Multi-scale Clustering of Functional Data with Application to Hydraulic Gradients in Wetlands

10.6339/JDS.2011.09(3).937

Mark C. Greenwood；Richard S. Sojda；Julia L. Sharp；Rory G. Peck；Donald O. Rosenberry

Cluster analysis ； functional data analysis ； generalized additive model ； wetlands ； hydrology ； groundwater

Journal of Data Science

9卷3期（2011 / 07 / 01）

399 - 426

英文

A new set of methods are developed to perform cluster analysis of functions, motivated by a data set consisting of hydraulic gradients at several locations distributed across a wetland complex. The methods build on previous work on clustering of functions, such as Tarpey and Kinateder (2003) and Hitchcock et al. (2007), but explore functions generated from an additive model decomposition (Wood, 2006) of the original time series. Our decomposition targets two aspects of the series, using an adaptive smoother for the trend and circular spline for the diurnal variation in the series. Different measures for comparing locations are discussed, including a method for efficiently clustering time series that are of different lengths using a functional data approach. The complicated nature of these wetlands are highlighted by the shifting group memberships depending on which scale of variation and year of the study are considered.

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