{"ID":2865659,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.22969","arxiv_id":"2509.22969","title":"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.","short_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 functi...","url_abs":"https://arxiv.org/abs/2509.22969","url_pdf":"https://arxiv.org/pdf/2509.22969v2","authors":"[\"Samuel Singh\",\"Shirley Coyle\",\"Mimi Zhang\"]","published":"2025-09-26T22:10:23Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}