Geometric Data Manipulation with Clifford Algebras and Möbius Transforms

Abstract

We propose the usage of Möbius transformations, defined in the context of Clifford algebras, for geometrically manipulating a point cloud data lying in a vector space of arbitrary dimension. We present this method as an application to signal classification in a dimensionality reduction framework. We first discuss a general situation where data analysis problems arise in signal processing. In this context, we introduce the construction of special Möbius transformations on vector spaces Rn, customized for a classification setting. A computational experiment is presented indicating the potential and shortcomings of this framework.

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