Topological Structure of Linear Manifold Clustering

Topological Structure of Linear Manifold Clustering

In the topological data analysis, the first step is a construction of a simplicial complex from a discrete points set D sampled from some manifold. In this paper, we present an algorithm for the efficient computation of such simplicial complex which utilizes clustering structure, comprised of subspace clusters, of the point set for speeding up a complex construction procedure while keeping relevant topological invariants of the underlying sampled manifold. Experiments show that the proposed construction algorithm provides smaller complexes with less noise which gives a better homological picture than other construction methods as well as an improved construction performance and a topological invariant interpretability on a geometrical level.