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Exploiting Representation Curvature for Boundary Detection in Time Series
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Proposes RECURVE, a boundary detection method for time series that uses the curvature of a representation trajectory (instead of consecutive distances) as the change metric, with theory based on an equilateral random walk.
Problem
Representation-based time-series boundary detection relies on consecutive representation distances, which fail to separate intra- and inter-segment points when class changes are gradual or subtle.
Approach
Treat the sequence of point representations as a trajectory and use the turning-angle curvature (normalized and smoothed, 1 minus curvature) as the change metric; intra-segment points have higher curvature because representations are confined within class-specific balls, a property argued to be insensitive to the degree of change between classes.
Key results
- RECURVE+TPC reaches AUC 0.955 on mHealth at p=20 vs 0.849 for the second-best method, a gain of up to 12.7% in AUC.
- RECURVE+TPC outperforms TS-CP2 on all four datasets in AUC and LOC under both thresholding schemes.
- On HAPT with p=5 and TPC, AUC on gradual changes improves about 32% over TS-CP2 versus about 21% on abrupt changes.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace consecutive-distance change scoring with curvature scoring using TPC representations | TS-CP2/TPC boundary detection · WISDM, HAPT, mHealth, and 50salads (p=10) | AUC: WISDM: 0.820±0.012 -> 0.901±0.004; HAPT: 0.695±0.006 -> 0.913±0.001; mHealth: 0.561±0.013 -> 0.954±0.003; 50salads: 0.68 | Helped |
| Use curvature scoring with TNC representations | RECURVE+TNC · mHealth (p=10) | AUC: 0.849±0.113 -> 0.980±0.004 | Helped |
| Use curvature scoring with TNC representations | RECURVE+TNC · WISDM, HAPT, and 50salads (p=10) | AUC: WISDM: 0.702±0.000 -> 0.889±0.004; HAPT: 0.873±0.004 -> 0.867±0.017; 50salads: 0.684±0.003 -> 0.595±0.016 | Mixed |
| Vary w from 0.25× to 4.00× the default (ablation) | RECURVE+TPC · WISDM, HAPT, mHealth, and 50salads | AUC: WISDM: 0.832±0.015, 0.891±0.006, 0.901±0.004, 0.892±0.003, 0.861±0.002; HAPT: 0.901±0.004, 0.914±0.002, 0.913±0.001, 0.8 | Mixed |
| Vary w from 0.25× to 4.00× the default (ablation) | RECURVE+TNC · WISDM, HAPT, mHealth, and 50salads | AUC: WISDM: 0.824±0.016, 0.869±0.009, 0.889±0.004, 0.897±0.002, 0.871±0.002; HAPT: 0.842±0.011, 0.850±0.012, 0.867±0.017, 0.8 | Mixed |
| Increase representation dimensionality d′ from 0.25× to 4.00× the default (ablation) | RECURVE+TPC and RECURVE+TNC · WISDM, HAPT, mHealth, and 50salads | AUC | Mixed |
Surprising findings
- Consecutive-distance change metrics show a strong correlation with inter-class embedding distance, so they weaken for gradual changes, while the curvature metric is insensitive to change degree.
- RECURVE+TNC is weaker than RECURVE+TPC on 50salads (AUC about 0.59-0.60 vs 0.72-0.73), so the best representation method varies by dataset.
Limitations
- False positives when segments are shorter than the window parameter w, since w is set from mean segment length.
- Performance may degrade when segment lengths have high variance.
- Theoretical analysis relies on an equilateral random walk assumption and simulation-based results for the curvature-radius relation.
Experimental setup
Datasets: WISDM HAPT mHealth 50salads
Benchmarks: WISDM HAPT mHealth 50salads
Metrics: AUC LOC (mean location distance)
Baselines: RuLSIF KL-CPD TS-CP2
Builds on: TS-CP2 TNC RuLSIF KL-CPD
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