Moving Up the Cluster Tree with the Gradient Flow
Ery Arias-castro Aa, Wanli Qiaob
- aDepartment of Mathematics, University of California, San Diego, CA 92093 USA
- bDepartment of Statistics, George Mason University, Fairfax, VA 22030 USA
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Abstract
Abstract. This paper establishes a strong correspondence between two important clustering approaches that emerged in the 1970s: 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. This correspondence is drawn by showing that the gradient ascent flow provides a natural way to move up the cluster tree.
TL;DRIt is shown that one can move up the cluster tree by following the gradient ascent flow, establishing 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 clusters by gradient lines or gradient flow. (Semantic Scholar)