Knowledge and Information Systems

, Volume 55, Issue 3, pp 695–718 | Cite as

Time series classification with feature covariance matrices

  • Hamza Ergezer
  • Kemal Leblebicioğlu
Regular Paper


In this work, a novel approach utilizing feature covariance matrices is proposed for time series classification. In order to adapt the feature covariance matrices into time series classification problem, a feature vector is defined for each point in a time series. The feature vector comprises local and global information such as value, derivative, rank, deviation from the mean, the time index of the point and cumulative sum up to the point. Extracted feature vectors for the time instances are concatenated to construct feature matrices for the overlapping subsequences. Covariances of the feature matrices are used to describe the subsequences. Our main purpose in this work is to introduce and evaluate the feature covariance representation for time series classification. Therefore, in classification stage, firstly, 1-NN classifier is utilized. After showing the effectiveness of the representation with 1-NN classifier, the experiments are repeated with SVM classifier. The other novelty in this work is that a novel distance measure is introduced for time series by feature covariance matrix representation. Conducted experiments on UCR time series datasets show that the proposed method mostly outperforms the well-known methods such as DTW, shapelet transform and other state-of-the-art techniques.


Time series classification Time series representation Feature covariance matrices 


  1. 1.
  2. 2.
    Time series classification website (2017).
  3. 3.
    Ahmed N, Atiya AF, Gayar N, El-Shishiny H (2010) An empirical comparison of machine learning models for time series forecasting. Econom Rev 29(5–6):594–621MathSciNetCrossRefGoogle Scholar
  4. 4.
    Arsigny V, Fillard P, Pennec X, Ayache N (2006) Log-euclidean metrics for fast and simple calculus on diffusion tensors. Magn Reson Med 56(2):411–421CrossRefGoogle Scholar
  5. 5.
    Ayadi ME, Kamel M, Karray F (2011) Survey on speech emotion recognition: features, classification schemes, and databases. Pattern Recogn 44(3):572–587CrossRefzbMATHGoogle Scholar
  6. 6.
    Bagnall A, Lines J, Hills J, Bostrom A (2015) Time-series classification with cote: the collective of transformation-based ensembles. IEEE Trans Knowl Data Eng 27(9):2522–2535CrossRefGoogle Scholar
  7. 7.
    Bailly A, Malinowski S, Tavenard R, Guyet T, Chapel L (2015) Bag-of-temporal-sift-words for time series classification. In: ECML/PKDD workshop on advanced analytics and learning on temporal dataGoogle Scholar
  8. 8.
    Barachant A, Bonnet S, Congedo M, Jutten C (2013) Classification of covariance matrices using a riemannian-based kernel for bci applications. Neurocomputing 112:172–178CrossRefGoogle Scholar
  9. 9.
    Bay Herbert TT, Gool LV (2006) Surf: speeded up robust features. In: European conference on computer vision, pp 404–417Google Scholar
  10. 10.
    Baydogan MG, Runger G, Tuv E (2013) A bag-of-features framework to classify time series. IEEE Trans Pattern Anal Mach Intell 35(11):2796–2802CrossRefGoogle Scholar
  11. 11.
    Chebbi Z, Moakher M (2012) Means of hermitian positive-definite matrices based on the log-determinant alpha-divergence function. Linear Algebra Appl 436(7):1872–1889MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Chen Y, Keogh E, Hu B, Begum N, Bagnall A, Mueen A, Batista G (2015) The UCR time series classification archive.
  13. 13.
    Dalal N, Triggs B (2005) Histograms of oriented gradients for human detection. IEEE Conf Comput Vis Pattern Recogn 1:886–893Google Scholar
  14. 14.
    Deng H, Runger G, Tuv E, Vladimir M (2013) A time series forest for classification and feature extraction. Inf Sci 239:142–153MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Erdem E, Erdem A (2013) Visual saliency estimation by nonlinearly integrating features using region covariances. J Vis 13(4), article no. 11. doi: 10.1167/13.4.11
  16. 16.
    Ergezer H, Leblebicioğlu K (2016) Anomaly detection and activity perception using covariance descriptor for trajectories. In: European conference on computer vision, Springer, Berlin, pp 728–742Google Scholar
  17. 17.
    Esling P, Agon C (2012) Time-series data mining. ACM Comput Surv (CSUR) 45(1), article no. 12Google Scholar
  18. 18.
    Freifeld O (2014) Statistics on manifolds with applications to modeling shape deformations. Ph.D. Thesis, Brown UniversityGoogle Scholar
  19. 19.
    Förstner W, Moonen B (2003) A metric for covariance matrices. Geodesy-The Challenge of the 3rd Millennium. Springer, BerlinGoogle Scholar
  20. 20.
    Fu Z, Lu G, Ting K, Zhang D (2011) Music classification via the bag-of features approach. Pattern Recogn Lett 32(14):1768–1777CrossRefGoogle Scholar
  21. 21.
    Fulcher BD, Jones NS (2014) Highly comparative feature-based time-series classification. IEEE Trans Knowl Data Eng 26(12):3026–3037CrossRefGoogle Scholar
  22. 22.
    Guo K, Ishwar P, Konrad J (2013) Action recognition from video using feature covariance matrices. IEEE Trans Image Process 22(6):2479–2494MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Hills J, Lines J, Baranauskas E, Mapp J, Bagnall A (2014) Classification of time series by shapelet transformation. Data Min Knowl Disc 28(4):851–881MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Jeong Y, Jeong M, Omitaomu O (2011) Weighted dynamic time warping for time series classification. Pattern Recogn 44(9):2231–2240CrossRefGoogle Scholar
