Simultaneous clustering and optimization (SCO) has recently drawn much attention due to its wide range of practical applications. Many methods have been previously proposed to solve this problem and obtain the optimal model. However, when a dataset evolves over time, those existing methods have to update the model frequently to guarantee accuracy; such updating is computationally infeasible. In this paper, we propose a new formulation of SCO to handle evolving datasets. Specifically, we propose a new variant of the alternating direction method of multipliers (ADMM) to solve this problem efficiently. The guarantee of model accuracy is analyzed theoretically for two specific tasks: ridge regression and convex clustering. Extensive empirical studies confirm the effectiveness of our method.

中文翻译：

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演化数据集的同时聚类和优化

由于其广泛的实际应用，同时聚类和优化（SCO）最近引起了很多关注。之前已经提出了许多方法来解决这个问题并获得最佳模型。然而，当数据集随着时间的推移而演变时，那些现有的方法必须经常更新模型以保证准确性；这种更新在计算上是不可行的。在本文中，我们提出了一种新的 SCO 公式来处理不断发展的数据集。具体来说，我们提出了乘法器交替方向法（ADMM）的一种新变体来有效地解决这个问题。模型精度的保证针对两个具体任务进行了理论上的分析：岭回归和凸聚类。大量的实证研究证实了我们方法的有效性。