A Transductive Framework of Distance Metric Learning by Spectral Dimensionality Reduction

author: Fuxin Li, Institute of Automation, Chinese Academy of Sciences
published: June 23, 2007,   recorded: June 2007,   views: 5981


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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.

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