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<p>Convex clustering formulates the clustering problem as a convex optimization task that encourages similar data points to merge into clusters by minimizing a combination of fitting error and a penalty on differences between cluster centroids. This method has attracted considerable attention due to its capacity to address the challenges associated with local optimal solutions and numerical instability prevalent in traditional nonconvex clustering methods. However, it typically relies on the standard Euclidean metric for measuring distance, which can lead to decreased performance, especially in the presence of outlier features. Additionally, it is not particularly robust against outlier samples. To address these issues, we separate the data into cluster and outlier components, effectively eliminating the outlier features. By incorporating self-paced learning, we develop a model that adaptively selects relevant examples while minimizing interference from outlier instances. This approach enhances robustness by removing outlier features and samples, forming a biconvex clustering framework with strong statistical properties. We propose an efficient, convergent algorithm and establish a finite sample bound for prediction error. Experiments on artificial and benchmarking datasets show improved clustering effectiveness compared to classical convex clustering methods.</p>

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A new robust biconvex clustering method with self-paced learning

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Jinyao Ma,
  • Jiaojiao Jiang,
  • Haibin Zhang

摘要

Convex clustering formulates the clustering problem as a convex optimization task that encourages similar data points to merge into clusters by minimizing a combination of fitting error and a penalty on differences between cluster centroids. This method has attracted considerable attention due to its capacity to address the challenges associated with local optimal solutions and numerical instability prevalent in traditional nonconvex clustering methods. However, it typically relies on the standard Euclidean metric for measuring distance, which can lead to decreased performance, especially in the presence of outlier features. Additionally, it is not particularly robust against outlier samples. To address these issues, we separate the data into cluster and outlier components, effectively eliminating the outlier features. By incorporating self-paced learning, we develop a model that adaptively selects relevant examples while minimizing interference from outlier instances. This approach enhances robustness by removing outlier features and samples, forming a biconvex clustering framework with strong statistical properties. We propose an efficient, convergent algorithm and establish a finite sample bound for prediction error. Experiments on artificial and benchmarking datasets show improved clustering effectiveness compared to classical convex clustering methods.