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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.22969 |
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| _version_ | 1866915542053421056 |
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| author | Singh, Samuel Coyle, Shirley Zhang, Mimi |
| author_facet | Singh, Samuel Coyle, Shirley Zhang, Mimi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shape-Informed Clustering of Multi-Dimensional Functional Data via Deep Functional Autoencoders Singh, Samuel Coyle, Shirley Zhang, Mimi Machine Learning 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. |
| title | Shape-Informed Clustering of Multi-Dimensional Functional Data via Deep Functional Autoencoders |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2509.22969 |