Fitting a Simplicial Complex using a Variation of k-means

Abstract

We give a simple and effective two stage algorithm for approximating a point cloud $\mathcal{S}\subset {\mathbb{R}}^m$ by a simplicial complex $K$. The first stage is an iterative fitting procedure that generalizes k-means clustering, while the second stage involves deleting redundant simplices. A form of dimension reduction of $\mathcal{S}$ is obtained as a consequence.

References in corpus (1)

• Hardness of embedding simplicial complexes in ${\mathbb{R}}^d$