| Abstract: |
Spatiotemporal data arise in many scientific areas and are difficult to analyze, since there are significant challenges for representation, comparison, and pattern discovery. This complex spatiotemporal variability is hard to characterize using conventional feature engineering or low-dimensional summaries. In this work, we introduce a machine-learning pipeline for unsupervised representation learning and clustering of dynamic three-dimensional curves and identifying emergent dynamical regimes directly from data. The framework is motivated by the analysis of biological flagellar motion but is designed as a general approach for structured geometric time series.
The proposed framework combines geometric preprocessing, representation learning, and density-based clustering to analyze time-resolved three-dimensional curves. Raw trajectories are first transformed to remove rigid-body degrees of freedom through anchoring, principal-axis alignment, and scale normalization, ensuring invariance to translation, rotation, and global scaling. Local differential-geometric descriptors, including curvature and torsion, are then computed along the filament to capture intrinsic deformation patterns over time. These descriptors are organized into high-dimensional spatiotemporal feature tensors that encode the evolution of waveform geometry.
To extract compact representations of these signals, we train a neural autoencoder that learns a low-dimensional latent manifold describing dominant modes of motion. The learned embedding captures nonlinear structure in the data and enables efficient comparison between trajectories and dominant modes of waveform variability while significantly reducing dimensionality.
The proposed pipeline illustrates how geometric feature extraction combined with representation learning can enable unsupervised discovery of structure in complex dynamical systems. |