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A multivariate approach for clustering functional data in one and multiple dimensions
Last modified: 2024-05-14
Abstract
Clustering techniques play a crucial role in unsupervised classification, offering a way to organize complex datasets into coherent groups. While the literature extensively covers clustering techniques in multivariate analysis, the landscape changes when it comes to functional data.
Functional datasets present a unique challenge due to their infinite-dimensional nature, making traditional clustering methods less straightforward to apply. To tackle this challenge, we propose to transform the initial functional dataset into a multivariate one.
In one-dimensional functional datasets, the original definitions of epigraph and hypograph are considered to obtain the new dataset. For multivariate functional data, new versions of these indexes are introduced. By applying the epigraph and hypograph indexes to obtain a multivariate dataset from a functional one, we reduce dimensionality, rendering the new dataset compatible with standard clustering techniques for multivariate data.
Validation of our approach, with both simulated and real datasets, underscores its efficacy in revealing meaningful patterns within functional data. This research serves as a conduit between functional and multivariate analysis, offering a practical solution for clustering functional datasets.
Functional datasets present a unique challenge due to their infinite-dimensional nature, making traditional clustering methods less straightforward to apply. To tackle this challenge, we propose to transform the initial functional dataset into a multivariate one.
In one-dimensional functional datasets, the original definitions of epigraph and hypograph are considered to obtain the new dataset. For multivariate functional data, new versions of these indexes are introduced. By applying the epigraph and hypograph indexes to obtain a multivariate dataset from a functional one, we reduce dimensionality, rendering the new dataset compatible with standard clustering techniques for multivariate data.
Validation of our approach, with both simulated and real datasets, underscores its efficacy in revealing meaningful patterns within functional data. This research serves as a conduit between functional and multivariate analysis, offering a practical solution for clustering functional datasets.
Keywords
clustering, functional data analysis, multivariate analysis, epigraph, hypograph