The kernel function plays a central role in modern pattern classification for its ability to capture the inherent affinity structure of the underlying data manifold. While the kernel function can be chosen by human experts with domain knowledge, it is often more principled and promising to learn it directly from data. This idea of kernel learning has been studied considerably in machine learning and pattern recognition. However, most kernel learning algorithms assume fully supervised setups requiring expensive class label annotation for the training data. In this paper we consider kernel learning in the semi-supervised setup where only a fraction of data points need to be labeled. We propose two approaches: the first extends the idea of label propagation along the data similarity graph, in which we simultaneously learn the kernel and impute the labels of the unlabeled data. The second aims to minimize the dual loss in the support vector machines (SVM) classifier learning with respect to the kernel parameters and the missing labels. We provide reasonable and effective approximate solution methods for these optimization problems. These approaches exploit both labeled and unlabeled data in kernel leaning, where we empirically demonstrate the effectiveness on several benchmark datasets with partially labeled learning setups.

Keywords: Kernel learning, Semi-supervised learning, Pattern classification, Optimization

No potential conflict of interest relevant to this article was reported.