論文

査読有り
2016年3月

Orthogonal Connectivity Factorization: Interpretable Decomposition of Variability in Correlation Matrices

NEURAL COMPUTATION
  • Aapo Hyvarinen
  • ,
  • Jun-ichiro Hirayama
  • ,
  • Vesa Kiviniemi
  • ,
  • Motoaki Kawanabe

28
3
開始ページ
445
終了ページ
484
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1162/NECO_a_00810
出版者・発行元
MIT PRESS

In many multivariate time series, the correlation structure is nonstationary, that is, it changes over time. The correlation structure may also change as a function of other cofactors, for example, the identity of the subject in biomedical data. A fundamental approach for the analysis of such data is to estimate the correlation structure (connectivities) separately in short timewindows or for different subjects and use existing machine learning methods, such as principal component analysis (PCA), to summarize or visualize the changes in connectivity. However, the visualization of such a straightforward PCA is problematic because the ensuing connectivity patterns are much more complex objects than, say, spatial patterns. Here, we develop a new framework for analyzing variability in connectivities using the PCA approach as the starting point. First, we show how to analyze and visualize the principal components of connectivity matrices by a tailor-made rank-two matrix approximation in which we use the outer product of two orthogonal vectors. This leads to a new kind of transformation of eigenvectors that is particularly suited for this purpose and often enables interpretation of the principal component as connectivity between two groups of variables. Second, we show how to incorporate the orthogonality and the rank-two constraint in the estimation of PCA itself to improve the results. We further provide an interpretation of these methods in terms of estimation of a probabilistic generative model related to blind separation of dependent sources. Experiments on brain imaging data give very promising results.

Web of Science ® 被引用回数 : 4

リンク情報
DOI
https://doi.org/10.1162/NECO_a_00810
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000371155800001&DestApp=WOS_CPL
URL
http://dblp.uni-trier.de/db/journals/neco/neco28.html#journals/neco/HyvarinenHKK16
ID情報
  • DOI : 10.1162/NECO_a_00810
  • ISSN : 0899-7667
  • eISSN : 1530-888X
  • DBLP ID : journals/neco/HyvarinenHKK16
  • Web of Science ID : WOS:000371155800001

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