基于模型的纵向数据轨迹异常识别算法

doi:10.11896/jsjkx.250800004

摘要/Abstract

摘要： 纵向数据因能够反映同一对象随时间变化的动态轨迹,在公共健康等领域的研究中受到广泛关注。对纵向数据的清洗过程,是保障纵向数据建模质量和下游分析可信度的重要前置环节。为此,提出一种基于广义线性模型(GLM)多项式拟合与自适应聚类的纵向数据轨迹异常检测方法。通过该算法可获得正常与异常的二分类标签,并将其与真实标签进行比较。在4个独立的数据集(包括2个模拟纵向数据集、1个UCR公开数据集和1个真实数据集)上,与多种典型的纵向数据聚类算法进行了系统对比实验。实验结果显示,所提出的方法在不同数据集和评价指标上均展现出良好的检测性能和泛化性能。将该方法应用于某市小学生连续6年的身高测试数据中的结果,进一步验证了其在实际纵向健康数据中的异常轨迹检测能力和准确性。该方法为公共健康监测与干预、疾病进展评估及临床决策支持等提供了有力支撑。

关键词: 纵向轨迹, 异常轨迹检测, 数据清洗, 无监督聚类

Abstract: Longitudinal data have attracted considerable attention in fields such as public health because they capture the dynamic trajectories of the same subjects over time.Data cleaning process ensures the quality of longitudinal data modelling and directly influences downstream analysis quality.To address this issue,this paper proposes a novel anomaly detection method which integrates generalized linear model(GLM)-based polynomial fittingand adaptive clustering.The approach assigns binary normal and abnormal labels to individual trajectories and compares them with ground-truth annotations.On four independent datasets(two simulated longitudinal cohorts,one additional UCR dataset,and one real-world clinical dataset) a systematically comparison against established R-package methods is conducted.Experimental results demonstrate superior detection performance and robust generalizability across diverse settings.Applying the proposed method to six years of height data from primary school students in a specific city further demonstrates its effectiveness and accuracy in detecting outlier trajectories in practical longitudinal health data.This method offers robust support for public health surveillance and intervention,disease progression assessment,and clinical decision support.

Key words: Longitudinal trajectory, Trajectory anomalies detection, Data cleaning, Unsupervised clustering

中图分类号:

TP311.14

董东, 金朋超. 基于模型的纵向数据轨迹异常识别算法[J]. 计算机科学, 2026, 53(6A): 250800004-8. https://doi.org/10.11896/jsjkx.250800004

DONG Dong, JIN Pengchao. Model-based Trajectory Anomalies Detection Algorithm for Longitudinal Data[J]. Computer Science, 2026, 53(6A): 250800004-8. https://doi.org/10.11896/jsjkx.250800004

