Feature Extraction with Geometric Algebra for Semi-Supervised Learning of Time-Series Spatial Vector

Abstract

In fields of machine learning of patterns most conventional methods of feature extraction do not pay much attention to the geometric properties of data, even in cases where the data have spatial features. In this study we introduce geometric algebras to systematically extract invariant geometric features from spatial data given in a vector space. A geometric algebra is a multidimensional generalization of complex numbers and of quaternions, and able to accurately describe oriented spatial objects and relations between them. We further propose a kernel to measure similarity between two series of spatial vectors based on Hidden Markov Models. As an apllication, we demonstrate our new method with the semi-supervised learning of online hand-written digits. The result shows that the feature extraction with geometric algebra improved recognition rate in one-to-one semi-supervised learning problems of online hand-written digits.