Shape-Informed Clustering of Multi-Dimensional Functional Data via Deep Functional Autoencoders

• URL: http://arxiv.org/abs/2509.22969v1
• Date: Fri, 26 Sep 2025 22:10:23 GMT
• Title: Shape-Informed Clustering of Multi-Dimensional Functional Data via Deep Functional Autoencoders
• Authors: Samuel V. Singh, Shirley Coyle, Mimi Zhang,
• Abstract summary: FAEclust is a novel functional autoencoder framework for cluster analysis of multi-dimensional functional data.<n>We introduce 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.
• Score: 3.899824115379245
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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