Hartigan's Method: k-means Clustering without Voronoi
Hartigan one-point terminal geometry (30 Aug 2026)
- Does not transfer
its objective is additive SSE. It gives no nuisance block, profiled criterion, information price, or population funnel, and in particular does not make an exchange-stable partition a Voronoi partition.
Telgarsky & Vattani study greedy one-point relocation for finite ordinary k-means, including strict descent and the geometry separating a terminal partition from its induced Voronoi partition. It is the nearest published precedent for the exchange-stability notion used in the DS16 measurements.
AISTATS 2010, PMLR 9:820-827. Finite one-point relocation geometry and separation from the induced Voronoi partition for ordinary k-means; no profiled-Fisher or population-funnel result.
Cited by
- Publication-grade audit of the DS18 exact off-(L) basin and empirical transferAUDIT-DS-NONCENTERED-GLOBAL-BASIN-TRANSFER
- Publication-grade audit of DS16 stable margins and the compile verdictAUDIT-DS-STABLE-MARGINS-COMPILE
- Exact off-class global basin transfers to empirical exchange-stable optimaDS-NONCENTERED-GLOBAL-BASIN-TRANSFER
- Conditional centering empties the margin-certified stable branchDS-STABLE-BASINS-CENTERED-OBSTRUCTION
- Exchange-stable Ds states span both margin regimes; ascent selects the funnel at scaleDS-STABLE-STATE-SELECTION
Relevant to
Claims this source bears on without being cited in their proofs.