complex valued-, partially observed problems, as well as to problems dealing with nonparametric source dynamics. Here, we shall review the advances on this field.
| Type: | Article |
|---|---|
| Title: | Separation theorem for independent subspace analysis and its consequences |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.patcog.2011.09.007 |
| Publisher version: | http://dx.doi.org/10.1016/j.patcog.2011.09.007 |
| Language: | English |
| Additional information: | © 2012. This manuscript version is published under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International licence (CC BY-NC-ND 4.0). This licence allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licences are available at http://creativecommons.org/licenses/by/4.0. |
| Keywords: | complex valued models, controlled models, independent subspace analysis, linear systems, nonparametric source dynamics, partially observed systems, post nonlinear systems, separation principles |
| UCL classification: | UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1433154 |
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