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We propose a novel method to determine the dissimilarity between subjects forfunctional data clustering. Spline smoothing or interpolation is common to dealwith data of such type. Instead of estimating the best-representing curve foreach subject as fixed during clustering, we measure the dissimilarity betweensubjects based on varying curve estimates with commutation of smoothingparameters pair-by-pair (of subjects). The intuitions are that smoothingparameters of smoothing splines reflect inverse signal-to-noise ratios and thatapplying an identical smoothing parameter the smoothed curves for two similarsubjects are expected to be close. The effectiveness of our proposal is shownthrough simulations comparing to other dissimilarity measures. It also hasseveral pragmatic advantages. First, missing values or irregular time pointscan be handled directly, thanks to the nature of smoothing splines. Second,conventional clustering method based on dissimilarity can be employedstraightforward, and the dissimilarity also serves as a useful tool for outlierdetection. Third, the implementation is almost handy since subroutines forsmoothing splines and numerical integration are widely available. Fourth, thecomputational complexity does not increase and is parallel with that incalculating Euclidean distance between curves estimated by smoothing splines.

Distance for Functional Data Clustering Based on Smoothing Parameter Commutation