Title: Joint sparse curves clustering and alignment
Authors: Valeria Vitelli - University of Oslo (Norway) [presenting]
Abstract: The problem of curve clustering in presence of misalingment is considered. This is a frequent situation when dealing with functional data. A method to jointly cluster and align curves, which efficiently decouples amplitude and phase variability by detecting amplitude clusters while simultaneously disclosing clustering structures in the phase, is described, and its efficacy is demonstrated on a couple of real applications. On the other hand, finding sparse solutions to clustering problems has emerged as a hot topic in statistics in recent years, due to the technological improvements in measurement systems leading to the spread of high-dimensional data in many real applications. This problem has not yet been properly treated in the literature on functional data, even though it is often of much interest to select the curves' most relevant features while jointly solving a classification problem. Functional sparse clustering can be analytically defined as a variational problem with a hard thresholding constraint ensuring the sparsity of the solution: this problem is shown to be well-posed, to have a unique optimal solution, and to provide good insights in real applications. Finally, a possible approach to deal with sparse functional clustering when curves are misaligned is also proposed, and some preliminary results are shown.