Functional data clustering via piecewise constant nonparametric density estimation

In this paper, we present a novel way of analyzing and summarizing a collection of curves, based on piecewise constant density estimation. The curves are partitioned into clusters, and the dimensions of the curves points are discretized into intervals. The cross-product of these univariate partitions forms a data grid of cells, which represents a nonparametric estimator of the joint density of the curves and point dimensions. The best model is selected using a Bayesian model selection approach and retrieved using combinatorial optimization algorithms. The proposed method requires no parameter setting and makes no assumption regarding the curves; beyond functional data, it can be applied to distributional data. The practical interest of the approach for functional data and distributional data exploratory analysis is presented on two real world datasets.

► We present a novel way of analyzing and summarizing a collection of curves.
► It is based on piecewise constant density estimation of curve dimensions.
► It makes no assumption regarding the curves and require no parameter setting.
► Beyond functional data, it can be applied to distributional data.
► Its practical interest is assessed on a large dataset of 70 000 handwritten digits.