参考文献

[1] DIGGLE P.Analysis of longitudinal data [M].Oxford:Oxford University Press,2002:1-3.
[2] LU Z.Clustering longitudinal data:A review of methods and software packages [J].International Statistical Review,2025,93(3):425-458.
[3] TOPHAM G L,WASHBURN I J,HUBBS-TAIT L,et al.TheFamilies and Schools for Health Project:a longitudinal cluster randomized controlled trial targeting children with overweight and obesity [J].International Journal of Environmental Research and Public Health,2021,18(16):8744.
[4] POULAKIS K,PEREIRA J B,MUEHLBOECK J S,et al.Multi-cohort and longitudinal bayesian clustering study of stage and subtype in Alzheimer's disease [J].Nature Communications,2022,13(1):4566.
[5] SALMANPOUR M R,SHAMSAEI M,HAJIANFAR G,et al.Longitudinal clustering analysis and prediction of Parkinson's disease progression using radiomics and hybrid machine learning [J].Quantitative Imaging in Medicine and Surgery,2022,12(2):906.
[6] MATSON G,MCELROY S,LEE Y,et al.Longitudinal analysis of COVID-19 impacts on mobility:an early snapshot of the emerging changes in travel behavior [J].Transportation Research Record,2023,2677(4):298-312.
[7] HUANG D Y C,EVANS E,HARA M,et al.Employment tra-jectories:Exploring gender differences and impacts of drug use [J].Journal of Vocational Behavior,2011,79(1):277-289.
[8] LI C N,FENG G W,YAO H,et al.Survey on trajectory anomaly detection [J].Journal of Software,2024,35(2):927-974.
[9] CÔTÉ P O,NIKANJAM A,AHMED N,et al.Data cleaningand machine learning:a systematic literature review [J].Automated Software Engineering,2024,31(2):54.
[10] GRÜN B,LEISCH F.flexmix:Flexible Mixture Modeling:Rpackage version 2.3-20 [EB/OL].https://CRAN.R-project.org/package=flexmix.
[11] LEISCH F.FlexMix:A General Framework for Finite Mixture Models and Latent Class Regression in R [J].Journal of Statistical Software,2004,11(8):1-18.
[12] GRÜN B,LEISCH F.Fittingfinite mixtures of generalized linear regressions in R [J].Computational Statistics & Data Analysis,2007,51(11):5247-5252.
[13] GRÜN B,LEISCH F.FlexMixversion 2:finite mixtures withconcomitant variables and varying and constant parameters [J].Journal of Statistical Software,2008,28(4):1-35.
[14] GENOLINI C,ALACOQUE X,SENTENAC M,et al.kml and kml3d:Rpackages to cluster longitudinal data [J].Journal of Statistical Software,2015,65(4):1-34.
[15] GENOLINI C,FALISSARD B,KIENER P.kml:K-means for longitudinal data:R package version 2.5-0 [EB/OL].https://CRAN.R-project.org/package=kml.
[16] PROUST-LIMA C,PHILIPPS V,LIQUET B.Estimation ofextended mixed models using latent classes and latent processes:The R package lcmm [J].Journal of Statistical Software,2017,78(2):1-56.
[17] PROUST-LIMA C,PHILIPPS V,DIAKITE A,et al.lcmm:Extended mixed models using latent classes and latent processes:R package version 2.2.1 [EB/OL].https://cran.r-project.org/package=lcmm.
[18] ZHOU Y,CHEN H,IAO S,et al.fdapace:Functionaldata analysis and empirical dynamics:R package version 0.6.0 [EB/OL].https://CRAN.R-project.org/package=fdapace.
[19] REN R,FANG K.FADPclust:Functional data clustering using adaptive density peak detection [EB/OL].https://CRAN.R-project.org/package=FADPclust.
[20] KNORR E M,NG R T,TUCAKOV V.Distance-based outliers:algorithms and applications [J].The VLDB Journal,2000,8(3):237-253.
[21] LEE J G,HAN J,LI X.Trajectory outlier detection:A partition-and-detect framework [C]//2008 IEEE 24th International Conference on Data Engineering.IEEE,2008:140-149.
[22] LIU L,QIAO S,ZHANG Y,et al.An efficient outlying trajecto-ries mining approach based on relative distance [J].InternationalJournal of Geographical Information Science,2012,26(10):1789-1810.
[23] GENOLINI C,FALISSARD B.KmL:k-means for longitudinal data [J].Computational Statistics,2010,25(2):317-328.
