Regularization on Discrete Spaces

Abstract. We consider the classification problem on a finite set of objects. Some of them are labeled, and the task is to predict the labels of the remaining unlabeled ones. Such an estimation problem is generally referred to as transductive inference. It is well-known that many meaningful inductive or supervised methods can be derived from a regularization framework, which minimizes a loss function plus a regularization term. In the same spirit, we propose a general discrete regularization framework defined on finite object sets, which can be thought of as discrete analogue of classical regularization theory. A family of transductive inference schemes is then systemically derived from the framework, including our earlier algorithm for transductive inference, with which we obtained encouraging results on many practical classification problems. The discrete regularization framework is built on discrete analysis and geometry on graphs developed by ourselves, in which a number of dis...

• Type: Conference
• Year: 2005
• Where: DAGM
• Authors: Dengyong Zhou, Bernhard Schölkopf
• Keywords: DAGM 2005, Discrete Regularization Framework, Regularization Framework, Transductive Inference