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

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• 作者：Piercesare Secchi ; Simone Vantini ; Paolo Zanini ; ^{paolo.zanini@polimi.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Blind source separation ; Dimensional reduction ; Electroencephalography ; Independent component analysis ; Multi-resolution analysis ; Treelets
• 刊名：Computational Statistics & Data Analysis
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：95
• 期：Complete
• 页码：133-149
• 全文大小：1306 K

文摘

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.