A New Framework for Distance-based Functional Clustering

We develop a new framework for clustering functional data, based on a distance matrix similar to the approach in clustering multivariate data using spectral clustering. First, we smooth the raw observations using appropriate smoothing techniques with desired smoothness, through a penalized fit. The next step is to create an optimal distance matrix either from the smoothed curves or their available derivatives. The choice of the distance matrix depends on the nature of the data. Finally, we create and implement the spectral clustering algorithm. We applied our newly developed approach, Functional Spectral Clustering (FSC) on sets of simulated and real data. Our proposed method showed better performance than existing methods with respect to accuracy rates