Multi-Manifold Semi-Supervised Learning

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Andrew Goldberg, Xiaojin Zhu, Aarti Singh, Zhiting Xu, Robert Nowak ;
Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, PMLR 5:169-176, 2009.

Abstract

We study semi-supervised learning when the data consists of multiple intersecting manifolds. We give a finite sample analysis to quantify the potential gain of using unlabeled data in this multi-manifold setting. We then propose a semi-supervised learning algorithm that separates different manifolds into decision sets, and performs supervised learning within each set. Our algorithm involves a novel application of Hellinger distance and size-constrained spectral clustering. Experiments demonstrate the benefit of our multi-manifold semi-supervised learning approach.

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