Generalization error bounds in semi-supervised classification under the cluster assumption

We consider semi-supervised classification when part of the available data is unlabeled. These unlabeled data can be useful for the classification problem when we make an assumption relating the behavior of the regression function to that of the marginal distribution. Seeger (2000) proposed the well-known cluster assumption as a reasonable one. We propose a mathematical formulation of this assumption and a method based on density level sets estimation that takes advantage of it to achieve fast rates of convergence both in the number of unlabeled examples and the number of labeled examples.

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Philippe Rigollet
• Keywords: Classification Problem, CORR 2006, Education, Unlabeled Data, Well-known Cluster Assumption