chapter  13
24 Pages

## Clustering Functional Data

ByDavid B. Hitchcock, Mark C. Greenwood

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 13.2 Existing Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

13.2.1 Origins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 13.2.2 More Existing Work: Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274

13.3 Examples, Applications, Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 13.3.1 Software for Functional Data Clustering . . . . . . . . . . . . . . . . . . . . . . . . 277 13.3.2 Illustrative Real Data Examples and Applications . . . . . . . . . . . . . . . . . 278

13.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

Functional data are data that arise as curves. These curves may be functions of time, space, or some other independent variable(s). Clustering of functional data may be based on characteristics of the curves such as positions, shapes, or derivatives. Clustering algorithms may be based on specialized dissimilarity measures, may be based on clustering the coefficients of basis function expansions of the data, or may cluster the functions directly. We review the ever-growing literature of methods for clustering functional data. Early methods emphasized clustering basis coefficients, while later research put forth model-based methods and incorporated more complex dependency structures. We discuss available software for functional clustering and give two illustrative examples on real and simulated data. We discuss open problems for future research in clustering functional data.