Statistical Properties of $k$-means Clustering for Data Missing Completely at Random
The classical $k$-means clustering cannot be directly used to incomplete data, and existing $k$-means-based clustering for missing data primarily focus on improving the practical accuracy of clustering, whereas most of them lack theoretical guarantees in the asymptotic sense. In this paper, we investigate the statistical properties of $k$-means clustering in the presence of missing data. We first establish the $\sqrt{n}$-excess risk bound and prove the consistency of the estimated cluster centers under general missing mechanisms. For the Missing Completely at Random (MCAR) mechanism, we further derive the $\sqrt{n}$-convergence rate and asymptotic normality of the estimated cluster center...
| Authors | Xin Guan |
|---|---|
| Primary category | stat.ML |
| Published | 2 July 2026 |
| Last updated at source | 2 July 2026 |
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