Laplacian regularized kernel minimum squared error and its application to face recognition

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, labeled examples are usually insufficient and unlabeled examples are abundant 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 regularization term. As a result, the labels of labeled and unlabeled examples vary smoothly along the geodesics on the manifold. Experimental results on several synthetic and real-world datasets illustrate the effectiveness of our algorithm. Finally our algorithm is applied to face recognition and achieves the comparable results compared to the other supervised and semi-supervised methods.