基于信息熵的鲁棒稀疏子类判别分析  

Robust Sparse Subclass Discriminant Analysis Based on Information Entropy

作　　者：杨源 周跃进 Yang Yuan;Zhou Yuejin(Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学,安徽淮南232001

出　　处：《廊坊师范学院学报（自然科学版）》2024年第3期42-52,共11页Journal of Langfang Normal University(Natural Science Edition)

基　　金：深部煤矿采动响应与灾害防控国家重点实验室基金资助项目(SKLMRDPC22KF03)。

摘　　要：线性判别分析(Linear discriminant analysis,LDA)作为一种有监督的降维方法,已经广泛应用于各个领域。然而,传统的LDA存在以下缺点:1)LDA假设数据是高斯分布和单一模态的;2)LDA对异常值和噪声十分敏感;3)LDA的判别投影方向对特征的可解释性低且对降维数较为敏感。为克服以上问题,提出了基于信息熵的鲁棒稀疏子类判别分析(Robust sparse subclass discriminant analysis based on information entropy,RSSDAIE)新方法。具体而言,对每个类别划分不同数量的子类后,重新定义类内散射矩阵和类间散射矩阵,使其更适应现实数据。另外,引入L_(21)范数、稀疏矩阵和正交重构矩阵以确保RSSDAIE具有更高的鲁棒性、更好的可解释性和更低的维度敏感性。同时采用交替方向乘子法对目标函数求解,避免类内散射矩阵不可逆的情形。在多个数据集上进行了对比实验,证明了RSSDAIE在数据适用类型、降低噪声影响、减少降维数影响等方面更有优越性,分类准确率更高。Linear discriminant analysis(LDA),as a supervised dimension reduction method,has been widely applied in various fields.However,traditional LDA has the following drawbacks:1)LDA assumes that the data are Gaussian distributed and unimodal.2)LDA is very sensitive to outlier and noise.3)the discriminant projection direction of LDA has low interpretability of features and is sensitive to the number of dimension reduction.In this paper,a novel method called robust sparse subclass discriminant analysis based on information entropy(RSSDAIE)is proposed to solve the above problems.Specifically,to make RSSDAIE more consistent with real data,each class is divided into different subclasses,and the within-class and between-class scattering matrix are redefined.The L_(21),norm,a sparse matrix and orthogonal reconstruction matrix are also simultaneously introduced to ensure that RSSDAIE has more robustness and interpretability and reduces the dimensional sensitivity.The objective function is solved by the alternating direction multiplier method to avoid the irreversibility of the within-class scattering matrix.Extensive experiments on several datasets prove that RSSDAIE has more superior advantage in adapting to data types,reducing the effect of noise and dimensionality and has higher classification accuracy compared with other related methods.

关 键 词：类内多模态 信息熵 判别分析 L_(21)范数 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]