Kernel methods have recently become popular in bioinformatics machine learning. Kernel methods allow linear algorithms to be applied to non-linear learning situations. By using kernels, non-linear learning problems can benefit from the statistical and runtime stability traditionally enjoyed by linear learning problems. However, traditional kernel learning frameworks use implicit feature spaces whose mathematical properties were hard to characterize. In order to address this problem, recent research has proposed a vector learning framework that uses landmark vectors which are unlabeled vectors belonging to the same distribution and the same input space as the training vectors. This thesis introduces an extension to the landmark vector learning framework that allows it to utilize two new classes of landmark vectors in the input space. This augmented learning framework is named the power landmark vector learning framework. A theoretical description of the power landmark vector learning framework is given along with proofs of new theoretical results. Experimental results show that the performance of the power landmark vector learning framework is comparable to traditional kernel learning frameworks.

Kernel methods have recently become popular in bioinformatics machine learning. Kernel methods allow linear algorithms to be applied to non-linear learning situations. By using kernels, non-linear learning problems can benefit from the statistical and runtime stability traditionally enjoyed by linear learning problems. However, traditional kernel learning frameworks use implicit feature spaces whose mathematical properties were hard to characterize. In order to address this problem, recent research has proposed a vector learning framework that uses landmark vectors which are unlabeled vectors belonging to the same distribution and the same input space as the training vectors. This thesis introduces an extension to the landmark vector learning framework that allows it to utilize two new classes of landmark vectors in the input space. This augmented learning framework is named the power landmark vector learning framework. A theoretical description of the power landmark vector learning framework is given along with proofs of new theoretical results. Experimental results show that the performance of the power landmark vector learning framework is comparable to traditional kernel learning frameworks.