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.