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Title: A novel two-step iterative approach for clustering functional data Authors:  Zuzana Rostakova - Slovak Academy of Sciences (Slovakia) [presenting]
Roman Rosipal - Slovak Academy of Sciences (Slovakia)
Abstract: An important task in functional data analysis is to divide a dataset into subgroups with similar profiles, or clusters. We address a problem in which classical functional data clustering techniques may fail when curve misalignment is present. Solutions in which registration or temporal alignment of the whole dataset precede the clustering step result in rapid distortions in the curve shapes when a dataset consists of many different curve profiles. Methods developed for simultaneous registration and clustering of curves mainly deal with linear transformation of time. This solution may also lead to unsatisfactory alignment when profiles of the curves are complex or the source of misalignment has a nonlinear character. We propose and validate a novel two-step approach, which iteratively combines clustering using a modified Dynamic Time Warping algorithm with the registration step applied separately to curves within estimated clusters. On generated and real functional data representing the sleep process we demonstrate the validity of the approach by measuring improvement in similarity between aligned curves in comparisons to: a) the case when clustering and registration steps are applied separately and b) other methods (e.g. $k$-means alignment, joined probabilistic curve clustering and alignment) for simultaneous curve registration and clustering.