  25. 25.
    Karlsson I, Papapetrou P, Boström H (2016) Generalized random shapelet forests. Data Min Knowl Disc 30(5):1053–1085MathSciNetCrossRefGoogle Scholar
  26. 26.
    Kate RJ (2016) Using dynamic time warping distances as features for improved time series classification. Data Min Knowl Disc 30(2):283–312MathSciNetCrossRefGoogle Scholar
  27. 27.
    Keogh EJ, Pazzani MJ (2001) Derivative dynamic time warping. In: Proceedings of the 2001 SIAM international conference on data miningGoogle Scholar
  28. 28.
    Laptev I (2005) On space-time interest points. Int J Comput Vis 64(2–3):107–123CrossRefGoogle Scholar
  29. 29.
    Lee JM (2006) Riemannian manifolds: an introduction to curvature, vol 176. Springer, BerlinGoogle Scholar
  30. 30.
    Lin J, Keogh E, Wei L, Lonardi S (2007) Experiencing sax: a novel symbolic representation of time series. Data Min Knowl Disc 15(2):107–144MathSciNetCrossRefGoogle Scholar
  31. 31.
    Lines J, Bagnall A (2015) Time series classification with ensembles of elastic distance measures. Data Min Knowl Disc 29:565–592MathSciNetCrossRefGoogle Scholar
  32. 32.
    Lowe D (1999) Object recognition from local scale-invariant features. Proc Seventh IEEE Int Conf Comput Vis 2:1150–1157CrossRefGoogle Scholar
  33. 33.
    Mikolajczyk K et al (2005) A performance evaluation of local descriptors. IEEE Trans Pattern Anal Mach Intell 27(10):1615–1630CrossRefGoogle Scholar
  34. 34.
    Mohan A, Papageorgiou C, Poggio T (2001) Example-based object detection in images by components. IEEE Trans Pattern Anal Mach Intell 23(4):349–361CrossRefGoogle Scholar
  35. 35.
    Mueen A, Keogh E, Youngin N (2011) Logical-shapelets: an expressive primitive for time series classification. In: Proceedings of 17th ACM SIGKDD internatinal conference knowledge discovery data mining, pp 1154–1162Google Scholar
  36. 36.
    Pongpaichet S, Tang M, Jalali L, Jain R (2016) Using photos as micro-reports of events. In: In Proceedings of the 2016 ACM on international conference on multimedia retrieval, pp 87–94. ACMGoogle Scholar
  37. 37.
    Porikli F, Tuzel O, Meer P (2006) Covariance tracking using model update based on lie algebra. In: CVPR, pp 728–735Google Scholar
  38. 38.
    Ratanamahatana C, Keogh E (2005) Three myths about dynamic time warping data mining. In: In Proceedings of SIAM international conference on data mining (SDM’05), pp 506–510Google Scholar
  39. 39.
    Ratanamahatana CA, Keogh E (2004) Making time-series classification more accurate using learned constraints. In: Proceedings of SIAM international conference on data mining (SDM04), pp 11–22Google Scholar
  40. 40.
    Ratanamahatana CA, Lin J, Gunopulos D, Keogh E, Vlachos M, Das G (2005) Mining time series data. In: Data mining and knowledge discovery handbook 1069–1103, Springer, USGoogle Scholar
  41. 41.
    Sadatnejad K, Ghidary SS (2016) Kernel learning over the manifold of symmetric positive definite matrices for dimensionality reduction in a bci application. Neurocomputing 179:152–160CrossRefGoogle Scholar
  42. 42.
    Tang M, Agrawal P, Nie F, Pongpaichet S, Jain R (2016) A graph based multimodal geospatial interpolation framework. In: In 2016 IEEE international conference on multimedia and expo (ICME), pp 1–6Google Scholar
  43. 43.
    Tang M, Nie F, Pongpaichet S, Jain R (2017) From photo streams to evolving situations. arXiv preprint arXiv:1702.05878
  44. 44.
    Tang M, Wu X, Agrawal P, Pongpaichet S, Jain R (2017) Integration of diverse data sources for spatial PM2. 5 data interpolation. IEEE Trans Multimedia 19(2):408–417.Google Scholar
  45. 45.
    Tuzel O, Porikli F, Meer P (2006) Region covariance: a fast descriptor for detection and classification. In: European conference on computer vision. Springer, Berlin, pp 589–600Google Scholar
  46. 46.
    Tuzel O, Porikli F, Meer P (2008) Pedestrian detection via classification on riemannian manifolds. IEEE Trans Pattern Anal Mach Intell 30(10):1713–1727CrossRefGoogle Scholar
  47. 47.
    Wang X, Mueen A, Ding H, Trajcevski G, Scheuermann P, Keogh E (2013) Experimental comparison of representation methods and distance measures for time series data. Data Min Knowl Disc 26(2):275–309MathSciNetCrossRefGoogle Scholar
  48. 48.
    Ye L, Keogh E (2009) Time series shapelets: A new primitive for data mining. In: Proceedings of 15th ACM SIGKDD international conference on knowledge discovery data mining, pp 947–956Google Scholar
  49. 49.
    Zhang Q, Goldman S, Yu W, Fritts J (2002) Content-based image retrieval using multiple-instance learning. ICML 2:682–689Google Scholar
  50. 50.
    Zhao J, Itti L (2016) Classifying time series using local descriptors with hybrid sampling. IEEE Trans Knowl Data Eng 28(3):623–637CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd. 2017

Authors and Affiliations

  1. 1.Department of Electrical and Electronics EngineeringMiddle East Technical University (METU)AnkaraTurkey
  2. 2.MGEO Division, Department of EO System DesignAselsan IncAnkaraTurkey

Personalised recommendations