Semi-supervised Kernel Minimum Squared Error Based on Manifold Structure

摘要

Kernel Minimum Squared Error (KMSE) has been receiving much attention in data mining and pattern recognition in recent years. Generally speaking, training a KMSE classifier, which is a kind of supervised learning, needs sufficient labeled examples. However, there are usually a large amount of unlabeled examples and few labeled examples in real world applications. In this paper, we introduce a semi-supervised KMSE algorithm, called Laplacian regularized KMSE (LapKMSE), which explicitly exploits the manifold structure. We construct a p nearest neighbor graph to model the manifold structure of labeled and unlabeled examples. Then, LapKMSE incorporates the structure information of labeled and unlabeled examples in the objective function of KMSE by adding a Laplacian regularized term. As a result, the labels of labeled and unlabeled examples vary smoothly along the geodesies on the manifold. Experimental results on several synthetic and real-world datasets illustrate the effectiveness of our algorithm.