Multidimensional partitioning and bi-partitioning : analysis and application to gene expression datasets

Kalna, Gabriela and Vass, J. Keith and Higham, Desmond J. (2008) Multidimensional partitioning and bi-partitioning : analysis and application to gene expression datasets. International Journal of Computer Mathematics, 85 (3/4). pp. 475-485. ISSN 0020-7160

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    Abstract

    Eigenvectors and, more generally, singular vectors, have proved to be useful tools for data mining and dimension reduction. Spectral clustering and reordering algorithms have been designed and implemented in many disciplines, and they can be motivated from several dierent standpoints. Here we give a general, unied, derivation from an applied linear algebra perspective. We use a variational approach that has the benet of (a) naturally introducing an appropriate scaling, (b) allowing for a solution in any desired dimension, and (c) dealing with both the clustering and bi-clustering issues in the same framework. The motivation and analysis is then backed up with examples involving two large data sets from modern, high-throughput, experimental cell biology. Here, the objects of interest are genes and tissue samples, and the experimental data represents gene activity. We show that looking beyond the dominant, or Fiedler, direction reveals important information.

    ORCID iDs

    Kalna, Gabriela, Vass, J. Keith and Higham, Desmond J. ORCID logoORCID: https://orcid.org/0000-0002-6635-3461;
    • Item type:Article
      ID code:13545
      Dates:
      Date
      Event
      March 2008
      Published
      Keywords:data mining dimension reduction, feature selection, graphLaplacian, Fiedler vector, microarray, singular value decomposition, tumour classication, Mathematics, Computational Theory and Mathematics, Applied Mathematics, Computer Science Applications
      Subjects:Science > Mathematics
      Department:Faculty of Science > Mathematics and Statistics > Mathematics
      Faculty of Science > Mathematics and Statistics
      Depositing user: Mrs Irene Spencer
      Date deposited:08 Jan 2010 19:14
      Last modified:17 Jul 2021 01:40
      URI:https://strathprints.strath.ac.uk/id/eprint/13545
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