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Method for Joint Clustering in Graph and Correlation Spaces

Method for Joint Clustering in Graph and Correlation Spaces Graph algorithms are often used to analyze and interpret biological data. One of the widely used approaches is to solve the problem of identifying an active module, where a connected subgraph of a biological network is selected, which best reflects the difference between two biological states being considered. In this work, we extend this approach to the case of a larger number of biological states and formulate the problem of joint clustering in graph and correlation spaces. To solve this problem, an iterative method is proposed, which takes as the input the graph \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$G$$\end{document} and the matrix \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$X$$\end{document}, in which the rows correspond to vertices of the graph. As the output, the algorithm generates a set of subgraphs of graph \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$G$$\end{document} so that each subgraph is connected and the rows corresponding to its vertices have a high pairwise correlation. The efficiency of the method is confirmed by an experimental study using simulated data. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Automatic Control and Computer Sciences Springer Journals

Method for Joint Clustering in Graph and Correlation Spaces

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Publisher
Springer Journals
Copyright
Copyright © Allerton Press, Inc. 2021. ISSN 0146-4116, Automatic Control and Computer Sciences, 2021, Vol. 55, No. 7, pp. 647–657. © Allerton Press, Inc., 2021. Russian Text © The Author(s), 2020, published in Modelirovanie i Analiz Informatsionnykh Sistem, 2020, No. 2, pp. 180–193.
ISSN
0146-4116
eISSN
1558-108X
DOI
10.3103/s0146411621070026
Publisher site
See Article on Publisher Site

Abstract

Graph algorithms are often used to analyze and interpret biological data. One of the widely used approaches is to solve the problem of identifying an active module, where a connected subgraph of a biological network is selected, which best reflects the difference between two biological states being considered. In this work, we extend this approach to the case of a larger number of biological states and formulate the problem of joint clustering in graph and correlation spaces. To solve this problem, an iterative method is proposed, which takes as the input the graph \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$G$$\end{document} and the matrix \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$X$$\end{document}, in which the rows correspond to vertices of the graph. As the output, the algorithm generates a set of subgraphs of graph \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$G$$\end{document} so that each subgraph is connected and the rows corresponding to its vertices have a high pairwise correlation. The efficiency of the method is confirmed by an experimental study using simulated data.

Journal

Automatic Control and Computer SciencesSpringer Journals

Published: Dec 1, 2021

Keywords: active module; clustering; gene expression; biological networks

References