BalLOT: Balanced $k$-means clustering with optimal transport

Wenyan Luo; Dustin G. Mixon

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arXiv · 2512.05926

BalLOT: Balanced $k$-means clustering with optimal transport

Wenyan Luo·Dustin G. Mixon

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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 a variety of numerical experiments before proving several theoretical guarantees. First, we 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. Finally, we propose initialization schemes that achieve one-step recovery of planted clusters.

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BibTeX RIS

Wenyan Luo, Dustin G. Mixon. 2025-12-05. BalLOT: Balanced $k$-means clustering with optimal transport. https://arxiv.org/abs/2512.05926

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