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From high-dimensional to functional data: stringing via manifold learning. (English) Zbl 1444.62155

Aneiros, Germán (ed.) et al., Functional and high-dimensional statistics and related fields. Selected papers presented at the 5th international workshop on functional and operatorial statistics, IWFOS 2021, Brno, Czech Republic, June 23–25, 2021. Cham: Springer. Contrib. Stat., 115-122 (2020).
Summary: The study of high-dimensional data is becoming a common trend in modern research. Recently, stringing emerged as a methodology to treat high-dimensional sample vectors as realizations of smooth stochastic processes. Under the hypothesis of noisy and order-perturbed measurements, stringing introduces smooth transitions between predictors and takes advantage of Functional Data Analysis (FDA) to study the data. Once a functional representation is achieved, it is possible to visualize intrinsic patterns, or fit functional regression models. We propose manifold learning as an alternative to multidimensional scaling in the reordering step. In a simulation study we show that our proposal achieves smaller relative order errors, and that it can recover more complex relationships between predictors.
For the entire collection see [Zbl 1446.62001].

MSC:

62R10 Functional data analysis
62R30 Statistics on manifolds

Software:

fda (R)
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References:

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