基于自适应对偶图与非凸约束的嵌入特征选择  

Adaptive dual graphs and non-convex constraint based embedded feature selection

作　　者：尚荣华 徐开明 焦李成 Ronghua SHANG;Kaiming XU;Licheng JIAO(School of Artificial Intelligence,Xidian University,Xi'an 710071,China)

机构地区：[1]西安电子科技大学人工智能学院,西安710071

出　　处：《中国科学：信息科学》2021年第10期1640-1657,共18页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:61773304);重大研究计划(批准号:91438201);教育部“长江学者和创新团队发展计划”(批准号:IRT 15R53)资助项目。

摘　　要：在传统的特征选择方法中,为了保证行的稀疏性,经常采用l_(1)范数或者l_(2,1)范数来约束评价矩阵.作为凸正则项,它们在多数情况下可以发挥良好的作用.然而在处理冗余性特征时,一些非凸正则项有望表现出更好的性能.借助自适应流形学习与非凸约束的优点,本文提出了一种新的算法,叫做基于自适应对偶图与非凸约束的嵌入特征选择(adaptive dual graphs and non-convex constraint based embedded feature selection, DNEFS).借助稀疏回归框架, DNEFS同时保留了数据空间与特征空间的流形结构信息.通过运用信息熵原理,对偶图中的局部流形信息可以自适应的学习与更新,因此可以获得更好的特征选择效果.不同于传统的凸约束,本文引入了一个新的非凸正则项,这一正则项由l_(2,1)范数与Frobenius范数的差分构成,并记为l_(2,1-2)范数.通过使用这一新正则项, DNEFS可以更好地处理冗余性的特征.本文运用交替迭代更新的方式来优化目标函数,并在6个基准数据集上测试DNEFS算法的性能.通过与6种对比算法做对比,实验结果表明提出的DNEFS优于对比算法的性能.In traditional feature selection methods, to guarantee the sparsity of the rows, l_(1)-norm or l_(2,1)-norm is often used to constrain the evaluation matrix. As convex regularization terms, they work well in most cases.However, when dealing with redundant features, some non-convex regularization terms tend to show better performance. With the advantages of adaptive manifold learning and non-convex constraints, a novel algorithm is proposed in this paper, called adaptive dual graphs and non-convex constraint based embedded feature selection(DNEFS). With the framework of sparse regression, DNEFS preserves the manifold structure information of both data space and feature space, simultaneously. Meanwhile, by using the principle of information entropy, the local manifold information in dual graphs can be learned and updated adaptively, resulting in a better feature selection effect. Different from traditional convex constraints, a novel non-convex regularization term is introduced in this paper. This regularization term consists of the difference between l_(2,1)-norm and Frobenius norm, and is written as l_(2,1-2)-norm. By using this novel regularization term, DNEFS can handle redundant features more efficiently.Then, an alternating iterative updating method is used in this paper to optimize the objective function, and six benchmark datasets are used to test the performance of DNEFS. By comparing with six comparison algorithms,the experimental results show that DNEFS can achieve better performance.

关 键 词：对偶图 流形结构 非凸约束 嵌入 特征选择 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]