M.T. Pham, K. Tachibana, E.S.M. Hitzer, S. Buchholz, T. Yoshikawa, T. Furuhashi
Feature Extraction with Geometric Algebra from Geometric Data
accepted by Proceedings of The Institute of Statistical Mathematics (Tokyo), December, Vol. 56, No. 2 (2008). [Japanese]

Abstract: Most conventional methods of feature extraction for pattern recognition do not pay much attention to geometric properties of data, even in the case where the data have spatial features. In this study we introduce Geometric Algebra to undertake various kinds of feature extractions from spatial data. A Geometric Algebra is a generalization of complex numbers and of quaternions, and it is able to describe spatial objects and relations between them. This paper proposes to use Geometric Algebra to extract geometric features systematically from data given in a vector space. We show the results of classification of hand-written digits, which were classified by feature extraction with the proposed method.

Keywords. Geometric Algebra, Feature extraction, Gaussian mixture model, Pattern recognition, Mixture of experts.


Proceedings of The Institute of Statistical Mathematics (Tokyo)


[Geometric Calculus Japan index]