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-nums (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:由于许多关键领域的各种应用,在未受监督的学习中,集群是最基本的和最基本的问题之一。最近由Pelckmans等人(2005年)、Lindsten等人(2011年)和Hocking等人(2011年)提出的“核心”模型模型得到了很多关注。Sun等人(2018年)建立的“核心”模型的优势是完全恢复方面的理论保障。它也为设计解决“核心”模型的有效算法提供了巨大的机会。基于Sun等人(2018年)的半斯莫特牛顿扩大了Lagrangian方法(2018年)的半斯莫特牛顿(Sun等人)(Sun等人(2018年))证明了它优于乘数交替方向法(ADMMM)和“交替最小化法”(AMA)的功能。在本文中,我们提出了以“核心”模型为基础的“远程矩阵模型”模型。提出了高效的主要惩罚算法以解决所产生的模型。进行了广泛的数字实验,以证明拟议的模型和主要惩罚算法的效率。