# Automatic Epileptic Seizure Detection in EEG Signals Using Multi-Domain Feature Extraction and Nonlinear Analysis

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Materials

#### 2.2. Signal Pre-Processing: Wavelet Threshold De-Noising

#### 2.3. Feature Extraction

#### 2.3.1. Feature Extraction in the Time Domain, Frequency Domain and Time-Frequency Domain

#### 2.3.2. Feature Extraction via Nonlinear Analysis

- Procedure 1, IMF extraction procedure:
- Extract local max and local min magnitudes from signal $x\left[n\right]$;
- Obtain the envelope ${\epsilon}_{max}\left[n\right]$ by connecting all of the maximums with cubic spline interpolation, and similarly obtain the envelope ${\epsilon}_{min}\left[n\right]$ by connecting all of the minimums with cubic spline interpolation;
- Compute the average of ${\epsilon}_{max}\left[n\right]$ and ${\epsilon}_{min}\left[n\right]$, and denote as $\alpha \left[n\right]$:$$\alpha \left[n\right]=\frac{{\epsilon}_{max}\left[n\right]+{\epsilon}_{min}\left[n\right]}{2}$$
- Extract the detail $d\left[n\right]$ from $x\left[n\right]$ as:$$d\left[n\right]=x\left[n\right]-\alpha \left[n\right]$$
- Check whether the detail $d\left[n\right]$ satisfy the above conditions mentioned for IMF or not;
- Repeat Steps 1–5, until $d\left[n\right]$ satisfies the conditions for IMF.

- Procedure 2, approximate entropy calculation:
- Let the values containing N samples in each sub-band be $X=\left(\right)open="["\; close="]">x\left(1\right),x\left(2\right),x\left(3\right),\cdots ,x\left(N\right)$;
- Let ${X}_{m}\left(\mathrm{i}\right)$ be a sub-sequence of X such that ${X}_{m}\left(\mathrm{i}\right)=[x\left(i\right),x\left(\right)open="("\; close=")">i+1,x\left(\right)open="("\; close=")">i+2$$x\left(\right)open="("\; close=")">i+m-1$ for $1\le i\le N-m+1$, where m is the length of the sub-sequence;
- Let r represent the noise filter level that is defined as [33]:$$r=k\times SD,\phantom{\rule{1.em}{0ex}}k=0,0.1,\cdots ,0.9$$
- Let ${X}_{m}\left(\mathrm{i}\right)$ represent a set of sub-sequences obtained from ${X}_{m}\left(\mathrm{j}\right)$ by varying j from 1–($N-m$). Each sequence ${X}_{m}\left(\mathrm{j}\right)$ in the set of ${X}_{m}\left(\mathrm{j}\right)$ is compared with ${X}_{m}\left(\mathrm{i}\right)$, and in this process, two parameters, namely ${C}_{i}^{m}\left(r\right)$ and ${C}_{i}^{m+1}\left(r\right)$, are defined as follows:$${C}_{i}^{m}\left(r\right)=\frac{{\sum}_{j=1}^{N-m}{k}_{j}}{N-m+1},\phantom{\rule{25.6073pt}{0ex}}$$$$\mathrm{where}\phantom{\rule{5.69046pt}{0ex}}k=\left(\right)open="\{"\; close>\begin{array}{c}1,\text{}if\left(\right)open="|"\; close="|">x\left(\right)open="("\; close=")">i+t-x\left(\right)open="("\; close=")">j+t\hfill \\ r\phantom{\rule{5.69046pt}{0ex}}for\phantom{\rule{5.69046pt}{0ex}}0\le tm\end{array}0,\text{}otherwise\hfill $$
- The approximate entropy is calculated by using ${C}_{i}^{m}\left(r\right)$ and ${C}_{i}^{m+1}\left(r\right)$ as follows:$$ApEn=\frac{1}{N-m+1}{\displaystyle \sum _{i=1}^{N-m+1}}\mathrm{ln}{C}_{i}^{m}\left(r\right)-\frac{1}{N-m}{\displaystyle \sum _{i=1}^{N-m}}\mathrm{ln}{C}_{i}^{m+1}\left(r\right)$$

