Spatially weighted functional clustering of river network data

Variograms for kriging and clustering of spatial functional data with phase variation

Spatial, amplitude and phase variations in spatial functional data are confounded. Conclusions from the popular functional trace-variogram, which quantifies spatial variation, can be misleading when analyzing misaligned functional data with phase variation. To remedy this, we describe a framework that extends amplitude-phase separation methods in functional data to the spatial setting, with a view towards performing clustering and spatial prediction. We propose a decomposition of the trace-variogram into amplitude and phase components, and quantify how spatial correlations between functional observations manifest in their respective amplitude and phase. This enables us to generate separate amplitude and phase clustering methods for spatial functional data, and develop a novel spatial functional interpolant at unobserved locations based on combining separate amplitude and phase predictions. Through simulations and real data analyses, we demonstrate advantages of our approach when compared to standard ones that ignore phase variation, through more accurate predictions and more interpretable clustering results.

The Choice of an Appropriate Information Dissimilarity Measure for Hierarchical Clustering of River Streamflow Time Series, Based on Calculated Lyapunov Exponent and Kolmogorov Measures

The purpose of this paper was to choose an appropriate information dissimilarity measure for hierarchical clustering of daily streamflow discharge data, from twelve gauging stations on the Brazos River in Texas (USA), for the period 1989–2016. For that purpose, we selected and compared the average-linkage clustering hierarchical algorithm based on the compression-based dissimilarity measure (NCD), permutation distribution dissimilarity measure (PDDM), and Kolmogorov distance (KD). The algorithm was also compared with K-means clustering based on Kolmogorov complexity (KC), the highest value of Kolmogorov complexity spectrum (KCM), and the largest Lyapunov exponent (LLE). Using a dissimilarity matrix based on NCD, PDDM, and KD for daily streamflow, the agglomerative average-linkage hierarchical algorithm was applied. The key findings of this study are that: (i) The KD clustering algorithm is the most suitable among others; (ii) ANOVA analysis shows that there exist highly significant differences between mean values of four clusters, confirming that the choice of the number of clusters was suitably done; and (iii) from the clustering we found that the predictability of streamflow data of the Brazos River given by the Lyapunov time (LT), corrected for randomness by Kolmogorov time (KT) in days, lies in the interval from two to five days.