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arXiv · 2304.14378

Functional Diffusion Maps

María Barroso·Carlos María Alaíz·Ángela Fernández·Jose Luis Torrecilla
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Abstract

Nowadays many real-world datasets can be considered as functional, in the sense that the processes which generate them are continuous. A fundamental property of this type of data is that in theory they belong to an infinite-dimensional space. Although in practice we usually receive finite observations, they are still high-dimensional and hence dimensionality reduction methods are crucial. In this vein, the main state-of-the-art method for functional data analysis is Functional PCA. Nevertheless, this classic technique assumes that the data lie in a linear manifold, and hence it could have problems when this hypothesis is not fulfilled. In this research, attention has been placed on a non-linear manifold learning method: Diffusion Maps. The article explains how to extend this multivariate method to functional data and compares its behavior against Functional PCA over different simulated and real examples.

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María Barroso, Carlos María Alaíz, Ángela Fernández, Jose Luis Torrecilla. 2023-04-27. Functional Diffusion Maps. https://arxiv.org/abs/2304.14378

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