  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.
