Shape-Informed Clustering of Multi-Dimensional Functional Data via Deep Functional Autoencoders
This work addresses the challenge of clustering complex functional data for applications in fields like bioinformatics and signal processing, representing an incremental advancement through novel regularization and clustering objectives.
The authors tackled the problem of clustering multi-dimensional functional data by developing FAEclust, a functional autoencoder framework that incorporates shape-informed clustering to handle phase variations, achieving state-of-the-art performance with improvements of up to 15% in clustering accuracy on benchmark datasets.
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.