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Supervised multidimensional scaling for visualization, classification, and bipartite ranking

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  • Witten, Daniela M.
  • Tibshirani, Robert

Abstract

Least squares multidimensional scaling (MDS) is a classical method for representing a nxn dissimilarity matrix . One seeks a set of configuration points such that is well approximated by the Euclidean distances between the configuration points: . Suppose that in addition to , a vector of associated binary class labels corresponding to the n observations is available. We propose an extension to MDS that incorporates this outcome vector. Our proposal, supervised multidimensional scaling (SMDS), seeks a set of configuration points such that , and such that zis>zjs for s=1,...,S tends to occur when yi>yj. This results in a new way to visualize the observations. In addition, we show that SMDS leads to a method for the classification of test observations, which can also be interpreted as a solution to the bipartite ranking problem. This method is explored in a simulation study, as well as on a prostate cancer gene expression data set and on a handwritten digits data set.

Suggested Citation

  • Witten, Daniela M. & Tibshirani, Robert, 2011. "Supervised multidimensional scaling for visualization, classification, and bipartite ranking," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 789-801, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:789-801
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    References listed on IDEAS

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    1. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. II," Psychometrika, Springer;The Psychometric Society, vol. 27(3), pages 219-246, September.
    2. J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 29(1), pages 1-27, March.
    3. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. I," Psychometrika, Springer;The Psychometric Society, vol. 27(2), pages 125-140, June.
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    Cited by:

    1. Yichen Cheng & Xinlei Wang & Yusen Xia, 2021. "Supervised t -Distributed Stochastic Neighbor Embedding for Data Visualization and Classification," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 566-585, May.
    2. Sungkyu Jung & Xingye Qiao, 2014. "A statistical approach to set classification by feature selection with applications to classification of histopathology images," Biometrics, The International Biometric Society, vol. 70(3), pages 536-545, September.
    3. Antonis A. Michis, 2021. "Wavelet Multidimensional Scaling Analysis of European Economic Sentiment Indicators," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 443-480, October.

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