An algorithm for fuzzy clustering based on conformal geometric algebra

Abstract

Geometric algebra(GA) is a generalization of complex numbers and quaternions. It is able to describe spatial objects and the geometric relations between them. ConformalGA(CGA) is a part of GA and it’s vector is found that points, lines, planes, circles and spheres gain particularly natural and computationally amenable representations. So, CGA based hard clustering(hard conformal clustering(HCC)) is able to detect a cluster distributed over a sphere, plane, or their intersections such as a straight line or arc. However because HCC is a hard clustering, it is only divide data into crisp cluster. This paper applies fuzzy technique to HCC and proposes an algorithm of fuzzy conformal clustering(FCC). This paper shows that using the proposed algorithm, data was able to belong to more one cluster which is presented by a vector in CGA.