chapter  12
24 Pages

Time-Series Clustering

ByJorge Caiado, Elizabeth Ann Maharaj, and Pierpaolo D’Urso

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 12.2 Existing Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

12.2.1 Model-Based Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 12.2.2 Observation-Based Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 12.2.3 Feature-Based Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

12.2.3.1 Time-Domain Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 12.2.3.2 Frequency-Domain Features . . . . . . . . . . . . . . . . . . . . . . . . . . 249 12.2.3.3 Wavelet Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

12.3 Examples and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 12.3.1 Example 1-Data with Switching Time Series . . . . . . . . . . . . . . . . . . . . 254 12.3.2 Example 2-Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 12.3.3 Application 1-Autocorrelation-Based Clustering . . . . . . . . . . . . . . . . . 256 12.3.4 Application 2-Cepstral-Based Fuzzy Clustering . . . . . . . . . . . . . . . . . 257

12.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

The literature on time-series clustering methods has increased considerably over the last two decades with a wide range of applications in many different fields, including geology, environmental sciences, finance, economics, and biomedical sciences. Clustering of time series can technically be put into three groups, viz., methods based on the actual observations, on features derived for the time series and on parameters estimates of fitted models. Selections of work from each of these three groups are presented together with some examples and applications.