# Statistical Model-Based Classification to Detect Patient-Specific Spike-and-Wave in EEG Signals

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Database

#### 2.2. Methodology

#### 2.2.1. Morlet Wavelet

#### 2.2.2. Generalized Gaussian Distribution

#### 2.2.3. Feature Parameters

#### 2.2.4. k-Nearest Neighbors Classification

## 3. Results

- Scale parameter $\left({\varsigma}_{t}\right)$ vs. variance $\left({\sigma}_{t}^{2}\right)$: for class 1 (SWD), one observes a direct relationship between the variance and sigma, where both parameters grow proportionally. For class 0 (non-SWD), both sigma and variance remain in a limited range of values.
- Scale parameter $\left({\varsigma}_{t}\right)$ vs. median $\left(\tilde{{x}_{t}}\right)$: as sigma grows, median increases then decreases for both SWD and non-SWD, but is larger for SWD. A cone-shaped pattern can be observed.
- Variance $\left({\sigma}_{t}^{2}\right)$ vs. median $\left(\tilde{{x}_{t}}\right)$: as the variance grows, the median increases then decreases for SWD, while it remains in a small range (cluster) for non-SWD.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

EEG | Electroencephalography |

FLENI | Fight against Pediatric Neurological Disease |

GGD | Generalized Gaussian distribution |

k-NN | k-nearest neighbors |

SWD | Spike-and-wave discharge |

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**Figure 1.**(

**a**) A sample SWD signal and the Morlet wavelet. Note that the scales are different. (

**b**) Example of 6 channels of one monopolar raw EEG, with SWD patterns in all channels.

**Figure 3.**Illustration of the variation of time-scale for Morlet continuous wavelet (

**a**) for SWD with ${f}_{c}=1.2308$ Hz, and (

**b**) for non-SWD with ${f}_{c}=0.8125$. Note that, the energy distribution pattern is different when comparing SWD and non-SWD.

**Figure 4.**3D scatter plot of the feature vector $[\varsigma ,{\sigma}_{t}^{2},\tilde{{x}_{t}}]$ for class 0 (non-spike-and-waves events, blue dots), and class 1 (spike-and-waves events, red dots). The SWD events tend to be more dispersed than non-SWD events.

**Figure 5.**Scatter plots of the signals used for training, with ${\varsigma}_{t}$, ${\sigma}_{t}^{2}$, and $\tilde{{x}_{t}}$ parameters class 0 (non-spike-and-waves events, blue dots), and class 1 (spike-and-waves events, red dots), showing the data dispersion of the proposed approach. In (

**a**) Scale parameter (${\varsigma}_{t}$) vs. variance (${\sigma}_{t}^{2}$). For class 1 (SWD), we can see the direct relationship between the variance and sigma, both grow proportionally, while for class 0 (non-SWD) both sigma and variance remain in a range of values. (

**b**) Scale parameter (${\varsigma}_{t}$) vs. median ($\tilde{{x}_{t}}$). As sigma grows, the median increases then decreases for both SWD and non-SWD, but is larger for SWD. (

**c**) variance (${\sigma}_{t}^{2}$) vs. median ($\tilde{{x}_{t}}$). As variance grows, the median increases then decreases for SWD, while it remains in a small range for non-SWD.

**Table 1.**Some state-of-the-art methods for the spike-and-wave discharge (SWD) estimation in electroencephalography (EEG) signals in humans, compared in terms of classification techniques, features, and reported performance.Abbreviations are as follows: high Specificity, rule in (SpPIn), According to the frequency and magnitude weighted average (WA), According to an estimated threshold (AET).

Method | Features | Classifier | Accuracy in % | Ref. |
---|---|---|---|---|

Generalized Gaussian distribution (GGD) | GGD parameters, variance and median from time–frequency Morlet decomposition | 10-NN | 92 | our |

Kendall’s Tau-b Coefficient | Kendall’s Tau-b coefficient significance | SpPIn | 94 | [39] |

Ramanujan Filter Bank (RFB) | Spectrum from RFB | Empirical | >80 | [40] |

t-location-scale distribution (TLS) | TLS parameters | 1-NN | 100 | [20] |

Cross-correlation | Correlation coefficient | Decision trees | 97 | [9] |

Walsh transformation (WT) | First and second orden from WT | Bayesian | >70 | [33] |

Hilbert–Huang transform | Intrinsic mode functions energy | WA | - | [34] |

Cross-correlation | Wavelet spectrum correlation | AET | 100 | [41] |

**Table 2.**Mean, standard deviation, variance and bound values for sigma parameter $\left(\varsigma \right)$ for class 0 (non-spike-and-wave) and class 1 (spike-and-wave).

