计算机应用

• 人工智能与仿真 •    下一篇

基于Hessian正则化和非负约束的低秩表示子空间聚类算法

范莉莉1,卢桂馥1,唐肝翌1,杨丹2   

  1. 1. 安徽工程大学计算机与信息学院
    2. 安徽工程科技学院
  • 收稿日期:2021-07-08 修回日期:2021-09-03 发布日期:2021-09-16 出版日期:2021-09-16
  • 通讯作者: 范莉莉

Low-rank representation subspace clustering method based on Hessian regularization and non-negative constraint

  • Received:2021-07-08 Revised:2021-09-03 Online:2021-09-16 Published:2021-09-16

摘要: 针对低秩表示子空间聚类方法(LRR)没有考虑数据局部结构,在学习中可能会造成局部相似信息丢失的问题,提出了一种基于Hessian正则化和非负约束的低秩表示子空间聚类算法(LRR-HN),来探索数据的全局结构和局部结构。首先,利用Hessian正则化良好的推测能力来保持数据的局部流形结构,使数据局部拓扑结构的表达能力更强;其次,考虑到获得的系数矩阵往往有正有负,而负值往往没有实际意义的特点,引入非负约束来保证模型解的有效性,使其在数据局部结构描述上更有意义;最后,通过最小化核范数寻求数据全局结构的低秩表示,从而更好地聚类高维数据。此外,本文利用自适应惩罚的线性交替方向法,设计了一种求解LRR-HN的有效算法,并在一些实际数据集上,采用正确率(AC)和归一化互信息(NMI)对所提出的算法进行了评估。ORL数据集上的实验表明,LRR-HN算法与LRR算法相比,AC和NMI分别提高了11%和9.74%;与自适应低秩表示(ALRR)算法相比,AC和NMI分别提高了5%和1.05%。实验结果表明,LRR-HN算法与现有的一些算法相比,AC和NMI均有较大的提升,体现出了其良好的聚类性能。

Abstract: Focused on the issue that the low-rank representation subspace clustering method (LRR) does not consider the local structure of the data and may cause the loss of local similar information during learning, an algorithm named Low-Rank Representation subspace clustering method based on Hessian regularization and Non-negative constraint (LRR-HN) was proposed to explore the global and local structure of the data. Firstly, the good speculative ability of Hessian regularization was used to maintain the local manifold structure of the data, so that the local topological structure of the data was more expressive. Secondly, considering that the obtained coefficient matrix often has positive and negative values, and the negative values often have no practical significance, non-negative constraints were introduced to ensure the effectiveness of the model solution and made it more meaningful in the description of the local structure of the data. Finally, the low-rank representation of the global structure of the data was sought by minimizing the nuclear norm, in order to cluster high-dimensional data better. In addition, an effective algorithm for solving LRR-HN was designed by using the linearized alternating direction method with adaptive penalty, and the proposed algorithm was evaluated by AC and NMI on some actual datasets. Experiments on ORL dataset showed that compared with LRR, the AC and NMI of LRR-HN increased by 11% and 9.74% respectively, and compared with Adaptive Low-Rank Representation (ALRR), the AC and NMI of it increased by 5% and 1.05% respectively. The experimental results show that LRR-HN has greater improvement in AC and NMI than other existing algorithms, which reflects its excellent clustering performance.

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