Dec 2025· arXiv.org· Vol abs/2512.05926· 0 citations· 35 references
Computer ScienceMathematics
TL;DR
An optimal transport approach to alternating minimization called BalLOT is introduced, and it is shown that it delivers a fast and effective solution to the fundamental problem of balanced $k$-means clustering.
Abstract
We consider the fundamental problem of balanced $k$-means clustering. In particular, we introduce an optimal transport approach to alternating minimization called BalLOT, and we show that it delivers a fast and effective solution to this problem. We establish this with several theoretical guarantees and a variety of numerical experiments. On the theory front, we first prove that for generic data, BalLOT produces integral couplings at each step. Next, we perform a landscape analysis to provide theoretical guarantees for both exact and partial recoveries of planted clusters under the stochastic ball model. We also propose initialization schemes that achieve one-step recovery of planted clusters. To conclude, we present numerical experiments that corroborate our theoretical results.
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