Rule-Based EEG Classifier Utilizing Local Entropy of Time–Frequency Distributions
Abstract
:1. Introduction
2. Materials and Methods
2.1. Signal Analysis in the Time–Frequency Domain
- Identification of signal characteristics (such as time and frequency variations and the number of signal components);
- Extracting components from their mixtures and background noise;
- Ability to synthesize extracted components in the time domain;
- Analysis of features (such as instantaneous amplitude, frequency, and bandwidth of each component).
2.1.1. Spectrogram
2.1.2. Wigner–Ville Distribution (WVD)
2.1.3. The Quadratic Class of Time–Frequency Distributions
2.2. Measuring TFDs’ Information Content Using the Global Rényi Entropy
The Local or Short-Term Rényi Entropy (STRE)
2.3. Instantaneous Frequency Estimation
2.4. Component Extraction Procedure
2.5. Real data
3. Results
EEG Analyzer Implemented in a Virtual Computer Instrument
- Load multi-channel EEG signals: The user imports multi-channel EEG records as a MAT file (for real and imagined limb movements), which are then shown in the first row of the proposed instrument.
- Run EEG analysis: By clicking on this button, the EEG analysis is started by employing STRE- and IF-based algorithms.
- Displaying results: The results are shown in twelve figures as follows. The first row of figures (from top to bottom) show EEG time series at F7, F8, and T4. The second row of figures show the TFDs of the EEGs of real limb movements, followed by the TFDs of the EEG signals of imagined movements, which are given in the third row. The fourth row of figures present the instantaneous number of EEG components obtained using the STRE for both real and imagined movements.
- Numerical results: The application provides numerical results in terms of the average of the dominant EEG component IFs at F7, F8, and T4 for the real and imagined limb movements. Based on these dominant components’ IFs, the analyzed limb movements are estimated. In addition, the instrument shows elapsed time for both the STRE and IF estimations, as well as the total elapsed time for overall EEG analysis.
- Selecting TFD and windows’ sizes and types: The user is allowed to choose a TFD from the provided list of TFDs, and depending on the chosen TFD, they are allowed to set the analyzing window width and type (Hamming, Hanning, rectangular, triangular, Gauss, and Kaiser).
- STRE and TFD parameters: In addition, prior to running EEG analysis, the user is allowed to select values of the STRE sensitivity parameter, the TFD threshold for reducing noise and low-energy cross-terms, and the component extraction threshold.
- TFD display options: The proposed instrument allows display of the TFDs as imagesc (TFD is displayed as an image), contour (TFD values are treated as heights above a plan), mesh (TFD is treated as colored parametric mesh), and surf (plots colored parametric surface).
- References: By clicking on this button, related papers and previous works of the authors that led to the development of the proposed instrument are given.
