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]