Density based clustering on manifolds with applications to creative design

Density based clustering is an effective and basic clustering techniques for data with spatial attributes. Although there are many proposed algorithms and applications for density based spatial clustering, one of its widely used assumptions is that the data is distributed in a smooth space, the Euclidean space Rⁿ for example. On the other hand, manifolds are approximately curved spaces which are locally like smooth spaces but not smooth spaces. The purpose of this paper is to propose new density based clustering algorithms on manifolds, that is, on curved spaces. This is achieved mainly with the help of tangent spaces that are determined by manifold learning. Applications are presented for the automatic classification in creative design.