基于ADMM的拉普拉斯约束表示型聚类算法  

Laplacian regularizer clustering via ADMM implementation

作　　者：王万良[1] 朱文博[1] 郑建炜[1] WANG Wanliang,ZHU Wenbo,ZHENG Jianwei(College of Computer Science and Technology,Zhejiang University of Technology,Hangzhou 310023,Chin)

机构地区：[1]浙江工业大学计算机科学与技术学院,浙江杭州310023

出　　处：《浙江工业大学学报》2018年第4期363-368,381,共7页Journal of Zhejiang University of Technology

基　　金：国家自然科学基金资助项目(61602413;61502424;61379123);浙江省自然科学基金资助项目(LY15F030014)

摘　　要：作为数据挖掘领域的关键技术,子空间分割对在联合子域内所分布的输入数据进行潜在的流型聚类.谱聚类因具备出色的性能被作为子空间分割算法中的首选,其性能主要依赖于由输入样本构造的关联矩阵.在平滑聚类算法的基础上结合拉普拉斯矩阵学习机制,提出一种用联合样本系数以及关联矩阵学习的新型聚类模型.同时,为快速获取清晰的对角块结构,对目标函数增加低秩正则项约束,并通过交替方向最小乘子法进行模型优化求解.所提方法称为基于ADMM(Alternating direction minimizing multiplier)的拉普拉斯约束表示型聚类算法(Laplacian regularizer clustering,LRC).通过实证结果表明:所提方法具有更高的聚类效果和更快的运行效率,综合性能优于相关的聚类方法.As a key technology in the field of data mining,subspace segmentation is used to segment a set of data drawn from the union of subspaces into its underlying subspace.Spectral clustering is preferred as a subspace segmentation method whose performance is heavily dependent on the affinity matrix that is usually constructed from the original data or its corresponding representation.Based on smooth representation clustering approach and the Laplacian matrix learning mechanism,a new clustering model based on representations of data and affinity matrices is proposed.Furthermore,in order to fast acquire a clear diagonal block structure,the objective function is constrained by the low-rank regularization,and the model is optimized by alternating the direction minimizing multiplier,the proposed method is named as Laplacian regularizer clustering via ADMM implementation,LRC.The empirical results show that the proposed method has higher clustering effect and faster operation efficiency,overall performance is better than the relevant clustering method.

关 键 词：子流形分簇 拉普拉斯矩阵 交替方向最小乘子法 秩约束 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]