北大中文核心期刊
中国科学引文数据库（CSCD）来源期刊
中国科技核心期刊
入选数学领域高质量科技期刊
Scopus
EBSCO 

运筹学学报 >

2026 , Vol. 30 >Issue 3: 1 - 22

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2026.03.001

运筹与管理前沿：模型、算法及其应用专辑

一种基于嵌入空间的多变量插补算法及其应用研究

  • 张沈锴 ,
  • 李婷 ,
  • 万平澜 ,
  • 韩德仁
展开
  • 1. 北京航空航天大学数学科学学院, 北京 102206;
    2. 江苏师范大学数学与统计学院, 江苏徐州 221116

收稿日期: 2026-05-21

  网络出版日期: 2026-09-12

基金资助

中国中医科学院科技创新工程(No.CI2023C064YLL),国家自然科学基金(Nos.12131004,12471282),国家重点研发计划(No.2024YFA1012901)

收起

A multivariate imputation algorithm based on embedding space and its application research

  • ZHANG Shenkai ,
  • LI Ting ,
  • WAN Pinglan ,
  • HAN Deren
Expand
  • 1. School of Mathematical Sciences, Beihang University, Beijing 102206, China;
    2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, Jiangsu, China

Received date: 2026-05-21

  Online published: 2026-09-12

Fold

摘要

为解决短期高维数据稀疏与缺失带来的分析难题,本研究提出基于广义(q,p)嵌入空间的多变量时序插补算法。该算法通过同时提取所需插补节点前q个与后p个时刻的多变量联合状态信息,对变量之间的内在关系构建双向约束,从而实现对高维复杂数据的缺失值填补和数据扩增。在高血压中医临床数据上的实验表明,相较原始数据,经算法扩增后的时序数据可使基于长短期记忆网络的“痰瘀互结证”预测分类准确率提升13.0%;对于缺失值填补,基于插补修复数据的痰证与血瘀证插补诊断准确率分别达到84.2%和77.2%。

关键词： Takens定理; 随机分布嵌入; 多变量时序插补; 长短期记忆网络; 高血压病; 痰瘀互结证

本文引用格式

张沈锴 , 李婷 , 万平澜 , 韩德仁 . 一种基于嵌入空间的多变量插补算法及其应用研究[J]. 运筹学学报, 2026 , 30(3) : 1 -22 . DOI: 10.15960/j.cnki.issn.1007-6093.2026.03.001

Abstract

To address the challenges of sparsity and missingness in short-term high-dimensional data, this study proposes a multivariate time series imputation algorithm based on the generalized (q, p) embedding space. The proposed algorithm simultaneously extracts the multivariate joint state information from the q preceding and p succeeding time points around the target imputation node, and establishes bidirectional constraints on the intrinsic relationships among variables, thereby achieving missing value imputation and data augmentation for high-dimensional complex data. Experiments on Traditional Chinese Medicine clinical data for hypertension yield two principal findings. First, regarding predictive inference, the time series data augmented by the proposed algorithm yield a 13.0% improvement in the classification accuracy of the "syndrome of intermin-gled phlegm and blood stasis" based on Long Short-Term Memory. Second, regarding missing value imputation, the binary classification accuracies for the diagnosis of phlegm syndrome and blood stasis syndrome reach 84.2% and 77.2%, respectively.

Key words： Takens' theorem; random distributed embedding; multivariate time series imputation; long short-term memory; hypertension; syndrome of intermin-gled phlegm and blood stasis

