Unsupervised curve clustering using B-splines

Data in many different fields come to practitioners through a process naturally described as functional. Although data are gathered as finite vector and may contain measurement errors, the functional form have to be taken into account. We propose a clustering procedure of such data emphasizing the functional nature of the objects. The new clustering method consists of two stages: fitting the functional data by B-splines and partitioning the estimated model coefficients using a k-means algorithm. Strong consistency of the clustering method is proved and a real-world example from food industry is given.