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Left Hand Forward | Right Hand Forward | Left Hand Backward | Right Hand Backward | |||||
---|---|---|---|---|---|---|---|---|
Moved | Imagined | Moved | Imagined | Moved | Imagined | Moved | Imagined | |
FP1 | 0.051 | 0.050 | 0.050 | 0.052 | 0.052 | 0.051 | 0.050 | 0.050 |
FP2 | 0.051 | 0.051 | 0.053 | 0.052 | 0.052 | 0.056 | 0.052 | 0.050 |
F3 | 0.050 | 0.154 | 0.053 | 0.051 | 0.052 | 0.050 | 0.050 | 0.054 |
F4 | 0.051 | 0.050 | 0.053 | 0.051 | 0.052 | 0.050 | 0.052 | 0.050 |
C3 | 0.050 | 0.050 | 0.054 | 0.051 | 0.051 | 0.051 | 0.050 | 0.050 |
C4 | 0.050 | 0.051 | 0.055 | 0.053 | 0.050 | 0.050 | 0.050 | 0.053 |
P3 | 0.051 | 0.050 | 0.052 | 0.050 | 0.050 | 0.050 | 0.056 | 0.053 |
P4 | 0.052 | 0.051 | 0.050 | 0.052 | 0.052 | 0.050 | 0.050 | 0.051 |
O1 | 0.053 | 0.050 | 0.050 | 0.052 | 0.050 | 0.053 | 0.050 | 0.051 |
O2 | 0.052 | 0.052 | 0.050 | 0.051 | 0.052 | 0.050 | 0.050 | 0.050 |
F7 | 0.050 | 0.161 | 0.054 | 0.099 | 0.096 | 0.054 | 0.052 | 0.181 |
F8 | 0.053 | 0.053 | 0.088 | 0.051 | 0.057 | 0.056 | 0.079 | 0.050 |
T3 | 0.051 | 0.050 | 0.054 | 0.051 | 0.050 | 0.054 | 0.052 | 0.051 |
T4 | 0.052 | 0.051 | 0.082 | 0.050 | 0.080 | 0.055 | 0.192 | 0.050 |
T5 | 0.051 | 0.051 | 0.050 | 0.052 | 0.050 | 0.052 | 0.052 | 0.050 |
T6 | 0.050 | 0.052 | 0.051 | 0.054 | 0.050 | 0.053 | 0.053 | 0.050 |
FZ | 0.050 | 0.050 | 0.050 | 0.050 | 0.052 | 0.050 | 0.050 | 0.050 |
CZ | 0.050 | 0.052 | 0.053 | 0.050 | 0.050 | 0.051 | 0.050 | 0.053 |
PZ | 0.050 | 0.053 | 0.051 | 0.051 | 0.053 | 0.050 | 0.050 | 0.051 |
Left Hand Forward | Right Hand Forward | Left Hand Backward | Right Hand Backward | |||||
---|---|---|---|---|---|---|---|---|
Moved | Imagined | Moved | Imagined | Moved | Imagined | Moved | Imagined | |
FP1 | 0.051 | 0.050 | 0.052 | 0.060 | 0.051 | 0.052 | 0.051 | 0.051 |
FP2 | 0.050 | 0.053 | 0.052 | 0.055 | 0.050 | 0.051 | 0.053 | 0.050 |
F3 | 0.052 | 0.050 | 0.052 | 0.053 | 0.053 | 0.050 | 0.051 | 0.058 |
F4 | 0.050 | 0.050 | 0.053 | 0.055 | 0.051 | 0.050 | 0.079 | 0.050 |
C3 | 0.052 | 0.054 | 0.054 | 0.052 | 0.051 | 0.050 | 0.051 | 0.052 |
C4 | 0.052 | 0.053 | 0.054 | 0.051 | 0.051 | 0.050 | 0.051 | 0.052 |
P3 | 0.052 | 0.058 | 0.050 | 0.053 | 0.051 | 0.053 | 0.051 | 0.052 |
P4 | 0.051 | 0.051 | 0.053 | 0.052 | 0.050 | 0.051 | 0.050 | 0.052 |
O1 | 0.052 | 0.054 | 0.051 | 0.052 | 0.053 | 0.055 | 0.052 | 0.051 |
O2 | 0.052 | 0.053 | 0.052 | 0.052 | 0.052 | 0.057 | 0.052 | 0.052 |
F7 | 0.052 | 0.124 | 0.054 | 0.158 | 0.051 | 0.054 | 0.053 | 0.104 |
F8 | 0.051 | 0.059 | 0.087 | 0.058 | 0.052 | 0.054 | 0.073 | 0.052 |
T3 | 0.051 | 0.051 | 0.054 | 0.052 | 0.051 | 0.051 | 0.050 | 0.051 |
T4 | 0.052 | 0.052 | 0.051 | 0.051 | 0.082 | 0.055 | 0.107 | 0.051 |
T5 | 0.052 | 0.052 | 0.054 | 0.053 | 0.051 | 0.059 | 0.053 | 0.050 |
T6 | 0.052 | 0.052 | 0.051 | 0.052 | 0.050 | 0.056 | 0.053 | 0.052 |
FZ | 0.050 | 0.057 | 0.051 | 0.051 | 0.051 | 0.050 | 0.056 | 0.050 |
CZ | 0.053 | 0.053 | 0.055 | 0.053 | 0.052 | 0.051 | 0.053 | 0.050 |
PZ | 0.052 | 0.053 | 0.052 | 0.053 | 0.051 | 0.051 | 0.050 | 0.051 |
