Strong Consistency of Sparse K-means Clustering

2025/01/17 by Jeungju Kim, Kim, Jeungju, Johan Lim +1
Computer Science · #Advanced Clustering Algorithms Research #FOS: Mathematics #Face and Expression Recognition #Statistics Theory (math.ST) #Text and Document Classification Technologies

paper · pdf · doi:10.48550/arxiv.2501.09983

openalex publication_date 2025/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the strong consistency of the sparse K-means clustering for high dimensional data. We prove the consistency in both risk and clustering for the Euclidean distance. We discuss the characterization of the limit of the clustering under some special cases. For the general (non-Euclidean) distance, we prove the consistency in risk. Our result naturally extends to other models with the same objective function but different constraints such as l0 or l1 penalty in recent literature.

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