CASC: Causal Adversarial Subspace Clustering for Multivariate Spatiotemporal Data

Traditional deep subspace clustering methods often struggle with multivariate spatiotemporal data because they rely on geometric similarity, assume static subspace structures, and fail to capture the complex causal and long-range temporal dependencies inherent in such systems. This paper asks: can we transform deep subspace clustering into a causal-temporal regime discovery framework that effectively models evolving latent structures in high-dimensional spatiotemporal data?

The authors propose Causal Adversarial Subspace Clustering (CASC), an end-to-end framework that combines a U-Net-inspired architecture with stacked FAConvLSTM layers to preserve spatial and temporal structures. The model features a graph attention transformer-based self-expressive network at the bottleneck to capture local spatial relationships and long-range temporal interactions.

Crucially, the framework introduces two novel learning objectives:

1. Causal Subspace Preservation Loss: This aligns self-expression coefficients with latent causal relationships, ensuring clusters reflect underlying causal processes.
2. Dynamic Temporal Subspace Evolution Loss: This captures evolving subspace structures and temporal regime transitions in nonstationary environments.

The system is trained using a quality-verifying, energy-based temporal discriminator that guides the generator to produce more discriminative and cluster-friendly embeddings.

Experiments on three real-world multivariate spatiotemporal datasets demonstrate that CASC consistently produces more compact, better-separated, and temporally coherent clusters compared to state-of-the-art deep clustering methods. The framework shows substantial improvements in clustering accuracy, interpretability, and robustness by explicitly modeling the causal and temporal dynamics that govern the data.