基于可靠邻居与精确簇数的稀疏子空间聚类  

Sparse subspace clustering based on reliable neighbors and exact cluster number

作　　者：郑毅 马盈仓[1] 杨小飞[1] Zheng Yi;Ma Yingcang;Yang Xiaofei(School of Science,Xi’an Polytechnic University,Xi’an 710600,China)

机构地区：[1]西安工程大学理学院,西安710600

出　　处：《计算机应用研究》2021年第1期75-82,共8页Application Research of Computers

基　　金：国家自然科学基金资助项目(11501435);陕西省教育厅科研计划项目(18JS042);陕西省重点研发计划项目(2018KW-021)。

摘　　要：为了获得更加可靠的相似矩阵,并使其含有精确的连通分支数量,提出了一种新的稀疏子空间聚类算法。该算法利用K近邻思想从局部寻找可靠邻居,在距离度量方面,选用测地线距离进行计算,考虑了数据在高维空间分布的几何结构,使得数据的邻居关系更加合理。同时,利用Ky Fan定理,通过参数的自适应调节,使得相似矩阵包含精确的连通分支数量。此外,该算法打破了常规的两步走模式,同时进行相似矩阵的学习和谱聚类过程,将数据相似性度和分割进行了紧密的联系,进一步加强了对数据结构信息的挖掘和利用。在人造数据集、图像数据集以及真实数据集进行了实验,实验结果表明该算法是有效的。In order to obtain a more reliable similarity matrix and make it contain the exact number of connected branches,this paper proposed a new sparse subspace clustering algorithm.The algorithm used the K nearest neighbor idea to find reliable neighbors from the local.In the aspect of distance metric,the algorithm selected the geodesic distance for calculation,and considered the geometric structure of the data in the high-dimensional space,which made the neighbor relationship of the data more reasonable.At the same time,using the Ky Fan theorem,the adaptive matrix adjusted the parameters so that the similar matrix contained the exact number of connected branches.In addition,the algorithm broke the conventional two-step mode,and simultaneously performed similar matrix learning and spectral clustering process,which closely linked data similarity and segmentation,further strengthening the mining and utilization of data structure information.The results of the experiments on artificial datasets,image datasets and real datasets show that the algorithm is effective.

关 键 词：K近邻 测地线距离 子空间聚类 连通分支数量 相似矩阵 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]