Clustering has been one of the most basic and essential problems in unsupervised learning due to various applications in many critical fields. The recently proposed sum-of-norms (SON) model by Pelckmans et al. (2005), Lindsten et al. (2011) and Hocking et al. (2011) has received a lot of attention. The advantage of the SON model is the theoretical guarantee in terms of perfect recovery, established by Sun et al. (2018). It also provides great opportunities for designing efficient algorithms for solving the SON model. The semismooth Newton based augmented Lagrangian method by Sun et al. (2018) has demonstrated its superior performance over the alternating direction method of multipliers (ADMM) and the alternating minimization algorithm (AMA). In this paper, we propose a Euclidean distance matrix model based on the SON model. An efficient majorization penalty algorithm is proposed to solve the resulting model. Extensive numerical experiments are conducted to demonstrate the efficiency of the proposed model and the majorization penalty algorithm.

翻译：聚类作为无监督学习中最基础且关键的问题之一，在众多重要领域具有广泛应用。Pelckmans等人（2005）、Lindsten等人（2011）及Hocking等人（2011）提出的范数和（SON）模型近年来受到广泛关注。该模型的优势在于Sun等人（2018）所建立的完美恢复理论保证，同时也为设计高效求解算法提供了重要契机。Sun等人（2018）提出的基于半光滑牛顿法的增广拉格朗日法在性能上显著优于交替方向乘子法（ADMM）和交替最小化算法（AMA）。本文基于SON模型提出了一种欧几里得距离矩阵模型，并设计了高效的主化惩罚算法进行求解。通过大量数值实验验证了所提模型及主化惩罚算法的有效性。