Abstract
Cluster analysis of time series is usually performed by extracting and comparing relevant interesting features from the data. Quite a few numerical algorithms are available that search for highly separated data sets with strong internal cohesion so that some suitable objective function is minimized or maximized. Algorithms developed for classifying independent sample data are often adapted to the time series framework. On the other hand time series are dependent data and their statistical properties may serve to drive allocation of time series to groups by performing formal statistical tests. Which is the class of methods that has better chance of fulfilling its task is an open question. Some comparisons are presented concerned with the application of different algorithms to simulated time series. The data recorded for monitoring the visitors flow to archaeological areas, museums, and other sites of interest for displaying Italy’s cultural heritage are examined in some details.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Corduas, M. (1996). Uno studio sulla distribuzione asintotica della metrica autoregressiva, Statistica,56, 321–332.
Gómez, V., & Maravall, A. (1996). Programs TRAMO and SEATS: instructions for users, Technical Report 9628, The Banco de España, Servicios de Estudios.
Hartigan, J. A. (1975). Clustering algorithms. New York: Wiley.
Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification,2, 193–218.
Keogh, E., & Kasetty, S. (2003). On the need for time series data mining benchmarks: A survey and empirical demonstration. Data Mining and Knowledge Discovery,7, 349–371.
Liao, T. W. (2005). Clustering of time series data – a survey. Pattern Recognition,38, 1857–1874.
Maharaj, E. A. (2000). Clusters of time series. Journal of Classification,17, 297–314.
Marquardt, D. W. (1963). An algorithm for least squares estimation of nonlinear parameters. Journal of the Society of Industrial and Applied Mathematics,11, 431–441.
Murthy, C. A., & Chowdhury, N. (1996). In search of optimal clusters using genetic algorithms. Pattern Recognition Letters,17, 825–832.
Piccolo, D. (1989). On the measure of dissimilarity between ARIMA models. In Proceedings of the A. S. A. Meetings, Business and Economic Statistics Sect., Washington D. C., 231–236.
Piccolo, D. (1990). A distance measure for classifying ARIMA models. Journal of Time Series Analysis,11, 153–164.
Sarno, E. (2001). Further results on the asymptotic distribution of the Euclidean distance between MA models. Quaderni di Statistica,3, 165–175.
Wang, X., Smith, K. A., & Hyndman, R. J. (2005). Characteristic-based clustering for time series data. Data Mining and Knowledge Discovery,13, 335–364.
Zani, S. (1983). Osservazioni sulle serie storiche multiple e l’analisi dei gruppi. In D. Piccolo (Ed.), Analisi Moderna delle Serie Storiche (pp. 263–274). Milano: Franco Angeli.
Acknowledgements
This work was financially supported by grants from MIUR, Italy. R. Baragona gratefully acknowledges financial support from the EU Commission through MRTN-CT-2006-034270 COMISEF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Baragona, R., Vitrano, S. (2010). Statistical and Numerical Algorithms for Time Series Classification. In: Palumbo, F., Lauro, C., Greenacre, M. (eds) Data Analysis and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03739-9_39
Download citation
DOI: https://doi.org/10.1007/978-3-642-03739-9_39
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03738-2
Online ISBN: 978-3-642-03739-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)