Time-Series Prediction of the Oscillatory Phase of EEG Signals Using the Least Mean Square Algorithm-Based AR Model
Abstract
:1. Introduction
2. Materials and Methods
2.1. Algorithm Outline
- Re-reference the raw data and then downsample to 500 Hz.
- Optimize the frequency band (8–13 Hz) based on the peak/central frequency of each individual. The individual alpha frequency (IAF) is linked to the maximum EEG power within the alpha range. After finding the IAF, a passband for a band-pass filter is chosen. The low cutoff frequency for the band-pass filter is IAF-1 and high cutoff frequency is IAF+1.
- Apply a two-pass finite impulse response (FIR) band-pass filter with a filter order of 128 and the passband chosen in step 2 [28].
- Segment the data into 500 ms epochs.
- Compute the optimal AR model order using Akaike’s Information Criterion (AIC).
- Compute AR coefficients using the Yule–Walker equations.
- Select the adaptation size/learning rate of LMS.
- Select the number of filter taps (same as the AR model order).
- Compute the coefficients using LMS and then use those coefficients to predict the next sample until the prediction length in the AR equation.
- Calculate the time-series forward prediction for twice the prediction length (256 ms) for the LMS-based AR model (See Figure 1).
- Compute the means of the predicted segment and original segment and subtract the respective means from the predicted segment and original segment.
- Estimate the instantaneous phase and frequency of the original and predicted data segments by calculating the analytic signal via the Hilbert transform.
- Compute the phase difference between the original and predicted data segments.
- Calculate the phase locking value (PLV) between the original and predicted data.
2.2. Autoregressive (AR) Model
2.3. Least Mean Square (LMS)
2.4. Instantaneous Frequency and Phase
2.5. Participants
2.6. EEG Recording and Preprocessing
2.7. Statistical Analysis
3. Results
3.1. Shorter Prediction Length
3.2. Twice Prediction Length
3.3. Sampling Points Crossing the Significant Rayleigh’s Z Value
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Data Availability
References
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Subjects | Results of Channel O1 800 ms | |
---|---|---|
Autoregressive (AR) Model | Least Mean Square (LMS)-based AR Model | |
Time Points | Time Points | |
1. | 424 | 446 |
2. | 368 | 392 |
3. | 536 | 550 |
4. | 492 | 484 |
5. | 382 | 416 |
6. | 420 | 578 |
7. | 452 | 456 |
8. | 678 | 752 |
9. | 392 | 370 |
10. | 694 | * |
11. | 630 | 678 |
12. | 506 | 556 |
13. | 702 | 618 |
14. | 524 | 522 |
15. | 796 | * |
16. | 644 | 598 |
17. | 528 | 578 |
18. | * | 778 |
19. | 566 | 598 |
20. | 660 | 714 |
21. | 452 | 406 |
Prediction Time Point (ms) | p-Value | AR Model | LMS-Based AR Model |
---|---|---|---|
Rayleigh’s Z Value (Mean Values) | |||
64 | p < 0.001 | 582 | 568 |
128 | p < 0.001 | 384 | 403 |
256 | p < 0.001 | 113 | 131 |
340 | p = 0.010 | 50.5 | 61.18 |
400 | p = 0.070 | 29 | 35 |
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Shakeel, A.; Tanaka, T.; Kitajo, K. Time-Series Prediction of the Oscillatory Phase of EEG Signals Using the Least Mean Square Algorithm-Based AR Model. Appl. Sci. 2020, 10, 3616. https://doi.org/10.3390/app10103616
Shakeel A, Tanaka T, Kitajo K. Time-Series Prediction of the Oscillatory Phase of EEG Signals Using the Least Mean Square Algorithm-Based AR Model. Applied Sciences. 2020; 10(10):3616. https://doi.org/10.3390/app10103616
Chicago/Turabian StyleShakeel, Aqsa, Toshihisa Tanaka, and Keiichi Kitajo. 2020. "Time-Series Prediction of the Oscillatory Phase of EEG Signals Using the Least Mean Square Algorithm-Based AR Model" Applied Sciences 10, no. 10: 3616. https://doi.org/10.3390/app10103616