arXiv:2506.21291cs.LG2025-06被引 1

提出更优的k均值与高斯混合模型初始化方法,提升聚类质量。

Improved seeding strategies for k-means and k-GMM

  • 基于前瞻原则和多轮策略优化种子选择机制
  • 在SSE和对数似然上实现稳定常数倍改进
  • 适合需要高质量聚类初始化的研究与工程场景

本文重新审视k均值聚类与k-GMM(使用期望最大化算法拟合高斯混合模型)的随机初始化技术,明确其三个关键要素:种子采样所用度量、候选种子数量以及种子选择所用度量。分析揭示了新型初始化方法家族,利用前瞻原则——使种子选择与最终评估度量更一致,并采用多轮策略缓解随机性影响。实验表明,在最终指标(k均值为SSE,k-GMM为对数似然)上,本方法相比经典方法有稳定的常数倍改进,且开销适中。特别地,对于k均值,本方法优于近期提出的多交换策略,后者是首个超越贪心k-means++的方法。实验还揭示了k均值中常被忽视的性质,包括初始SSE与最终SSE间缺乏相关性、迭代初始化中的方差减小现象,以及贪心方法对候选池大小的敏感性。实际应用中,最有效的初始化方法有望成为标准技术。理论上,本文对初始化的正式化为新分析路径开辟了道路。

原文摘要 · Abstract (English)

We revisit the randomized seeding techniques for k-means clustering and k-GMM (Gaussian Mixture model fitting with Expectation-Maximization), formalizing their three key ingredients: the metric used for seed sampling, the number of candidate seeds, and the metric used for seed selection. This analysis yields novel families of initialization methods exploiting a lookahead principle--conditioning the seed selection to an enhanced coherence with the final metric used to assess the algorithm, and a multipass strategy to tame down the effect of randomization. Experiments show a consistent constant factor improvement over classical contenders in terms of the final metric (SSE for k-means, log-likelihood for k-GMM), at a modest overhead. In particular, for k-means, our methods improve on the recently designed multi-swap strategy, which was the first one to outperform the greedy k-means++ seeding. Our experimental analysis also shed light on subtle properties of k-means often overlooked, including the (lack of) correlations between the SSE upon seeding and the final SSE, the variance reduction phenomena observed in iterative seeding methods, and the sensitivity of the final SSE to the pool size for greedy methods. Practically, our most effective seeding methods are strong candidates to become one of the--if not the--standard techniques. From a theoretical perspective, our formalization of seeding opens the door to a new line of analytical approaches.

聚类初始化k均值GMM算法优化

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