Left Hand Forward | Right Hand Forward | Left Hand Backward | Right Hand Backward | |||||
---|---|---|---|---|---|---|---|---|
Moved | Imagined | Moved | Imagined | Moved | Imagined | Moved | Imagined | |
FP1 | 0.050 | 0.050 | 0.052 | 0.058 | 0.051 | 0.053 | 0.053 | 0.050 |
FP2 | 0.050 | 0.050 | 0.052 | 0.058 | 0.051 | 0.053 | 0.053 | 0.050 |
F3 | 0.050 | 0.054 | 0.052 | 0.054 | 0.051 | 0.053 | 0.050 | 0.055 |
F4 | 0.050 | 0.085 | 0.055 | 0.051 | 0.051 | 0.051 | 0.053 | 0.050 |
C3 | 0.052 | 0.054 | 0.055 | 0.054 | 0.051 | 0.050 | 0.051 | 0.053 |
C4 | 0.052 | 0.054 | 0.055 | 0.054 | 0.051 | 0.050 | 0.051 | 0.053 |
P3 | 0.051 | 0.054 | 0.050 | 0.054 | 0.051 | 0.050 | 0.051 | 0.051 |
P4 | 0.051 | 0.054 | 0.052 | 0.052 | 0.050 | 0.051 | 0.050 | 0.050 |
O1 | 0.051 | 0.054 | 0.050 | 0.052 | 0.055 | 0.054 | 0.051 | 0.054 |
O2 | 0.051 | 0.054 | 0.052 | 0.052 | 0.050 | 0.054 | 0.051 | 0.050 |
F7 | 0.051 | 0.174 | 0.054 | 0.156 | 0.051 | 0.056 | 0.053 | 0.099 |
F8 | 0.172 | 0.106 | 0.089 | 0.058 | 0.051 | 0.053 | 0.073 | 0.106 |
T3 | 0.051 | 0.106 | 0.055 | 0.054 | 0.051 | 0.050 | 0.051 | 0.053 |
T4 | 0.054 | 0.087 | 0.146 | 0.052 | 0.076 | 0.052 | 0.107 | 0.106 |
T5 | 0.051 | 0.054 | 0.054 | 0.054 | 0.051 | 0.056 | 0.053 | 0.053 |
T6 | 0.051 | 0.052 | 0.051 | 0.052 | 0.050 | 0.056 | 0.053 | 0.053 |
FZ | 0.050 | 0.050 | 0.052 | 0.058 | 0.052 | 0.050 | 0.050 | 0.050 |
CZ | 0.052 | 0.052 | 0.055 | 0.055 | 0.051 | 0.050 | 0.053 | 0.050 |
PZ | 0.051 | 0.054 | 0.052 | 0.052 | 0.051 | 0.050 | 0.053 | 0.053 |
Left Hand Forward | Right Hand Forward | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Moved | Imagined | Moved | Imagined | |||||||||
SNR | SP | WVD | RD | SP | WVD | RD | SP | WVD | RD | SP | WVD | RD |
FP1 | 3 | 3118 | 1035 | 7 | 3078 | 1376 | 4 | 3045 | 1138 | 20 | 2854 | 1710 |
FP2 | 35 | 2458 | 48 | 478 | 3034 | 772 | 22 | 2137 | 63 | 59 | 2627 | 309 |
F3 | 9 | 2776 | 1260 | 115 | 2659 | 1879 | 5 | 2356 | 390 | 212 | 2993 | 413 |
F4 | 19 | 2691 | 1501 | 21 | 2894 | 2060 | 3 | 3102 | 1472 | 181 | 2700 | 1591 |
C3 | 7 | 2819 | 829 | 25 | 2832 | 977 | 3 | 2877 | 167 | 3 | 2732 | 200 |
C4 | 3 | 2796 | 1008 | 4 | 2902 | 527 | 3 | 2806 | 238 | 3 | 2706 | 224 |
P3 | 8 | 2838 | 2850 | 11 | 2694 | 1535 | 13 | 2888 | 2690 | 1 | 2673 | 2319 |
P4 | 1 | 3255 | 310 | 1 | 3202 | 137 | 1 | 243 | 149 | 2 | 72 | 106 |
O1 | 25 | 2828 | 431 | 82 | 2699 | 558 | 1 | 2461 | 2163 | 50 | 2604 | 1139 |
O2 | 13 | 3203 | 2243 | 4 | 2581 | 2060 | 1 | 2982 | 3181 | 1 | 2846 | 95 |
F7 | 55 | 2552 | 281 | 96 | 2540 | 290 | 5 | 2811 | 2290 | 86 | 2820 | 1403 |
F8 | 283 | 3034 | 70 | 391 | 3309 | 121 | 287 | 2819 | 38 | 727 | 3088 | 202 |
T3 | 58 | 2603 | 1311 | 61 | 2482 | 90 | 7 | 2663 | 663 | 18 | 2797 | 946 |
T4 | 279 | 3090 | 26 | 279 | 3154 | 278 | 126 | 2816 | 432 | 563 | 3147 | 163 |
T5 | 7 | 3056 | 586 | 5 | 2906 | 639 | 8 | 2909 | 1932 | 17 | 3035 | 146 |
T6 | 3 | 2777 | 1384 | 1 | 2809 | 2604 | 3 | 2906 | 2064 | 4 | 2951 | 1570 |
FZ | 4 | 3097 | 967 | 54 | 3302 | 197 | 7 | 3010 | 171 | 59 | 3197 | 629 |
CZ | 20 | 2748 | 66 | 12 | 2434 | 1781 | 68 | 2355 | 942 | 14 | 2331 | 1256 |
