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Most conventional methods of feature extraction for pattern recognition do not pay sufficient attention to inherent geometric properties of data, even in the case where the data have spatial features. This paper introduces geometric algebra to 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 it ables to accurately describe oriented spatial objects and relations between them. This paper proposes to combine several geometric features using Gaussian mixture models. It applies the proposed method to the classification of hand-written digits.