Clustering by hill-climbing: Consistency results
The Annals of Statistics · 2025 · Volume 53 · Issue 6
Abstract
We consider several hill-climbing approaches to clustering as formulated by Fukunaga and Hostetler (IEEE Trans. Inf. Theory IT-21 (1975) 32–40) in the 1970s. We study both continuous-space and discrete-space (i.e., medoid) variants and establish their consistency.
Keywords
62G20, 62H30, clustering, dynamical systems, Euler scheme, Gradient flow, gradient lines, hill-climbing methods for clustering, Max Shift, Max Slope Shift, Mean Shift, Morse theory, ordinary differential equations
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