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Efficient Anomaly Detection of Irregular Sequences in Ct-Echo Model Space
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Proposes Continuous-time Echo Network (Ct-Echo), an ODE-augmented echo state network whose ridge-regression readout models represent irregular sequences, enabling anomaly detection by classifying in this model space.
Problem
Anomaly detection and classification of irregularly sampled sequences (non-uniform sampling, missing values) is costly for existing deep and ODE-based methods, which need heavy training and much labeled data.
Approach
Fit each irregular sequence with an ESN-style reservoir whose state transitions are continuous-time via an ODE solver (linear decay or leaky integrator), obtain the readout by ridge regression, then compare sequences via a 2-norm distance between readout models and classify with SVM/KNN in this model space.
Key results
- Proposed (Leaky) reaches 92.67% on CWRU sub-dataset D and 99.69% on SU B30 with 50% missing rate, outperforming baselines such as Warpformer (80.22%, 97.50%) on those splits.
- Ct-Echo fitting takes about 0.2 s on CWRU versus 76 s for GRU-∆t and 55 s for Warpformer (Proposed Decay, average training time).
- Proposed methods maintain higher accuracy as missing rates rise from 10% to 50%, with advantage most pronounced at missing rates of 30% or more.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Ct-Echo (Decay or Leaky) instead of the strongest baseline | Irregular-sequence classification · CWRU A, 50% missing | accuracy (%): 81.94 ± 1.13 -> 75.22 ± 2.10; 81.94 ± 1.13 -> 83.06 ± 0.88 | Mixed |
| Use Ct-Echo (Decay or Leaky) instead of the strongest baseline | Irregular-sequence classification · CWRU B, C, D, and E, 50% missing | accuracy (%): 67.67 ± 1.05 -> 75.78 ± 1.66; 67.67 ± 1.05 -> 82.83 ± 1.06; 68.89 ± 0.99 -> 80.72 ± 2.36; 68.89 ± 0.99 -> 87.67 ± 1.20; | Helped |
| Use Ct-Echo (Decay or Leaky) instead of the strongest baseline | Irregular-sequence classification · SU G20, 50% missing | accuracy (%): 97.39 ± 0.82 -> 94.31 ± 0.96; 97.39 ± 0.82 -> 91.25 ± 0.58 | Mixed |
| Use Ct-Echo (Decay or Leaky) instead of the strongest baseline | Irregular-sequence classification · SU G30, B20, B30, 50% missing | accuracy (%): 96.44 ± 0.50 -> 98.15 ± 0.55; 96.44 ± 0.50 -> 97.10 ± 0.58; 98.30 ± 0.29 -> 99.21 ± 0.28; 98.30 ± 0.29 -> 99.50 ± 0.11; | Helped |
| Use Ct-Echo (Decay or Leaky) instead of the strongest baseline | Irregular-sequence classification · WHU, 50% missing | accuracy (%): 93.33 ± 2.11 -> 95.56 ± 2.03; 93.33 ± 2.11 -> 96.67 ± 1.87 | Helped |
| Replace Ct-Echo-Decay with Ct-Echo-Leaky (ablation) | Proposed method · CWRU datasets, 50% missing | accuracy (%): 75.22 ± 2.10 -> 83.06 ± 0.88; 75.78 ± 1.66 -> 82.83 ± 1.06; 80.72 ± 2.36 -> 87.67 ± 1.20; 86.67 ± 1.22 -> 92.67 ± 0.81; | Helped |
| Replace Ct-Echo-Decay with Ct-Echo-Leaky (ablation) | Proposed method · SU datasets, 50% missing | accuracy (%): 94.31 ± 0.96 -> 91.25 ± 0.58; 98.15 ± 0.55 -> 97.10 ± 0.58; 99.21 ± 0.28 -> 99.50 ± 0.11; 99.69 ± 0.13 -> 99.69 ± 0.09 | Mixed |
| Use KNN instead of SVM for model-space classification (ablation) | Ct-Echo model space · SU datasets, 50% missing | accuracy (%): 94.31 ± 0.96 -> 87.23 ± 1.81; 91.25 ± 0.58 -> 86.17 ± 2.22; 98.15 ± 0.55 -> 96.92 ± 0.64; 97.10 ± 0.58 -> 96.54 ± 1.03; | Hurt |
Surprising findings
- SVM outperforms KNN in the Ct-Echo model space on the SU datasets.
Limitations
- Evaluated only on vibration/fault-diagnosis datasets (CWRU, SU, WHU); generalization to other domains untested.
- Ct-Echo-Decay and Ct-Echo-Leaky have hyperparameters (reservoir size, spectral radius, decay/leaky rate) set manually.
- Test set for WHU is small (90 sequences), limiting statistical confidence.
Experimental setup
Datasets: CWRU SU WHU
Benchmarks: CWRU SU WHU
Metrics: accuracy training time
Baselines: NFFT-SVM GRU-∆t GRU-Int mTANs Warpformer ODE-RNN Neural CDE MBM-Int MBM-∆t
Builds on: Echo State Network ODE-RNN Neural CDE model-based methods (learning in model space) cycle reservoir with regular jumps
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