Moving Up the Cluster Tree with the Gradient Flow

TL;DR

This paper demonstrates a theoretical connection between cluster trees and gradient flow, showing how to ascend the cluster hierarchy by following gradient ascent paths, bridging two classical clustering methods.

Contribution

It establishes a formal link between cluster trees and gradient flow, enabling movement up the cluster hierarchy via gradient ascent, which was previously unconnected.

Findings

Shows the correspondence between cluster trees and gradient flow.

Provides a method to move up the cluster hierarchy using gradient ascent.

Bridges two classical clustering approaches from the 1970s.

Abstract

The paper establishes a strong correspondence between two important clustering approaches that emerged in the 1970's: clustering by level sets or cluster tree as proposed by Hartigan and clustering by gradient lines or gradient flow as proposed by Fukunaga and Hostetler. We do so by showing that we can move up the cluster tree by following the gradient ascent flow.