A Transductive Framework of Distance Metric Learning by Spectral Dimensionality Reduction

Distance metric learning and nonlinear dimensionality reduction are two interesting and active topics in recent years. However, the connection between them is not thoroughly studied yet. In this paper, a transductive framework of distance metric learning is proposed and its close connection with many nonlinear spectral dimensionality reduction methods is elaborated. Furthermore, we prove a representer theorem for our framework, linking it with function estimation in an RKHS, and making it possible for generalization to unseen test samples. In our framework, it suffices to solve a sparse eigenvalue problem, thus datasets with 105 samples can be handled. Finally, experiment results on synthetic data, several UCI databases and the MNIST handwritten digit database are shown.