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Hierarchical independent component analysis: A multi-resolution non-orthogonal data-driven basis

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  • Secchi, Piercesare
  • Vantini, Simone
  • Zanini, Paolo

Abstract

A new method named Hierarchical Independent Component Analysis is presented, particularly suited for dealing with two problems regarding the analysis of high-dimensional and complex data: dimensional reduction and multi-resolution analysis. It takes into account the Blind Source Separation framework, where the purpose is the research of a basis for a dimensional reduced space to represent data, whose basis elements represent physical features of the phenomenon under study. In this case orthogonal basis could be not suitable, since the orthogonality introduces an artificial constraint not related to the phenomenological properties of the analyzed problem. For this reason this new approach is introduced. It is obtained through the integration between Treelets and Independent Component Analysis, and it is able to provide a multi-scale non-orthogonal data-driven basis. Furthermore a strategy to perform dimensional reduction with a non orthogonal basis is presented and the theoretical properties of Hierarchical Independent Component Analysis are analyzed. Finally HICA algorithm is tested both on synthetic data and on a real dataset regarding electroencephalographic traces.

Suggested Citation

  • Secchi, Piercesare & Vantini, Simone & Zanini, Paolo, 2016. "Hierarchical independent component analysis: A multi-resolution non-orthogonal data-driven basis," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 133-149.
    • Handle: RePEc:eee:csdana:v:95:y:2016:i:c:p:133-149
    DOI: 10.1016/j.csda.2015.09.014
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    References listed on IDEAS

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    1. Arnaud Delorme & Jason Palmer & Julie Onton & Robert Oostenveld & Scott Makeig, 2012. "Independent EEG Sources Are Dipolar," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-14, February.
    2. Pardalos, Panos M. & Yatsenko, Vitaliy & Sackellares, J. Chris & Shiau, Deng-Shan & Chaovalitwongse, Wanpracha & Iasemidis, Leonidas D., 2003. "Analysis of EEG data using optimization, statistics, and dynamical system techniques," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 391-408, October.
    3. Chattopadhyay, Asis Kumar & Mondal, Saptarshi & Chattopadhyay, Tanuka, 2013. "Independent Component Analysis for the objective classification of globular clusters of the galaxy NGC 5128," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 17-32.
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