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

Samuel Singh, Shirley Coyle, Mimi Zhang

Keywords: autoencoder, cluster analysis, functional data, manifold, multi-dimensional, neural network, phase variation, universal approximation

TL;DR: We developed a functional autoencoder framework for cluster analysis of multi-dimensional functional data, data that are random realizations of vector-valued random functions.

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.

Primary Area: General machine learning (supervised, unsupervised, online, active, etc.)

Submission Number: 2419