#### 2.4. Classification and Performance Evaluation

## 3. Results

#### 3.1. Wavelet Threshold Denoising and Feature Extraction

#### 3.2. Dimension Reduction in Feature Space

#### 3.3. Experiment Classification Results

## 4. Discussion and Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Four level decomposition of an EEG signal from five sub-bands of the clinical interest, where colored boxes indicate five sub-bands of the clinical interest.

**Figure 3.**Wavelet threshold de-nosing results. (

**a**) Original EEG signals in the time domain; (

**b**) Processed EEG signals in the time domain.

**Figure 4.**Different sub-band signals using four level wavelet decomposition from an original EEG signal. (a${}_{1}$) the approximation of 0–32 Hz, (a${}_{2}$) the approximation of 0–16 Hz, (a${}_{3}$) the approximation of 0–8 Hz, (a${}_{4}$) the approximation of 0–4 Hz; (d${}_{1}$) the detail of 32–64 Hz, (d${}_{2}$) the detail of 16–32 Hz, (d${}_{3}$) the detail of 8–16 Hz, (d${}_{4}$) the detail of 4–8 Hz.

**Figure 5.**Different sub-band signals using four level wavelet decomposition from the denoised EEG signal. (a${}_{1}$) the approximation of 0–32 Hz, (a${}_{2}$) the approximation of 0–16 Hz, (a${}_{3}$) the approximation of 0–8 Hz, (a${}_{4}$) the approximation of 0–4 Hz; (d${}_{1}$) the detail of 32–64 Hz, (d${}_{2}$) the detail of 16–32 Hz, (d${}_{3}$) the detail of 8–16 Hz, (d${}_{4}$) the detail of 4–8 Hz.

Feature Analyzed | Dimension | |
---|---|---|

Before | After | |

Standard Deviation | 5 | 2 |

Total Variation | 5 | 2 |

Relative Power FFT | 5 | 2 |

Standard Deviation & Relative power DWT | 10 | 2 |

EMD-PSR | 32 | 2 |

Entropy | 11 | 2 |

Min, Max, Mean DWT coefficients | 15 | 2 |

Feature Set | Classifiers | 5-Fold CV | 10-Fold CV | ||||
---|---|---|---|---|---|---|---|

SEN | SPE | ACC | SEN | SPE | ACC | ||

Time domain | KNN | 97.72 ± 0.83 | 99.74 ± 0.44 | 98.73 ± 0.43 | 91.98 ± 1.10 | 99.95 ± 0.11 | 98.36 ± 0.24 |

LDA | 85.88 ± 1.92 | 100.00 ± 0.00 | 92.94 ± 0.96 | 83.56 ± 0.88 | 99.75 ± 0.04 | 96.52 ± 0.18 | |

NB | 92.92 ± 1.31 | 96.56 ± 0.57 | 94.74 ± 0.74 | 92.94 ± 0.70 | 98.47 ± 0.16 | 97.37 ± 0.18 | |

LR | 95.84 ± 0.86 | 98.28 ± 0.69 | 97.06 ± 0.53 | 95.76 ± 0.62 | 98.12 ± 0.65 | 96.94 ± 0.45 | |

SVM | 97.04 ± 0.82 | 99.46 ± 0.90 | 98.25 ± 0.61 | 93.46 ± 1.08 | 99.95 ± 0.11 | 98.65 ± 0.23 | |

Frequency domain | KNN | 91.86 ± 1.85 | 89.36 ± 1.66 | 90.61 ± 1.15 | 92.68 ± 1.75 | 91.00 ± 1.23 | 91.84 ± 1.03 |

