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

NeurIPS 2025 · Probabilistic and scientific modeling › Molecules and proteins · approach: Sparse graphical and tensor models · 1 citations (OpenAlex)

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Proposes FAEclust, a deep functional autoencoder with continuous-basis functional weights, regularized penalties, and a convex-clustering objective with SRV-based shape-aware similarity, for clustering multi-dimensional and manifold-valued functional data.

Problem

Clustering multi-dimensional functional data, where nonlinear inter-dimension relationships, manifold-valued curves, and phase variation make linear multivariate FPCA-based methods inadequate.

Approach

A functional autoencoder whose functional weights are basis expansions with penalized coefficients, with a universal-approximation nonlinear decoder, trained jointly with a Calinski-Harabasz-style clustering loss and a convex clustering step that uses an SRV (Fisher-Rao) shape-aware similarity.

Key results

• FAEclust achieves the best AMI on 12 of 17 real Euclidean datasets and ranks top-2 on 15 of 17.
• On five manifold-valued simulations, FAEclust attains the best mean AMI on all five (e.g., Hyperbolic 0.798 vs. 0.410 for VANO).
• Under random time warping, mean AMI/ARI across 12 scenarios changes by only 0.013 on average, and FAEclust has the highest scores in 11 of 12 warped scenarios against seven baselines.

Measured effects reported in the paper

Surprising findings

• On BasicMotions, FAEclust has lower AMI (0.539) than FAE (0.676) and VANO (0.592), and on ERing and JapaneseVowels it does not rank first.

Limitations

• Baseline FNN and FAE were re-implemented by the authors since no official implementations exist, which may affect fairness of comparison.
• Model selection of cluster number relies on internal validation indices such as silhouette or Davies-Bouldin, not guaranteed to be optimal.
• Experiments on real data use one-dimensional and multi-dimensional UEA/UCR datasets; performance is not uniformly best (e.g., BM, ERing, JV).

Experimental setup

Datasets: UEA & UCR Time Series Classification Repository (17 datasets) simulated manifold-valued functional data (Hypersphere, Hyperbolic, Swiss roll, Lorenz, Pendulum) 12 simulation scenarios from prior work

Benchmarks: UEA & UCR Time Series Classification Repository (17 datasets) manifold simulations (Hypersphere, Hyperbolic, Swiss roll, Lorenz, Pendulum) 12 simulation scenarios with time warping

Metrics: AMI ARI

Baselines: funHDDC funclust FADPclust FNN FAE VANO

Builds on: functional neural networks functional autoencoder (Hsieh et al.) VANO convex clustering square-root velocity framework

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