A Conformal Geometric Algebra Based Clustering Method and Its Applications

Clustering is one of the most useful methods for understanding similarity among data. However, most conventional clustering methods do not pay sufficient attention to the geometric distributions of data. Geometric algebra (GA) is a generalization of complex numbers and quaternions able to describe spatial objects and the geometric relations between them. This paper uses conformal GA (CGA), which is a part of GA. This paper transforms data from a real Euclidean vector space into a CGA space and presents a new clustering method using conformal vectors. In particular, this paper shows that the proposed method was able to extract the geometric clusters which could not be detected by conventional methods.