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Driving innovations in manufacturing: Open Access research from DMEM

Strathprints makes available Open Access scholarly outputs by Strathclyde's Department of Design, Manufacture & Engineering Management (DMEM).

Centred on the vision of 'Delivering Total Engineering', DMEM is a centre for excellence in the processes, systems and technologies needed to support and enable engineering from concept to remanufacture. From user-centred design to sustainable design, from manufacturing operations to remanufacturing, from advanced materials research to systems engineering.

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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.