基于L2,1-范数的函数型数据稀疏典型相关分析OA
Sparse Canonical Correlation Analysis with L2,1-Norm for Functional Data
函数型数据的典型相关分析是多元统计领域中用于识别两个函数型数据集间最优线性相关性的关键方法.然而,这些数据集中的部分函数可能出现异常情况,如偏离整体趋势的突变或波动,进而导致结果失准.针对该问题,本文提出一种改进方法:基于L2,1-范数的函数型数据稀疏典型相关分析.该方法通过优化正交基函数的选取来抑制离群值,提升分析的精度与可靠性.数值实验表明,基于L2,1-范数的方法在性能上显著优于传统方法.
Functional canonical correlation analysis is a key method in multivariate statistics for identifying optimal linear correlations between two functional datasets.However,some functions within these datasets may exhibit anomalies such as sudden changes or fluctuations that deviate from the overall trend,resulting to inaccurate results.To address this,we propose an improved method:Sparse functional canonical correlation analysis based on the L2,1-norm.This approach reduces outliers by optimizing the selection of orthogonal basis functions,thereby enhancing the accuracy and reliability of the analysis.Nu-merical experiments show that the L2,1-norm-based method significantly outperforms traditional methods.
张泽江;杨志霞;叶俊佑;汪玉兰
新疆大学 数学与系统科学学院,新疆 乌鲁木齐 830017新疆大学 数学与系统科学学院,新疆 乌鲁木齐 830017新疆大学 数学与系统科学学院,新疆 乌鲁木齐 830017新疆大学 数学与系统科学学院,新疆 乌鲁木齐 830017
数理科学
函数型典型相关分析L2,1-范数函数型数据异常值正交基函数
functional canonical correlation analysisL2,1-normfunctional dataoutliersorthogonal basis function
《新疆大学学报（自然科学版中英文）》 2026 (3)
305-323,19
The National Natural Science Foundation of China"Optimization models and algorithms for interpretable lear-ning machines on complex data"(12461058)Xinjiang Key Laboratory of Applied Mathematics(XJDX1401).
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