参考文献

[1] Epperson J F. An introduction to numerical methods and analysis [M]. New Jersey: John Wiley & Sons, 2013.
[2] Troyanskaya O, Cantor M, Sherlock G, et al. Missing value estimation methods for DNA microarrays [J]. Bioinformatics, 2001, 17(6): 520-525.
[3] Van Buuren S, Groothuis-Oudshoorn K. Mice: multivariate imputation by chained equations in R [J]. Journal of Statistical Software, 2011, 45(3): 1-67.
[4] Dou P, Shen H, Li Z, et al. Time series remote sensing image classification framework using combination of deep learning and multiple classifiers system [J]. International Journal of Applied Earth Observation and Geoinformation, 2021, 103: 102477.
[5] Han D R, Su Y S, Xie J X. Randomized Douglas-Rachford methods for linear systems: improved accuracy and efficiency [J]. SIAM Journal on Optimization, 2024, 34(1): 1045-1070.
[6] Hu L Y, Xie J X, Cai X J, et al. A distributed Douglas-Rachford splitting method for solving linear constrained multi-block weakly convex problems [J]. Inverse Problems and Imaging, 2025, 19(4): 632-659.
[7] 江亚宁, 蔡邢菊, 韩德仁. 求解结构型逆变分不等式问题的黄金比率型 Douglas-Rachford 分裂方法 [J]. 计算数学, 2025, 47(4): 624-642.
[8] Packard N H, Crutchfield J P, Farmer J D, et al. Geometry from a time series [J]. Physical Review Letters, 1980, 45(9): 712.
[9] Takens F. Detecting strange attractors in turbulence [C]//Dynamical Systems and Turbulence, Warwick 1980, 1981: 366-381.
[10] Li D, Lv J, Liu F, et al. Hypertension burden and control in mainland China: analysis of nationwide data 2003|2012[J]. International Journal of Cardiology, 2015, 184: 637-644.
[11] Wang Z, Chen Z, Zhang L, et al. Status of hypertension in China: results from the China Hypertension Survey, 2012|2015[J]. Circulation, 2018, 137(22): 2344-2356.
[12] Lewington S, Clarke R, Qizilbash N, et al. Age-specific relevance of usual blood pressure to vascular mortality: a meta-analysis of individual data for one million adults in 61 prospective studies [J]. Lancet, 2002, 360(9349): 1903-1913.
[13] Lloyd-Jones D M, Larson M G, Leip E P, et al. Lifetime risk for developing congestive heart failure: the framingham heart study [J]. Circulation, 2002, 106(24): 3068-3072.
[14] Klag M J, Whelton P K, Randall B L, et al. Blood pressure and end-stage renal disease in men [J]. The New England Journal of Medicine, 1996, 334(1): 13-18.
[15] 曹东义. 证候是疾病微观变化的动态反映 [J]. 中医药通报, 2006, 5(6): 20-23.
[16] 郭蕾, 王永炎, 张志斌, 等. 证候动态时空特征的复杂性及相应的研究思路 [J]. 中医研究, 2006, 19(3): 1-3.
[17] 魏戌, 谢雁鸣, 田峰, 等. 病证结合构建慢病风险预测模型的思路与方法 [J]. 中国中医基础医学杂志, 2017, 23(6): 798-801.
[18] 张磊, 郭伟星, 李运伦, 等. 高血压痰瘀互结证证治源流及本质探析 [J]. 世界中医药, 2021, 16(10): 1561-1566.
[19] 郭瑞, 王恒和. 近 10 年高血压病中医证素-证候分布特征 [J]. 内蒙古中医药, 2019, 38(10): 144-147.
[20] 王丽颖, 李元, 李娜, 等. 1508 例高血压病患者中医证候分布调查研究 [J]. 中华中医药杂志, 2010, 25(12): 1960-1963.
[21] 徐璡, 李雪萍, 丁晓东, 等. 1331 例高血压病人中医证候分布特征及其影响因素分析 [J]. 中西医结合心脑血管病杂志, 2020, 18(21): 3521-3525.
[22] 程苗苗, 王承龙. 1018 例老年高血压病患者中医证型分布及相关因素分析 [J]. 江苏中医药, 2015, 47(1): 34-36.
[23] 王浩中. 原发性高血压的分级、危险分层、脉压差与中医证型的相关性研究 [D]. 成都: 成都中医药大学, 2006.
[24] 刘福明, 杜午奇, 沈乐, 等. 高血压病左室肥厚与中医证型的相关性研究 [J]. 浙江中医杂志, 2009, 44(12): 871-872.
[25] 宋磊, 鲁成, 王肖龙, 等. 高血压病中医证型与心血管危险因素的相关性研究 [J]. 中国中医急症, 2014, 23(7): 1224-1225.
[26] Miotto R, Wang F, Wang S, et al. Deep learning for healthcare: review, opportunities and challenges [J]. Brief Bioinform, 2018, 19(6): 1236-1246.
[27] Hochreiter S, Schmidhuber J. Long short-term memory [J]. Neural Computation, 1997, 9(8): 1735-1780.
[28] Lipton Z C, Kale D C, Elkan C, et al. Learning to diagnose with LSTM recurrent neural networks [PP/OL]. (2017-03-21) [2026-05-02]. https://arxiv.org/abs/1511.03677.
[29] Sauer T, Yorke J A, Casdagli M. Embedology [J]. Journal of Statistical Physics, 1991, 65(3-4): 579-616.
[30] Ma H, Leng S, Aihara K, et al. Randomly distributed embedding making short-term highdimensional data predictable [J]. Proceedings of the National Academy of Sciences of the United States of America, 2018, 115(43): E9994-E10002.
[31] Zeng Y, Han D R, Su Y S, et al. On adaptive stochastic heavy ball momentum for solving linear systems [J]. SIAM Journal on Matrix Analysis and Applications, 2024, 45(3): 1259-1286.
[32] Wang Q S, Cui C F, Han D R. A momentum accelerated algorithm for ReLU-based nonlinear matrix decomposition [J]. IEEE Signal Processing Letters, 2024, 31: 2865-2869.
Options
文章导航

/

〈 〉