LDA | 74.50 ± 1.53 | 95.96 ± 0.87 | 85.23 ± 0.87 | 75.10 ± 0.92 | 95.32 ± 0.55 | 85.21 ± 0.50 | |

NB | 84.04 ± 0.77 | 91.50 ± 1.14 | 87.77 ± 0.71 | 83.42 ± 0.67 | 90.70 ± 0.88 | 87.06 ± 0.64 | |

LR | 88.72 ± 1.59 | 91.44 ± 0.92 | 90.08 ± 0.80 | 90.10 ± 0.94 | 90.50 ± 0.57 | 90.30 ± 0.54 | |

SVM | 90.02 ± 1.91 | 90.10 ± 1.06 | 90.06 ± 1.10 | 91.02 ± 1.10 | 89.70 ± 0.90 | 90.36 ± 0.69 | |

Time-frequencydomain | KNN | 93.96 ± 1.98 | 98.69 ± 0.28 | 97.75 ± 0.48 | 94.48 ± 1.42 | 98.79 ± 0.16 | 97.92 ± 0.31 |

LDA | 72.28 ± 1.59 | 99.65 ± 0.16 | 94.18 ± 0.34 | 72.60 ± 1.40 | 99.66 ± 0.12 | 94.25 ± 0.29 | |

NB | 86.12 ± 1.44 | 95.28 ± 0.63 | 93.45 ± 0.59 | 86.80 ± 1.04 | 95.16 ± 0.43 | 93.48 ± 0.41 | |

LR | 93.08 ± 1.59 | 98.34 ± 0.74 | 97.29 ± 0.66 | 91.48 ± 1.20 | 93.82 ± 0.86 | 92.65 ± 0.68 | |

SVM | 94.48 ± 1.53 | 98.76 ± 0.31 | 97.90 ± 0.42 | 94.26 ± 1.34 | 98.77 ± 0.27 | 97.87 ± 0.33 | |

Nonlinear analysis | KNN | 96.72 ± 1.37 | 98.96 ± 0.28 | 98.51 ± 0.33 | 97.62 ± 0.82 | 99.03 ± 0.18 | 98.75 ± 0.24 |

LDA | 66.38 ± 2.54 | 99.60 ± 0.22 | 92.96 ± 0.54 | 65.10 ± 2.00 | 99.70 ± 0.17 | 92.78 ± 0.42 | |

NB | 76.26 ± 1.87 | 96.46 ± 0.46 | 92.42 ± 0.54 | 77.32 ± 1.22 | 96.67 ± 0.39 | 92.80 ± 0.43 | |

LR | 91.52 ± 1.55 | 98.93 ± 0.31 | 97.45 ± 0.44 | 94.24 ± 0.86 | 96.74 ± 1.09 | 95.49 ± 0.63 | |

SVM | 96.02 ± 1.83 | 98.98 ± 0.36 | 98.39 ± 0.44 | 96.56 ± 0.85 | 99.10 ± 0.30 | 98.59 ± 0.30 | |

Multi-domain and nonlinear analysis | KNN | 96.12 ± 1.11 | 99.15 ± 0.17 | 98.54 ± 0.25 | 96.58 ± 0.94 | 99.16 ± 0.16 | 98.65 ± 0.22 |

LDA | 90.00 ± 1.30 | 99.67 ± 0.14 | 97.74 ± 0.27 | 91.16 ± 0.95 | 99.71 ± 0.10 | 98.00 ± 0.22 | |

NB | 91.58 ± 1.34 | 95.26 ± 0.61 | 94.52 ± 0.58 | 91.48 ± 0.98 | 95.30 ± 0.46 | 94.53 ± 0.42 | |

LR | 95.64 ± 1.32 | 99.44 ± 0.16 | 98.68 ± 0.30 | 95.86 ± 1.02 | 99.51 ± 0.17 | 98.78 ± 0.26 | |

SVM | 97.04 ± 1.52 | 99.54 ± 0.22 | 99.04 ± 0.34 | 97.98 ± 1.07 | 99.56 ± 0.20 | 99.25 ± 0.28 |

Feature Set | Classifiers | 5-Fold CV | 10-Fold CV | ||||
---|---|---|---|---|---|---|---|

