Distance for Functional Data Clustering Based on Smoothing Parameter Commutation
This is an incremental improvement for researchers in functional data analysis, offering a pragmatic tool for clustering and outlier detection.
The paper tackles the problem of measuring dissimilarity for functional data clustering by proposing a method based on varying smoothing parameters pair-by-pair, rather than using fixed curve estimates. The result shows effectiveness through simulations compared to other dissimilarity measures, with advantages like handling missing values and maintaining computational efficiency.
We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each subject as fixed during clustering, we measure the dissimilarity between subjects based on varying curve estimates with commutation of smoothing parameters pair-by-pair (of subjects). The intuitions are that smoothing parameters of smoothing splines reflect inverse signal-to-noise ratios and that applying an identical smoothing parameter the smoothed curves for two similar subjects are expected to be close. The effectiveness of our proposal is shown through simulations comparing to other dissimilarity measures. It also has several pragmatic advantages. First, missing values or irregular time points can be handled directly, thanks to the nature of smoothing splines. Second, conventional clustering method based on dissimilarity can be employed straightforward, and the dissimilarity also serves as a useful tool for outlier detection. Third, the implementation is almost handy since subroutines for smoothing splines and numerical integration are widely available. Fourth, the computational complexity does not increase and is parallel with that in calculating Euclidean distance between curves estimated by smoothing splines.