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Automated State Estimation for Summarizing the Dynamics of Complex Urban Systems Using Representation Learning
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Proposes UFACR, which ranks features with K-means pseudo-labels, a random forest and SHAP, then learns a compact LSTM seq2seq representation for clustering wastewater plant states.
Problem
State estimation of partially observable complex urban systems (wastewater treatment plants) via clustering degrades as the number of sensors and feature dimensions grows.
Approach
Attention-based feature weighting from SHAP attributions of a classifier trained on K-means pseudo-labels, followed by an unsupervised LSTM encoder-decoder that compresses the weighted multivariate time series into a low-dimensional representation for clustering into operational states.
Key results
- On HRAP, UFACR silhouette is about 39% higher than the closest competitor (0.46 vs 0.33).
- On BSM2, UFACR silhouette is about 44% higher than the closest competitor.
- UFACR Davies-Bouldin score 0.88 on HRAP and 0.76 on BSM2, versus 1.24 (PCA) and 1.0 (TS-stat) for the closest competitors.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use UFACR instead of PCA | Unsupervised wastewater clustering · HRAP | Davies-Bouldin score: 1.24 -> 0.88 | Helped |
| Use UFACR instead of TS-stat | Unsupervised wastewater clustering · HRAP | Calinski-Harabasz score: 109 -> 850 | Helped |
| Use UFACR instead of TS-stat | Unsupervised wastewater clustering · BSM2 | Davies-Bouldin score: 1 -> 0.76 | Helped |
| Use UFACR instead of TS-stat | Unsupervised wastewater clustering · BSM2 | Calinski-Harabasz score: 409 -> 1175 | Helped |
| Use UFACR instead of the closest competitor | Unsupervised wastewater clustering · HRAP | Silhouette coefficient: 39% | Helped |
| Use UFACR instead of the closest competitor | Unsupervised wastewater clustering · BSM2 | Silhouette coefficient: 44% | Helped |
Limitations
- Evaluated on only two wastewater datasets, one real and one simulated.
- Cluster validation relies on intrinsic metrics and expert judgment rather than ground-truth states.
- Algorithm 1 final step clusters the raw X rather than the learned representation Z, which appears inconsistent with the described method.
Experimental setup
Datasets: HRAP (High Rate Algae Pond) real-world wastewater data BSM2 synthetic wastewater treatment data
Benchmarks: HRAP BSM2
Metrics: Silhouette coefficient Davies-Bouldin score Calinski-Harabasz score t-SNE visual inspection expert validation
Baselines: PCA DFT with PCA time-series statistics
Builds on: SHAP K-means LSTM seq2seq
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