Title: A unified framework for joint sparse clustering and alignment of functional data
Authors: Valeria Vitelli - University of Oslo (Norway) [presenting]
Abstract: When considering functional clustering, it is often of interest to also select the portions of the domain that are most relevant to the classification purposes. However, in case the functions show the presence of misalignment, this can confound the sparse clustering procedure, possibly leading to meaningless results. The only approach currently available in this situation consists in aligning the curves first, and then using a sparse functional clustering method to estimate the groups and select the domain. However, it has been already proved that aligning and clustering the curves jointly is beneficial for the analysis. The aim is thus to jointly perform all these tasks: functional clustering, aligning the curves, and performing domain selection. The proposed method is studied in its well-posedness, and its validity is explored for a variety of measures of closeness of functional data. Indeed, the choice of the functional metric is crucial both to the purposes of functional clustering, and for the properties required to the aligning function. The method is then tested on simulated data, and its use on neuroimaging data is also explored.