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Multidimensional Scaling for Genomic Data

In: Advances in Stochastic and Deterministic Global Optimization

Author

Listed:
  • Audrone Jakaitiene

    (Vilnius University)

  • Mara Sangiovanni

    (National Research Council)

  • Mario R. Guarracino

    (National Research Council)

  • Panos M. Pardalos

    (University of Florida)

Abstract

Scientists working with genomic data face challenges to analyze and understand an ever-increasing amount of data. Multidimensional scaling (MDS) refers to the representation of high dimensional data in a low dimensional space that preserves the similarities between data points. Metric MDS algorithms aim to embed inter-point distances as close as the input dissimilarities. The computational complexity of most metric MDS methods is over O(n 2), which restricts application to large genomic data (n ≫ 106). The application of non-metric MDS might be considered, in which inter-point distances are embedded considering only the relative order of the input dissimilarities. A non-metric MDS method has lower complexity compared to a metric MDS, although it does not preserve the true relationships. However, if the input dissimilarities are unreliable, too difficult to measure or simply unavailable, a non-metric MDS is the appropriate algorithm. In this paper, we give overview of both metric and non-metric MDS methods and their application to genomic data analyses.

Suggested Citation

  • Audrone Jakaitiene & Mara Sangiovanni & Mario R. Guarracino & Panos M. Pardalos, 2016. "Multidimensional Scaling for Genomic Data," Springer Optimization and Its Applications, in: Panos M. Pardalos & Anatoly Zhigljavsky & Julius Žilinskas (ed.), Advances in Stochastic and Deterministic Global Optimization, pages 129-139, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-29975-4_7
    DOI: 10.1007/978-3-319-29975-4_7
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    Cited by:

    1. Emilio Carrizosa & Cristina Molero-Río & Dolores Romero Morales, 2021. "Mathematical optimization in classification and regression trees," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 5-33, April.

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