Feature extraction by geometric algebra from geometric data
Most conventional methods of feature extraction for pattern
recognition do not pay sufficient attention to the inherent
geometric properties of data, even where data have characteristic
spatial features. In this study, we introduce geometric algebra to
systematically extract invariant geometric features from spatial
data given in a vector space. Geometric algebra is a multidimensional
generalization of complex numbers and of quaternions, and can
accurately describe oriented spatial objects and relations between
them. We further propose a combination of several geometric features
using Gaussian mixture models. We demonstrate our new method by
classification of hand-written digits and alphabetic characters.