The Hierarchical Spectral Merger Algorithm: A New Time Series Clustering Procedure
We present a new method for time series clustering which we call the Hierarchical Spectral Merger (HSM) method. This procedure is based on the spectral theory of time series and identifies series that share similar oscillations or waveforms. The extent of similarity between a pair of time series is measured using the total variation distance between their estimated spectral densities. At each step of the algorithm, every time two clusters merge, a new spectral density is estimated using the whole information present in both clusters, which is representative of all the series in the new cluster. The method is implemented in an R package HSMClust. We present two applications of the HSM method, one to data coming from wave-height measurements in oceanography and the other to electroencefalogram (EEG) data.
KeywordsHierarchical spectral merger clustering: Time series clustering Hierarchical clustering Total variation distance Time series Spectral analysis
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- BRODTKORB, P.A., JOHANNESSON, P., LINDGREN, G., RYCHLIK, I., RYDÉN, J., and SJÖ, E. (2010), “WAFO - A Matlab Toolbox for Analysis of Random Waves and Loads”, in Proceedings of the 10th International Offshore and Polar Engineering Conference, Vol. 3, Seattle, USA, pp. 343–350.Google Scholar
- CAIADO, J., MAHARAJ, E.A., and D’URSO, P. (2015), “Time Series Clustering”, in Handbook of Cluster Analysis, eds. C. Hennig, M. Meila, F. Murtagh, and R. Rocci, Handbooks of Modern Statistical Methods, Chap. 12, Chapman and Hall/CRC, pp. 241–263.Google Scholar
- CONTRERAS, P., and MURTAGH, F. (2015), "Hierarchical Clustering", in Handbook of Cluster Analysis, eds. C. Hennig, M. Meila, F. Murtagh, and R. Rocci, Handooks of Modern Statistiacl Methods, Chap. 12, Chapman and Hall/CRC, pp. 103–123.Google Scholar
- EUÁN, C. (2016), “Detection of Changes in Time Series: A Frequency Domain Approach”, PhD dissertation, CIMAT.Google Scholar
- GAVRILOV, M., ANGUELOV, D., INDYK, P., and MOTWANI, R. (2000), “Mining the Stock Market: Which Measure is Best”, in Proceedings of the 6 th ACM Internationall Conference on Knowledge Discovery and Data Mining, pp. 487–496.Google Scholar
- MAHARAJ, E.A., and ALONSO, A.M (2014), “Discriminant Analysis of Multivariate Time Series: Application to Diagnosis Based on ECG Signals”, Computational Statistics and Data Analysis, 70, 67–87.Google Scholar
- R CORE TEAM (2014), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria.Google Scholar