Abstract
Design of similarity between instances is important for many machine learning methods. Especially the kernel matrix, also known as the Gram matrix, plays a central role in the kernel machines such as support vector machine. As far as we know, however, design of kernels for the case where each instance is given by m-tuple of n-dimensional vectors has not been established. Geometric algebra (GA) is a generalization of complex numbers and of quaternions, and it is able to describe spatial objects and relations between them. In this study we introduce GA to extract geometric features from m-tuples of n-dimensional vectors. Then we evaluate kernel matrices induced from the geometric features under kernel alignment between them. We also apply a semi-supervised learning based on the kernels to analysis of questionnaire.
