Learning from Partially Labeled Data: Unsupervised and Semi-supervised Learning on Graphs and Learning with Distribution Shifting

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii This thesis focuses on two fundamental machine learning problems: unsupervised learn-ing, where no label information is available, and semi-supervised learning, where a small amount of labels are given in addition to unlabeled data. These problems arise in many real word applications, such as Web analysis and bioinformatics, where a large amount of data is available, but no or only a small amount of labeled data exists. Obtaining classification labels in these domains is usually quite difficult because it involves either manual labeling or physical experimentation. This thesis approaches these problems from two perspectives: graph based and distribution based. First, I investigate a series of graph based learning algorithms that are able to exploit information embedded in different types of graph structures. These algorithms allow labe