Shape-Informed Clustering of Multi-Dimensional Functional Data via Deep Functional Autoencoders
Abstract
We introduce FAEclust, a novel functional autoencoder framework for cluster analysis of multi-dimensional functional data, data that are random realizations of vector-valued random functions. Our framework features a universal-approximator encoder that captures complex nonlinear interdependencies among component functions, and a universal-approximator decoder capable of accurately reconstructing both Euclidean and manifold-valued functional data. Stability and robustness are enhanced through innovative regularization strategies applied to functional weights and biases. Additionally, we incorporate a clustering loss into the network's training objective, promoting the learning of latent representations that are conducive to effective clustering. A key innovation is our shape-informed clustering objective, ensuring that the clustering results are resistant to phase variations in the functions. We establish the universal approximation property of our non-linear decoder and validate the effectiveness of our model through extensive experiments.
Cite
@article{arxiv.2509.22969,
title = {Shape-Informed Clustering of Multi-Dimensional Functional Data via Deep Functional Autoencoders},
author = {Samuel Singh and Shirley Coyle and Mimi Zhang},
journal= {arXiv preprint arXiv:2509.22969},
year = {2025}
}