[24] WANG J,YUAN Y,NI T,et al.Anomalous trajectory detection and classification based on difference and intersection set distance [J].IEEE Transactions on Vehicular Technology,2020,69(3):2487-2500.
[25] MANGÉ V,ANEZIN Y,TOURNERET J Y,et al.Detectingabnormal ship trajectories using functional isolation forests and dynamic time warping [C]//32nd European Signal Processing Conference(EUSIPCO 2024).IEEE,2024:2342-2346.
[26] LIU Z,PI D,JIANG J.Density-based trajectory outlier detection algorithm [J].Journal of Systems Engineering and Electronics,2013,24(2):335-340.
[27] LUAN F,ZHANG Y,CAO K,et al.Based local density trajectory outlier detection with partition-and-detect framework [C]//2017 13th International Conference on Natural Computation,Fuzzy Systems and Knowledge Discovery(ICNC-FSKD).IEEE,2017:1708-1714.
[28] GUAN B,ZHANG Y,LIU L,et al.An improving algorithm of trajectory outliersdetection [C]//Advanced Technology in Teaching-Proceedings of the 2009 3rd International Conference on Teaching and Computational Science(WTCS 2009).Berlin:Springer,2012:907-914.
[29] PICIARELLI C,MICHELONI C,FORESTI G L.Trajectory-based anomalous event detection [J].IEEE Transactions on Circuits and Systems for Video Technology,2008,18(11):1544-1554.
[30] LI X,HAN J,KIM S,et al.Roam:Rule-and motif-based anomaly detection in massive moving object data sets [C]//Procee-dings of the 2007 SIAM International Conference on Data Mi-ning.Society for Industrial and Applied Mathematics,2007:273-284.
[31] LUO D,CHEN P,YANG J,et al.A new classification method for ship trajectories based on AIS data [J].Journal of Marine Science and Engineering,2023,11(9):1646.
[32] SYLVESTRE M P,BOULANGER L,et al.traj:Clustering offunctional data based on measures of change:R package version 2.2.1 [EB/OL].Available:https://CRAN.R-project.org/package=traj.
[33] TANG H,HUANG J,LIN H,et al.The global burden and biomarkers of cardiovascular disease attributable to ambient particu-late matter pollution [J].Journal of Translational Medicine,2025,23(1):359.
[34] MORENO-TORRES J G,RAEDER T,ALAIZ-RODRÍGUEZR,et al.A unifying view on dataset shift in classification [J].Pattern Recognition,2012,45(1):521-530.
[35] KOH P W,SAGAWA S,MARKLUND H,et al.Wilds:Abenchmark of in-the-wild distribution shifts [C]//International Conference on Machine Learning.PMLR,2021:5637-5664.
[36] BREIMAN L.Random forests [J].Machine Learning,2001,45:5-32.
[37] GENEUR R,POGGI J M,TULEAU-MALOT C.Variable se-lection using random forests [J].Pattern Recognition Letters,2010,31(14):2225-2236.
[38] DOBSON A J,BARNETT A G.An introduction to generalized linear models[M].Chapman and Hall/CRC,2018.
[39] PELLEG D,MOORE A.X-means:Extending K-means with Efficient Estimation of the Number of Clusters [C]//Proceedings of the Seventeenth International Conference on Machine Learning(ICML 2000).San Francisco:Morgan Kaufmann,2000:727-734.
[40] GENOLINI C,FALISSARD B.KmL:k-means for longitudinaldata [J].Computational Statistics,2010,25(2):317-328.
[41] WIJAYA Y A,KURNIADY D A,SETYANTO E,et al.Davies-Bouldin index algorithm for optimizing clustering case studies map school facilities [J].TEM J,2021,10(3):1099-1103.
[42] DAU H A,BAGNALL A,KAMGAR K,et al.The UCR time series archive [J].IEEE/CAA Journal of Automatica Sinica,2019,6(6):1293-1305.
[43] ALOIA M S,GOODWIN M S,VELICER W F,et al.Time series analysis of treatment adherence patterns in individuals with obstructive sleep apnea [J].Annals of Behavioral Medicine,2008,36(1):44-53.
[44] XIE J,GIRSHICK R,FARHADI A.Unsupervised deep embedding for clustering analysis [C]//International Conference on Machine Learning.PMLR,2016:478-487.
[45] HAN J W,KAMBER M,PEI J.Data Mining:Concepts andTechniques [M].Beijing:China Machine Press,2012:236-240.
[46] STEINLEY D.Properties of the Hubert-Arabie adjusted Rand index [J].Psychological Methods,2004,9(3):386-396.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed