电子学报2026，Vol.54Issue(1)：32-49,18.DOI:10.12263/DZXB.20250938
转置投影包络线性判别分析
Transposed Projection Envelope Linear Discriminant Analysis
摘要
Abstract
Linear discriminant analysis(LDA)is a widely used feature extraction method guided by Fisher's discrimi-nant criterion.It enhances the separability of dissimilar samples and the compactness of similar samples within the sub-space,thereby improving the quality of dimensionality reduction results.With its mature,interpretable,simple,and efficient advantages,it remains one of the research hotspots in both academia and industry to date.Numerous scholars have refined LDA to further enhance its performance.However,these LDA variants model directly at the original sample granularity,uti-lizing only the information inherent within the samples themselves.The data-information-knowledge(DIK)model indicates that human knowledge acquisition occurs across three levels:data,information,and knowledge.Data must first be trans-formed into information,from which knowledge is then learned.Human cognitive mechanisms reveal that the information layer encompasses not only the inherent properties of raw inputs but also correlation information among similar inputs.Analogously,in LDA's dimensionality reduction process,extracted features represent information that should also incorpo-rate correlation information among similar samples to enhance downstream task performance.Furthermore,existing re-search demonstrates that the correlation information between similar samples is crucial for machine learning model con-struction and knowledge acquisition.This indicates that existing LDA has limitations,as it does not fully utilize sample in-formation.To address these issues,this paper proposes transposed projection envelope linear discriminant analysis(TPEL-DA).First,transposed projection transforms original samples into envelope samples that encapsulate correlation informa-tion among similar samples.The core idea of transposed projection is to reduce the dimensionality of a batch of nearest neighbor samples along the sample dimension,ensuring the resulting envelope sample retain as much information as possi-ble from the original batch.Subsequently,Fisher's discriminant criterion is employed to learn a reduced-dimension sub-space based on these envelope samples.A distribution-difference penalty term is introduced to ensure the reduced sub-space's adaptability to the original samples.Finally,through joint optimization,this method enhances the discriminative fea-tures of samples projected into the subspace by incorporating the correlation information among similar samples.Thus,the resulting features simultaneously represent both the intrinsic information of individual samples and the correlation informa-tion among similar samples.Experimental results demonstrate that TPELDA outperforms relevant comparison methods across multiple datasets,achieving performance improvements ranging from 2.25%to 13.19%.Furthermore,combined with other experimental findings,the effectiveness of the proposed method is confirmed.关键词
线性判别分析/降维/关联信息/分布差异/包络学习/特征提取Key words
linear discriminant analysis/dimensionality reduction/correlation information/distribution discrepancy/envelope learning/feature extraction分类
信息技术与安全科学引用本文复制引用
李勇明,赵文强,李帆,张小恒,王品..转置投影包络线性判别分析[J].电子学报,2026,54(1):32-49,18.基金项目
国家自然科学基金(No.62201106) National Natural Science Foundation of China(No.62201106) （No.62201106）
