Topological graph clustering with thin position
This is an incremental approach for data clustering, potentially benefiting researchers in machine learning and topology.
The paper tackles the problem of clustering data points by introducing an algorithm based on the topological concept of thin position from knot theory and 3D manifolds, applied to graphs derived from distance or similarity metrics, but no concrete results or numbers are provided.
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a distance or similarity metric on the points, then look for highly connected subgraphs. We introduce such an algorithm based on ideas borrowed from the topological notion of thin position for knots and 3-dimensional manifolds.