PZ | 4 | 2909 | 766 | 4 | 3132 | 1383 | 2 | 3088 | 268 | 2 | 3231 | 58 |
SN | SP | WVD | RD | SP | WVD | RD | SP | WVD | RD | SP | WVD | RD |
FP1 | 10 | 3196 | 518 | 4 | 3081 | 360 | 5 | 2902 | 2633 | 3 | 2445 | 3030 |
FP2 | 57 | 2517 | 174 | 18 | 2864 | 37 | 861 | 2096 | 129 | 26 | 2773 | 3 |
F3 | 14 | 3155 | 1158 | 87 | 3217 | 51 | 2 | 3028 | 3075 | 73 | 3456 | 3135 |
F4 | 79 | 2739 | 1284 | 5 | 2843 | 1803 | 125 | 2638 | 1561 | 1 | 2691 | 2287 |
C3 | 12 | 3033 | 1239 | 4 | 2956 | 188 | 2 | 2790 | 3612 | 10 | 3070 | 492 |
C4 | 15 | 2993 | 124 | 4 | 2891 | 163 | 2 | 2816 | 3610 | 8 | 3182 | 316 |
P3 | 1 | 3109 | 2833 | 4 | 2778 | 2359 | 8 | 2446 | 347 | 3 | 2751 | 1319 |
P4 | 2 | 175 | 375 | 1 | 2937 | 3093 | 2 | 3148 | 3815 | 1 | 35 | 226 |
O1 | 3 | 2890 | 277 | 139 | 2934 | 342 | 19 | 2499 | 517 | 112 | 2516 | 426 |
O2 | 4 | 3319 | 3060 | 3 | 3081 | 3699 | 3 | 2672 | 2144 | 8 | 2803 | 2932 |
F7 | 97 | 2688 | 179 | 59 | 2572 | 2781 | 17 | 2660 | 1756 | 64 | 2633 | 1430 |
F8 | 343 | 3085 | 182 | 46 | 3140 | 192 | 195 | 3009 | 79 | 15 | 3023 | 48 |
T3 | 4 | 2719 | 332 | 87 | 2797 | 1498 | 8 | 2482 | 1189 | 2 | 2650 | 1257 |
T4 | 221 | 2774 | 153 | 6 | 2881 | 487 | 229 | 2931 | 126 | 606 | 2916 | 26 |
T5 | 9 | 2904 | 1495 | 16 | 3270 | 1814 | 11 | 3158 | 2748 | 8 | 3309 | 2095 |
T6 | 1 | 2628 | 1272 | 5 | 2783 | 2610 | 9 | 2434 | 1751 | 72 | 2663 | 1702 |
FZ | 98 | 3143 | 411 | 6 | 3311 | 35 | 5 | 3050 | 686 | 4 | 3108 | 1 |
CZ | 16 | 2218 | 1654 | 8 | 2004 | 312 | 12 | 2339 | 2934 | 8 | 2956 | 57 |
PZ | 3 | 171 | 193 | 2 | 3038 | 2740 | 2 | 2782 | 296 | 2 | 47 | 800 |
Left Hand Forward | Right Hand Forward | Left Hand Backward | Right Hand Backward | |
---|---|---|---|---|
Spectrogram | ||||
Accuracy | 0.90 | 0.94 | 0.86 | 0.99 |
Precision | 0.90 | 0.95 | 0.86 | 0.99 |
Recall | 0.90 | 0.94 | 0.86 | 0.99 |
F1 | 0.90 | 0.94 | 0.86 | 0.99 |
WVD | ||||
Accuracy | 0.86 | 0.78 | 0.99 | 0.90 |
Precision | 0.80 | 0.81 | 1.00 | 0.90 |
Recall | 0.98 | 0.74 | 0.99 | 0.90 |
F1 | 0.88 | 0.77 | 0.99 | 0.90 |
RD | ||||
Accuracy | 0.73 | 0.95 | 1.00 | 0.82 |
Precision | 0.73 | 0.95 | 1.00 | 0.82 |
Recall | 0.73 | 0.95 | 1.00 | 0.82 |
F1 | 0.73 | 0.95 | 1.00 | 0.82 |
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Lerga, J.; Saulig, N.; Stanković, L.; Seršić, D. Rule-Based EEG Classifier Utilizing Local Entropy of Time–Frequency Distributions. Mathematics 2021, 9, 451. https://doi.org/10.3390/math9040451
Lerga J, Saulig N, Stanković L, Seršić D. Rule-Based EEG Classifier Utilizing Local Entropy of Time–Frequency Distributions. Mathematics. 2021; 9(4):451. https://doi.org/10.3390/math9040451
Chicago/Turabian StyleLerga, Jonatan, Nicoletta Saulig, Ljubiša Stanković, and Damir Seršić. 2021. "Rule-Based EEG Classifier Utilizing Local Entropy of Time–Frequency Distributions" Mathematics 9, no. 4: 451. https://doi.org/10.3390/math9040451
APA StyleLerga, J., Saulig, N., Stanković, L., & Seršić, D. (2021). Rule-Based EEG Classifier Utilizing Local Entropy of Time–Frequency Distributions. Mathematics, 9(4), 451. https://doi.org/10.3390/math9040451