Unsupervised and Semi-supervised Support Vector Machines

Abstract

As an important branch in unsupervised learning, clustering analysis aims at partitioning a collection of objects into groups or clusters so that members within each cluster are more closely related to one another than objects assigned to different clusters. Clustering algorithms provide automated tools to help identify a structure from an unlabeled set, and there is a rich resource of prior works on this subject. Efficient convex optimization techniques have had a profound impact on the field of machine learning, such as quadratic programming and linear programming techniques to Support Vector Machine and other kernel machine training. Furthermore, Semi-definite Programming (SDP) extends the toolbox of optimization methods used in machine learning, beyond the current unconstrained, linear and quadratic programming techniques, which has provided effective algorithms to cope with the difficult computational problem in optimization and obtain high approximate solutions. In this chapter, we proposed several support vector machine algorithms for unsupervised and semi-supervised problems based on SDP.