您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (4): 84-91.doi: 10.6040/j.issn.1671-9352.0.2024.438

• • 上一篇    

基于深度与融合类信息的函数型数据重构方法

黄介武,陈星悦*,王淋杰,饶文康   

  1. 贵州民族大学数据科学与信息工程学院, 贵州 贵阳 550025
  • 发布日期:2026-04-08
  • 通讯作者: 陈星悦(2001— ),女,硕士研究生,研究方向为统计模型与统计计算. E-mail:2418231562@qq.com
  • 作者简介:黄介武(1977— ),男,教授,硕士生导师,博士,研究方向为统计模型与统计计算. E-mail:846221886@qq.com*通信作者:陈星悦(2001— ),女,硕士研究生,研究方向为统计模型与统计计算. E-mail:2418231562@qq.com
  • 基金资助:
    贵州省教育厅自然科学研究项目(黔教技［2023］012号,黔教技［2023］061号)

A depth-based and fusion class information reconstruction method for functional data

HUANG Jiewu, CHEN Xingyue*, WANG Linjie, RAO Wenkang   

  1. School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, Guizhou, China
  • Published:2026-04-08

PDF (PC)

4

摘要： 针对部分观测函数型数据,提出一种基于深度与融合类信息的重构方法。运用基于深度的重构方法以及从K均值聚类中获取的样本曲线类间信息,在不同分类情形下对每条部分观测样本曲线进行重构。然后,利用自加权集成学习算法动态赋权,将各类别下的重构曲线融合,得到最终的重构曲线。数值模拟和实例分析表明:当样本中部分观测样本曲线占比较大时,所提方法在均方预测误差准则下优于基于深度的重构方法及正则化回归方法;而在部分观测样本曲线占比较小时,正则化回归方法表现更优。

关键词: 部分观测函数型数据, 函数型数据重构, 数据深度, 类信息

Abstract: A depth-based and fusion class information reconstruction method is proposed for partially observed functional data. By applying the depth-based reconstruction method and the inter-class information of sample curves derived from K-means clustering, each partially observed sample curve is reconstructed under different classification scenarios. Then, with the weights dynamically assigned by the self-weighted ensemble learning algorithm, final reconstructed curves are obtained by combining the reconstructed curves of each class. Simulation studies and case analysis show that the proposed method outperforms the depth-based reconstruction method and the regularized regression method under the mean-square prediction error criterion when the proportion of partially observed sample curves in the sample is large. Conversely, the regularized regression method performs better when the proportion of partially observed sample curves is small.

Key words: partially observed functional data, reconstruction of functional data, data depth, class information

中图分类号: 

  • O212.1
[1] RAMSAY J O, SILVERMN B W. Functional data analysis[M]. New York: Springer, 2005: 19-34.
[2] JAMES G M, HASTIE T J, SUGAR C A. Principal component models for sparse functional data[J]. Biometrika, 2000, 87:587-602.
[3] CHIOU J M, ZHANG Y C, CHEN W H, et al. A functional data approach to missing value imputation and outlier detection for traffic flow data[J]. Transportmetrica B(Transport Dynamics), 2014, 2(2):106-129.
[4] KRAUS D. Components and completion of partially observed functional data[J]. Journal of the Royal Statistical Society Series B: Statistical Methodology, 2015, 77(4):777-801.
[5] KRAUS D, STEFANUCCI M. Ridge reconstruction of partially observed functional data is asymptotically optimal[J]. Statistics & Probability Letters, 2020, 165(20):108813.
[6] KNEIP A, LIEBL D. On the optimal reconstruction of partially observed functional data[J]. The Annals of Statistics, 2020, 48(3):1692-1717.
[7] LI P L, CHIOU J M. Functional clustering and missing value imputation of traffic flow trajectories[J]. Transportmetrica B:Transport Dynamics, 2021, 9(1):1-21.
[8] 高海燕,马文娟,薛娇. 融合类信息的函数型矩阵填充方法与应用[J]. 统计与决策,2023,39(23):40-45. GAO Haiyan, MA Wenjuan, XUE Jiao. Functional matrix completion method with class information and its application[J]. Statistics & Decision, 2023, 39(23):40-45.
[9] 杨玉杰,凌能祥. 不完全观测的部分函数型线性分位数回归模型及应用[J]. 山东大学学报(理学版),2025,60(3):100-106. YANG Yujie, LING Nengxiang. Partially linear quantile regression model and empirical research for incomplete functional data[J]. Journal of Shangdong University(Natural Science), 2025, 60(3):100-106.
[10] LIEBL D, RAMESEDER S. Partially observed functional data: the case of systematically missing parts[J]. Computational Statistics & Data Analysis, 2019, 131:104-115.
[11] ELÍAS A, JIMÉNEZ R, SHANG H L. Depth-based reconstruction method for incomplete functional data[J]. Computational Statistics, 2023, 38(3):1507-1535.
[12] DELAIGLE A, HALL P. Classification using censored functional data[J]. Journal of the American Statistical Association, 2013, 108(504):1269-1283.
[13] ELÍAS A, JIMÉNEZ R, PAGANONI A M, et al. Integrated depths for partially observed functional data[J]. Journal of Computational and Graphical Statistics, 2023, 32(2):341-352.
[14] ELÍAS A, JIMÉNEZ R, SHANG H L. On projection methods for functional time series forecasting[J]. Journal of Multivariate Analysis, 2022, 189:104890.
[15] TUKEY J W. Mathematics and the picturing of data[J]. Proceedings of the International Congress of Mathematicians, 1975, 2:523-531.
[16] LIU R Y. On a notion of simplicial depth[J]. Proceedings of the National Academy of Sciences, 1988, 85(6):1732-1734.
[17] MAHALANOBIS P C. On the generalized distance in statistics[J]. Sankhyā(The Indian Journal of Statistics), Series A, 2018, 80:S1-S7.
[18] FRAIMAN R, MUNIZ G. Trimmed means for functional data[J]. Test, 2001, 10:419-440.
[19] LÓPEZ-PINTADO S, ROMO J. On the concept of depth for functional data[J]. Journal of the American Statistical Association, 2009, 104(486):718-734.
[1] 张翠芸,郭精军,马爱琴. 基于离散观测的次分数Vasicek模型的参数估计[J]. 《山东大学学报(理学版)》, 2023, 58(11): 15-26.
[2] 娘毛措, 陈占寿, 成守尧, 汪肖阳. 具有长记忆误差的线性回归模型参数变点的在线监测[J]. 《山东大学学报(理学版)》, 2022, 57(4): 91-99.
[3] 任鹏程,徐静,李新民. 风险价值VaR的区间估计[J]. 山东大学学报（理学版）, 2017, 52(2): 85-90.
[4] 王小焕,吕广迎,戴利杰. Gronwall不等式的推广及应用[J]. 《山东大学学报(理学版)》, 2022, 57(6): 94-101.
[5] 张宪友,李东喜. 基于spike-and-slab先验分布的贝叶斯变量选择方法[J]. 《山东大学学报(理学版)》, 2021, 56(12): 84-93.
[6] 侯成婷,陈占寿. 基于LSCUSUM方法的RCA(1)模型参数变点检验[J]. 《山东大学学报(理学版)》, 2025, 60(3): 107-115.
[7] 段体城,许成凯,鲁紫婕,贾沛焱,谢素雅,杨文志. 混合误差下一阶适度爆炸自回归模型最小二乘估计[J]. 《山东大学学报(理学版)》, 2025, 60(3): 77-87.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发