Fitting a Simplicial Complex using a Variation of k-means
This addresses a computational geometry problem for researchers in data analysis and topology, but it appears incremental as it builds on existing k-means methods.
The paper tackles the problem of approximating a point cloud with a simplicial complex by introducing a two-stage algorithm that generalizes k-means clustering and removes redundant simplices, resulting in a form of dimension reduction.
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.