Many recent works have combined two machine learning topics, learning of supervised distance metrics and manifold embedding methods, into supervised nonlinear dimensionality reduction methods. We show that a combination of an early metric learning method and a recent unsupervised dimensionality reduction method empirically outperforms previous methods. In our method, the Riemannian distance metric measures local change of class distributions, and the dimensionality reduction method makes a rigorous tradeoff between precision and recall in retrieving similar data points based on the reduced-dimensional display. The resulting supervised visualizations are good for finding (sets of) similar data samples that have similar class distributions.

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The authors belong to Helsinki Institute for Information Technology HIIT and the Adaptive Informatics Research Centre. This work was supported by the Academy of Finland, decision number 123983, by the Portuguese Foundation for Science and Technology, scholarship number SFRH/BD/39642/2007, and in part by the PASCAL2 Network of Excellence.