A0580
Title: Geometric and topological perspectives on unsupervised functional data analysis
Authors: Fabian Scheipl - Ludwig-Maximilians-Universitaet Muenchen (Germany) [presenting]
Moritz Hermann - Ludwig-Maximilians-Universitaet Muenchen (Germany)
Abstract: Clustering, as well as outlier or anomaly detection, are important unsupervised tasks in functional data analysis. The problem from geometrical and topological perspectives is discussed, and a framework is provided for unsupervised FDA that exploits a functional data set's (metric) structure. The approach rests on the manifold assumption, i.e., that the observed, nominally infinite-dimensional functional data lie on or close to a much lower dimensional manifold and that this intrinsic structure can be inferred with manifold learning methods. It is shown that exploiting this structure can significantly improve the detection of outlying functions and provides a simple, robust and easily customizable way to apply well-established and highly-performant modern clustering algorithms to functional data. The framing also suggests a novel, precise, and widely applicable distinction between distributional and structural outliers based on the geometry and topology of the data manifold that clarifies conceptual ambiguities prevalent throughout the literature.