SEN | SPE | ACC | SEN | SPE | ACC | ||

Time domain | KNN | 94.12 ± 1.32 | 98.62 ± 0.60 | 96.37 ± 0.73 | 94.64 ± 1.00 | 98.66 ± 0.65 | 96.65 ± 0.58 |

LDA | 80.36 ± 1.05 | 97.60 ± 0.92 | 88.98 ± 0.73 | 79.92 ± 0.77 | 97.40 ± 0.69 | 88.66 ± 0.51 | |

NB | 89.90 ± 0.98 | 96.60 ± 0.57 | 93.25 ± 0.53 | 89.82 ± 0.95 | 96.84 ± 0.37 | 93.33 ± 0.52 | |

LR | 95.22 ± 0.97 | 96.84 ± 0.76 | 96.03 ± 0.64 | 95.20 ± 0.63 | 96.82 ± 0.82 | 96.01 ± 0.60 | |

SVM | 96.14 ± 0.80 | 98.34 ± 0.84 | 97.24 ± 0.63 | 96.00 ± 0.72 | 98.56 ± 0.57 | 97.28 ± 0.46 | |

Frequency domain | KNN | 83.84 ± 1.68 | 83.10 ± 1.93 | 83.47 ± 1.37 | 84.40 ± 1.11 | 83.60 ± 1.60 | 84.00 ± 1.00 |

LDA | 76.86 ± 0.96 | 90.96 ± 0.92 | 83.91 ± 0.66 | 76.70 ± 0.92 | 90.38 ± 0.52 | 83.54 ± 0.54 | |

NB | 79.80 ± 1.22 | 89.46 ± 0.96 | 84.63 ± 0.73 | 79.66 ± 0.79 | 89.68 ± 0.68 | 84.67 ± 0.52 | |

LR | 82.16 ± 1.42 | 87.24 ± 1.16 | 84.70 ± 0.78 | 82.14 ± 1.02 | 87.00 ± 0.96 | 84.57 ± 0.66 | |

SVM | 85.04 ± 1.56 | 84.12 ± 1.61 | 84.58 ± 0.83 | 85.30 ± 1.27 | 83.86 ± 1.17 | 84.58 ± 0.75 | |

Time-frequencydomain | KNN | 95.22 ± 0.92 | 93.78 ± 1.01 | 94.50 ± 0.79 | 95.24 ± 0.84 | 93.54 ± 1.06 | 94.39 ± 0.65 |

LDA | 78.72 ± 1.02 | 98.04 ± 0.60 | 88.38 ± 0.62 | 79.00 ± 0.49 | 98.18 ± 0.52 | 88.59 ± 0.40 | |

NB | 88.02 ± 1.10 | 95.52 ± 1.06 | 91.77 ± 0.76 | 88.38 ± 0.85 | 95.44 ± 1.08 | 91.91 ± 0.75 | |

LR | 91.22 ± 1.01 | 94.18 ± 1.52 | 92.70 ± 0.87 | 91.38 ± 0.60 | 94.18 ± 1.16 | 92.78 ± 0.65 | |

SVM | 94.70 ± 1.20 | 94.72 ± 1.44 | 94.71 ± 0.93 | 94.76 ± 0.97 | 95.44 ± 1.49 | 95.10 ± 0.90 | |

Nonlinear analysis | KNN | 95.60 ± 1.22 | 94.04 ± 1.26 | 94.82 ± 0.82 | 95.78 ± 0.90 | 95.00 ± 0.85 | 95.39 ± 0.61 |

