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Benchmarking time series classification -- Functional data vs machine learning approaches

Time series classification problems have drawn increasing attention in the machine learning and statistical community. Closely related is the field of functional data analysis (FDA): it refers to the range of problems that deal with the analysis of data that is continuously indexed over some domain. While often employing different methods, both fields strive to answer similar questions, a common example being classification or regression problems with functional covariates. We study methods from functional data analysis, such as functional generalized additive models, as well as functionality to concatenate (functional-) feature extraction or basis representations with traditional machine learning algorithms like support vector machines or classification trees. In order to assess the methods and implementations, we run a benchmark on a wide variety of representative (time series) data sets, with in-depth analysis of empirical results, and strive to provide a reference ranking for which method(s) to use for non-expert practitioners. Additionally, we provide a software framework in R for functional data analysis for supervised learning, including machine learning and more linear approaches from statistics. This allows convenient access, and in connection with the machine-learning toolbox mlr, those methods can now also be tuned and benchmarked.