Mean | std | Variance | Bounds | |
---|---|---|---|---|

Class 0 | 293 | 267.8017 | 71,718 | [12, 1275] |

Class 1 | 542 | 406.2597 | 165,047 | [31, 1811] |

**Table 3.**Mean, standard deviation, variance and bound values for the variance $\left({\sigma}_{t}^{2}\right)$ for class 0 (non-spike-and-wave) and class 1 (spike-and-wave).

Mean | std | Variance | Bounds | |
---|---|---|---|---|

Class 0 | 1.446 × 10${}^{6}$ | 4.235 × 10${}^{6}$ | 1.794 × 10${}^{13}$ | [9.46 × 10${}^{2}$, 3.162 × 10${}^{7}$] |

Class 1 | 4.32 × 10${}^{6}$ | 7.892 × 10${}^{6}$ | 6.228 × 10${}^{13}$ | [2.715 × 10${}^{3}$, 4.321 × 10${}^{7}$] |

**Table 4.**Mean, standard deviation, variance and bound values for median $\left(\tilde{{x}_{t}}\right)$ for class 0 (non-spike-and-wave) and class 1 (spike-and-wave).

Mean | std | Variance | Bounds | |
---|---|---|---|---|

Class 0 | 1.089 × 10${}^{3}$ | 1.002 × 10${}^{4}$ | 1.004 × 10${}^{8}$ | [−2.769 × 10${}^{4}$, 2.179 × 10${}^{4}$] |

Class 1 | −6.125 × 10${}^{3}$ | 2.672 × 10${}^{4}$ | 7.140 × 10${}^{8}$ | [−7.325 × 10${}^{4}$, 7.406 × 10${}^{4}$] |

**Table 5.**Results form other methods applied to the same dataset in percent (%), in terms of TPR = True Positives Rate or Sensitivity; TNR = True Negative Rate or Specificity; FPR = False positive Rate; ACC = Accuracy: and high Specificity, rule in (SpPIn). Training and testing have different numbers of patients due to different research settings.

Method | Features | Classifier | TPR | TNR | ACC | Training | Testing | Ref. |
---|---|---|---|---|---|---|---|---|

GGD | GGD parameters, variance and median from time-frequency Morlet wavelet decomposition | 10-NN | 95 | 87 | 92 | 212 | 96 | Actual |

Kendall’s Tau-b Coefficient | Kendall’s Tau-b coefficient significance in time domain | SpPIn | - | 94 | 94 | 300 | 300 | [39] |

TLS | TLS parameters in time domain | 1-NN | 100 | 100 | 100 | 192 | 46 | [20] |

Cross-correlation | Correlation coefficient in time domain | Decision trees | 86 | 98 | 97 | 96 | 46 | [9] |

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**MDPI and ACS Style**

Quintero-Rincón, A.; Muro, V.; D’Giano, C.; Prendes, J.; Batatia, H.
Statistical Model-Based Classification to Detect Patient-Specific Spike-and-Wave in EEG Signals. *Computers* **2020**, *9*, 85.
https://doi.org/10.3390/computers9040085

**AMA Style**

Quintero-Rincón A, Muro V, D’Giano C, Prendes J, Batatia H.
Statistical Model-Based Classification to Detect Patient-Specific Spike-and-Wave in EEG Signals. *Computers*. 2020; 9(4):85.
https://doi.org/10.3390/computers9040085

**Chicago/Turabian Style**

Quintero-Rincón, Antonio, Valeria Muro, Carlos D’Giano, Jorge Prendes, and Hadj Batatia.
2020. "Statistical Model-Based Classification to Detect Patient-Specific Spike-and-Wave in EEG Signals" *Computers* 9, no. 4: 85.
https://doi.org/10.3390/computers9040085