基于约束图的鲁棒半监督不相关岭回归聚类  

Robust semi-supervised uncorrelated ridge regression clustering based on constraint graph

作　　者：朱建勇 王敬文 杨辉 聂飞平 ZHU Jian-yong;WANG Jing-wen;YANG Hui;NIE Fei-ping(School of Electrical and Automation Engineering,East China Jiaotong University,Nanchang 330013,China;Key Laboratory of Advanced Control and Optimization of Jiangxi Province,Nanchang 330013,China;School of Artificial Intelligence,OPtics and ElectroNics(iOPEN),Northwestern Polytechnical University,Xi’an 710072,China)

机构地区：[1]华东交通大学电气与自动化工程学院,南昌330013 [2]江西省先进控制与优化重点实验室,南昌330013 [3]西北工业大学光电与智能研究院(iOPEN),西安710072

出　　处：《控制与决策》2025年第4期1321-1330,共10页Control and Decision

基　　金：国家自然科学基金项目(62363010);国家自然科学基金重大项目(61991404);江西省双千计划项目(SSQ2023018)。

摘　　要：岭回归由于简单高效被用于处理各种机器学习任务,并取得令人称赞的结果.然而,当岭回归直接应用于聚类时,易触发平凡解.为解决此问题,提出基于约束图的鲁棒不相关岭回归方法(RURCG).首先,利用广义不相关约束使得岭回归嵌入流形结构,保证其聚类时存在闭式解;然后,为了避免异常数据对聚类的影响,对岭回归的误差项施加二值向量,该向量的元素具有明确的物理意义,若数据正常,则其值为1,否则为0;接着,对岭回归嵌入拉普拉斯构造来获取数据的局部几何结构,使得聚类结构更为充分,其中涉及的图矩阵包含成对约束和标签信息;最后,运用迭代优化策略求解目标函数,通过在8个基准数据集上的仿真实验验证所提出方法的有效性.Ridge regression is utilized to tackle various machine learning tasks due to its simplicity and efficiency,and achieves praiseworthy results.However,when ridge regression is directly applied in clustering,it can easily lead to trivial solutions.To address this problem,this paper proposes a method of robust uncorrelated ridge regression with constraint graph(RURCG).Firstly,the method utilizes the generalized uncorrelated constraints to make the ridge regression embedded in the manifold structure,which guarantees the existence of a closed-form solution for its clustering.Then,to avoid the impact of outlier data for clustering,a binary vector is imposed on the error term of the ridge regression.The element values of this vector contain a definite physical meaning,with its value being 1 if the data are normal,otherwise,the value being 0.Next,a laplace construction is embedded in the ridge regression to obtain the local geometrical structure,which involves the graph matrix containing pairwise constraints and labeling information in order to make the clustering structure more adequate.Finally,an iterative optimization strategy is applied to solve the objective function,and simulation experiments on eight benchmark datasets verify the effectiveness of the proposed method.

关 键 词：半监督聚类 岭回归 不相关约束 二值向量 辅助信息 图正则化 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]