LDA | 91.38 ± 1.44 | 94.24 ± 1.48 | 92.81 ± 1.12 | 91.48 ± 1.02 | 94.84 ± 1.03 | 93.16 ± 0.82 | |

NB | 87.48 ± 1.24 | 94.12 ± 1.21 | 90.80 ± 0.84 | 86.74 ± 1.13 | 93.76 ± 0.86 | 90.25 ± 0.76 | |

LR | 94.60 ± 1.34 | 94.82 ± 1.03 | 94.71 ± 0.83 | 95.52 ± 1.06 | 95.62 ± 0.60 | 95.57 ± 0.66 | |

SVM | 95.04 ± 1.37 | 94.74 ± 1.11 | 94.89 ± 0.92 | 95.22 ± 1.38 | 94.72 ± 0.94 | 94.97 ± 0.80 | |

Multi-domain andnonlinear analysis | KNN | 96.80 ± 0.72 | 95.50 ± 1.12 | 96.15 ± 0.69 | 96.86 ± 0.63 | 95.82 ± 0.55 | 96.34 ± 0.39 |

LDA | 91.36 ± 1.52 | 96.28 ± 1.11 | 93.82 ± 1.11 | 91.56 ± 0.83 | 97.02 ± 0.68 | 94.29 ± 0.51 | |

NB | 92.52 ± 1.22 | 95.44 ± 1.04 | 93.98 ± 0.83 | 92.42 ± 1.02 | 95.64 ± 0.89 | 94.03 ± 0.70 | |

LR | 94.90 ± 1.20 | 96.98 ± 0.99 | 95.94 ± 0.87 | 95.16 ± 0.97 | 97.04 ± 0.89 | 96.10 ± 0.73 | |

SVM | 95.98 ± 1.12 | 96.86 ± 1.10 | 96.42 ± 0.82 | 96.04 ± 0.85 | 97.12 ± 0.74 | 96.58 ± 0.60 |

Problem | Authors | Methods | Accuracy |
---|---|---|---|

S-FNOZ | Tzalla et al. [3] | Time-frequency analysis, artificial neural network | 97.73% |

Guo et al. [39] | Multiwavelet transform, MLPNN | 98.27% | |

Rivero et al. [42] | Time frequency analysis, KNN | 98.40% | |

Kaleem et al. [40] | Variation of empirical mode decomposition | 98.20% | |

Kai Fu et al. [10] | HMS analysis, SVM | 98.80% | |

Niknazar M et al. [43] | Wavelet transform, RQA, ECOC | 98.67% | |

Musa Peker et al. [41] | Dual-tree complex wavelet transform, complex-valued neural networks | 99.15% | |

Jaiswal et al. [44] | Local neighbor Descriptive pattern, artificial neural network | 98.72% | |

This work | DWT, multi-domain feature extraction and nonlinear analysis | 99.25% |

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**MDPI and ACS Style**

Wang, L.; Xue, W.; Li, Y.; Luo, M.; Huang, J.; Cui, W.; Huang, C.
Automatic Epileptic Seizure Detection in EEG Signals Using Multi-Domain Feature Extraction and Nonlinear Analysis. *Entropy* **2017**, *19*, 222.
https://doi.org/10.3390/e19060222

**AMA Style**

Wang L, Xue W, Li Y, Luo M, Huang J, Cui W, Huang C.
Automatic Epileptic Seizure Detection in EEG Signals Using Multi-Domain Feature Extraction and Nonlinear Analysis. *Entropy*. 2017; 19(6):222.
https://doi.org/10.3390/e19060222

**Chicago/Turabian Style**

Wang, Lina, Weining Xue, Yang Li, Meilin Luo, Jie Huang, Weigang Cui, and Chao Huang.
2017. "Automatic Epileptic Seizure Detection in EEG Signals Using Multi-Domain Feature Extraction and Nonlinear Analysis" *Entropy* 19, no. 6: 222.
https://doi.org/10.3390/e19060222