Supervised multidimensional scaling for visualization, classification, and bipartite ranking

Daniela M. Witten and Robert Tibshirani

Computational Statistics & Data Analysis, 2011, vol. 55, issue 1, 789-801

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.

Keywords: Classification; Multidimensional; scaling; Unidimensional; scaling; Unsupervised; learning; Majorization; Ranking (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (3)

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