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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.05926 |
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| _version_ | 1866909946547798016 |
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| author | Luo, Wenyan Mixon, Dustin G. |
| author_facet | Luo, Wenyan Mixon, Dustin G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05926 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | BalLOT: Balanced $k$-means clustering with optimal transport Luo, Wenyan Mixon, Dustin G. Machine Learning Data Structures and Algorithms Information Theory Optimization and Control 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. |
| title | BalLOT: Balanced $k$-means clustering with optimal transport |
| topic | Machine Learning Data Structures and Algorithms Information Theory Optimization and Control |
| url | https://arxiv.org/abs/2512.05926 |