General plane-based clustering with distribution loss
General plane-based clustering with distribution loss
复制标题
具有分布损失的基于通用平面的聚类
DOI：
10.1109/tnnls.2020.3016078
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发表时间：
--
影响因子：
10.4
通讯作者：
Li-Ming Liu
中科院分区：
文献类型：
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作者：
Zhen Wang;Yuan-Hai Shao;Lan Bai;李春娜;Li-Ming Liu
在本文中，我们提出了一个基于平面聚类的通用模型。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，它包含了许多现有的基于平面的聚类方法，如k面聚类、近面聚类、双支持向量聚类及其扩展。在此一般模型下，可以得到适合特定目的的聚类方法。一般模型是一个与优化问题相对应的过程，其目的是使样本的总损失最小化。其中，样本的损失来源于簇内信息和簇间信息。我们讨论了理论终止条件，并证明了一般模型在有限步中终止于局部解或弱局部解。此外，我们提出了一个随输入数据波动的分布损失函数，并将其引入到一般模型中，从而得到基于平面的聚类方法（DPC）。由于DPC的统计特性，它可以精确地捕捉数据的分布，并在一般模型的基础上立即给出了它的有限终止于弱局部解的终止。实验结果表明，在许多合成数据集和基准数据集上，我们的聚类方法优于最先进的基于平面的聚类方法。
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.