NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Efficient Pattern Recognition Using a New Transformation Distance
Advances in Neural Information Processing Systems 5, [NIPS Conference]
An efficient boosting algorithm for combining preferences
The Journal of Machine Learning Research
In Defense of One-Vs-All Classification
The Journal of Machine Learning Research
Generalization Bounds for the Area Under the ROC Curve
The Journal of Machine Learning Research
Generalization Bounds for Ranking Algorithms via Algorithmic Stability
The Journal of Machine Learning Research
Discriminative dimensionality reduction mappings
IDA'12 Proceedings of the 11th international conference on Advances in Intelligent Data Analysis
Optimized bi-dimensional data projection for clustering visualization
Information Sciences: an International Journal
A regularized graph layout framework for dynamic network visualization
Data Mining and Knowledge Discovery
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Least squares multidimensional scaling (MDS) is a classical method for representing a nxn dissimilarity matrix D. One seeks a set of configuration points z"1,...,z"n@?R^S such that D is well approximated by the Euclidean distances between the configuration points: D"i"j~@?z"i-z"j@?"2. Suppose that in addition to D, a vector of associated binary class labels y@?{1,2}^n 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 z"1,...,z"n@?R^S such that D"i"j~@?z"i-z"j@?"2, and such that z"i"sz"j"s for s=1,...,S tends to occur when y"iy"j. 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.