In this article, we propose a general model for plane-based clustering. The general model reveals the relationship between cluster assignment and cluster updating during clustering implementation, and it contains many existing plane-based clustering methods, e.g., k-plane clustering, proximal plane clustering, twin support vector clustering, and their extensions. Under this general model, one may obtain an appropriate clustering method for a specific purpose. The general model is a procedure corresponding to an optimization problem, which minimizes the total loss of the samples. Thereinto, the loss of a sample derives from both within-cluster and between-cluster information. We discuss the theoretical termination conditions and prove that the general model terminates in a finite number of steps at a local or weak local solution. Furthermore, we propose a distribution loss function that fluctuates with the input data and introduce it into the general model to obtain a plane-based clustering method (DPC). DPC can capture the data distribution precisely because of its statistical characteristics, and its termination that finitely terminates at a weak local solution is given immediately based on the general model. The experimental results show that our DPC outperforms the state-of-the-art plane-based clustering methods on many synthetic and benchmark data sets.

中文翻译：

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具有分布损失的基于通用平面的聚类


在本文中，我们提出了基于平面的聚类的通用模型。通用模型揭示了聚类实现过程中聚类分配和聚类更新之间的关系，它包含许多现有的基于平面的聚类方法，例如k平面聚类、近端平面聚类、孪生支持向量聚类及其扩展。在这个通用模型下，人们可以获得适合特定目的的聚类方法。通用模型是对应于优化问题的过程，其最小化样本的总损失。其中，样本的损失来源于簇内和簇间信息。我们讨论了理论终止条件，并证明了一般模型在局部或弱局部解处以有限步数终止。此外，我们提出了一种随输入数据波动的分布损失函数，并将其引入到通用模型中以获得基于平面的聚类方法（DPC）。 DPC因其统计特性而能够精确地捕捉数据分布，并且根据一般模型立即给出有限终止于弱局部解的终止点。实验结果表明，我们的 DPC 在许多合成和基准数据集上优于最先进的基于平面的聚类方法。