判别性增强的稀疏子空间聚类

doi:10.19678/j.issn.1000-3428.0063621

计算机工程 ›› 2023, Vol. 49 ›› Issue (2): 98-104. doi: 10.19678/j.issn.1000-3428.0063621

判别性增强的稀疏子空间聚类

胡慧旗, 张维强, 徐晨

深圳大学数学与统计学院, 广东深圳 518060

收稿日期:2021-12-27 修回日期:2022-03-30 发布日期:2022-07-18
作者简介:胡慧旗(1998-),女,硕士研究生,主研方向为子空间聚类;张维强,副教授、博士;徐晨(通信作者),教授、博士。
基金资助:
国家自然科学基金“多视角聚类关键科学问题及其在图像分割中的应用研究”（61972264）；国家自然科学基金“基于高阶张量分解的复杂视频显著性目标探测模型”（61872429）；广东省自然科学基金“多视角聚类及其在健康信息学中的应用”（2019A1515010894）；深圳市高校稳定支持计划“基于深度神经网络的多视角聚类研究”（20200807165235002）。

Discriminant Enhanced Sparse Subspace Clustering

HU Huiqi, ZHANG Weiqiang, XU Chen

College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, Guangdong, China

Received:2021-12-27 Revised:2022-03-30 Published:2022-07-18

摘要/Abstract

摘要： 稀疏关系表示（SRR）是一种性能良好的子空间聚类算法，其利用一个数据样本和所有样本间的邻域关系作为新特征来学习自表示系数，由自表示系数矩阵构建相似度矩阵并通过谱聚类得到聚类结果。同时考虑相似度矩阵的稀疏性和聚集性，在SRR算法基础上提出一个判别性增强的稀疏子空间聚类模型。对邻域关系矩阵的自表示矩阵采用平方F范数代替SSR中的核范数，降低模型求解难度，并在邻域关系矩阵的自表示矩阵中引入新的正则项，保证自表示矩阵的类间判别性和邻域关系矩阵的类内聚集性，进一步优化聚类性能。实验结果表明：与SSC、LRR、LSR、BDR-B、SRR等模型相比，该模型具有较好的聚类性能；在MNIST、USPS、ORL数据集上，聚类错误率较SRR模型分别下降9.6、14.1、3.8个百分点；在Extended Yale B数据集上，针对2、3、5、8、10类聚类问题的聚类错误率较SRR模型分别下降0.39、0.72、1.32、2.73、3.28个百分点。

关键词: 子空间聚类, 相似度矩阵, 邻域关系, 判别性, 谱聚类

Abstract: The Sparse Relation Representation(SRR) algorithm shows good clustering performance.It uses the neighborhood relation between a data sample and other samples as new features to learn the self-representation coefficient, which is then used to construct the affinity matrix;spectral clustering is finally applied to realize segmentation.Considering both the sparsity and aggregation of a similarity matrix, this study proposes a discriminant-enhanced sparse subspace clustering model based on the SSR algorithm.The study's novelty is two-fold:first, to overcome the complexity induced by the nuclear norm in SSR, it uses the squared F norm to regularize the self-representation matrix;second, it introduces a new regularization term that can guarantee the inter-class discrimination of the self-expression coefficient matrix and grouping effect of the neighborhood relation matrix.The experimental results show that compared with SSC, LRR, LSR, BDR-B, SRR, and other models, this model has better clustering performance.On MNIST, USPS, and ORL datasets, the clustering error rate of this model is 9.6, 14.1, and 3.8 percentage points lower than that of the SRR model, respectively;on the Extended Yale B dataset, the clustering error rates of the model in the 2, 3, 5, 8, and 10 cluster problems are 0.39, 0.72, 1.32, 2.73, and 3.28 percentage points lower than in the SRR model, respectively.

Key words: subspace clustering, affinity matrix, neighborhood relation, discrimination, spectral clustering

中图分类号:

TP391.4

胡慧旗, 张维强, 徐晨. 判别性增强的稀疏子空间聚类[J]. 计算机工程, 2023, 49(2): 98-104.

HU Huiqi, ZHANG Weiqiang, XU Chen. Discriminant Enhanced Sparse Subspace Clustering[J]. Computer Engineering, 2023, 49(2): 98-104.

http://www.ecice06.com/CN/Y2023/V49/I2/98

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