# Improving the Accuracy and Training Speed of Motor Imagery Brain–Computer Interfaces Using Wavelet-Based Combined Feature Vectors and Gaussian Mixture Model-Supervectors

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of the Data

#### 2.1.1. BCI Competition II, Dataset III

#### 2.1.2. BCI Competition III, Dataset IIIb

#### 2.1.3. BCI Competition IV, Dataset 2b

#### 2.2. Combined Feature Vectors Based on Wavelets and PCA

#### 2.2.1. Feature Extraction by CWT

#### 2.2.2. Feature Extraction by DWT

- (1)
- Mean of the absolute values of the wavelet coefficients in each sub-band
- (2)
- Average power of the wavelet coefficients in each sub-band
- (3)
- Standard deviation of the wavelet coefficients in each sub-band
- (4)
- Ratio of the absolute mean values of adjacent sub-bands
- (5)
- Energy of the wavelet coefficients in each sub-band
- (6)
- Entropy of the wavelet coefficients in each sub-band
- (7)
- Skewness of the wavelet coefficients in each sub-band
- (8)
- Kurtosis of the wavelet coefficients in each sub-band

#### 2.2.3. Combined Feature Vectors by PCA

#### 2.3. GMM-Supervectors

#### 2.4. Support Vector Machine (SVM)

## 3. Experimental Results

#### 3.1. Performance of the Combined Features Vector

#### 3.2. Performance of a Fast and Robust SVM Training Method

#### 3.3. Comparison with State-of-the-Art Algorithms

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

BCI | Brain–Computer Interface |

CV | Cross-Validation |

CWT | Continuous Wavelet Transform |

CSP | Common spatial pattern |

DWT | Discrete Wavelet Transform |

EEG | Electroencephalography |

EM | Expectation–Maximization |

ERD | Event-Related Desynchronization |

ERS | Event-Related Synchronization |

FFT | Fast Fourier Transform |

GMM | Gaussian Mixture Model |

GMM-UBM | Gaussian Mixture Model Universal Background Model |

LDA | Linear Discriminant Analysis |

PCA | Principal Component Analysis |

STFT | Short-Time Fourier Transform |

SVMs | Support Vector Machines |

WT | Wavelet Transform |

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**Figure 1.**Block diagram of motor imagery brain-computer interface (BCI) using the wavelet-based combined feature vector and gaussian mixture model (GMM)-supervector.

**Figure 3.**Classification accuracy based on reduction rate of whole training data on individual subjects.

**Figure 4.**Computation time for training procedure based on reduction rate of whole training data on individual subjects.

Subject | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Number of Training Data Points | 140 | 540 | 540 | 400 | 400 | 400 | 420 | 420 | 400 | 400 | 440 | 400 |

Number of Test Data Points | 140 | 540 | 540 | 320 | 280 | 320 | 320 | 320 | 320 | 320 | 320 | 320 |

**Table 2.**Comparative results of the feature extraction methods in terms of the average classification accuracy (%).

Subject | DWT | CWT | Combined Feature Vectors | |||
---|---|---|---|---|---|---|

without PCA | with PCA | |||||

Accuracy | Number of Features | Accuracy | Number of Features | |||

1 | 92.9 | 94.1 | 96.4 | 96 | 97.5 | 33 |

2 | 73.3 | 81.4 | 83.1 | 96 | 83.1 | 40 |

3 | 62.5 | 80.7 | 80.5 | 96 | 83.3 | 39 |

4 | 75.2 | 77.7 | 79.1 | 96 | 76.7 | 35 |

5 | 52.6 | 60.1 | 60.0 | 96 | 61.4 | 34 |

6 | 55.4 | 55.6 | 51.8 | 96 | 56.2 | 32 |

7 | 95.5 | 96.2 | 96.2 | 96 | 96.1 | 30 |

8 | 88.3 | 87.4 | 94.0 | 96 | 94.1 | 32 |

9 | 79.2 | 87.8 | 90.2 | 96 | 88.1 | 34 |

10 | 74.8 | 72.6 | 81.4 | 96 | 80.7 | 36 |

11 | 90.6 | 87.7 | 89.3 | 96 | 90.0 | 32 |

12 | 78.7 | 83.3 | 84.2 | 96 | 84.8 | 34 |

Mean | 76.6 | 80.4 | 82.2 | 96 | 82.7 | 34.3 |

p-value | p < 0.05 | p < 0.05 | p = 0.20 | - | - | - |

Ranking | Methods | Subject 1 | |
---|---|---|---|

Maximal MI (bit) | Accuracy (%) | ||

1 | ALL-SVM | 0.84 | 97.50 |

2 | 30%-SVM | 0.67 | 93.79 |

3 | FSVM in [21] | 0.66 | 87.86 |

4 | SVM in [21] | 0.65 | 89.83 |

5 | NN in [65] | 0.64 | 90.00 |

6 | LDA in [65] | 0.63 | 89.29 |

7 | 1st winner | 0.61 | 89.29 |

8 | SVM in [65] | 0.58 | 90.00 |

9 | 2nd winner | 0.46 | 84.29 |

**Table 4.**Mutual information of the proposed combined feature vectors (100% and 30% of training data), methods in [21] and the winning methods of dataset II.

Ranking | Methods | Maximal MI(bit) | ||
---|---|---|---|---|

Subject 2 | Subject 3 | Mean | ||

1 | 1st winner | 0.4382 | 0.3489 | 0.3936 |

2 | ALL-SVM | 0.3447 | 0.3562 | 0.3505 |

3 | 30%-SVM | 0.3105 | 0.3216 | 0.3161 |

4 | 2nd winner | 0.4174 | 0.1719 | 0.2947 |

5 | FSVM in [21] | 0.0718 | 0.0863 | 0.0791 |

6 | SVM in [21] | 0.0718 | 0.0809 | 0.0764 |

**Table 5.**Maximum Kappa value of the proposed combined feature vectors (100% and 30% of training data), and winning methods of the dataset III.

Ranking | Methods | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | Mean |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | ALL-SVM | 0.54 | 0.24 | 0.12 | 0.92 | 0.88 | 0.76 | 0.61 | 0.80 | 0.70 | 0.62 |

2 | 1st winner | 0.40 | 0.21 | 0.22 | 0.95 | 0.86 | 0.61 | 0.56 | 0.85 | 0.74 | 0.60 |

3 | 30%-SVM | 0.51 | 0.17 | 0.12 | 0.92 | 0.83 | 0.76 | 0.55 | 0.79 | 0.67 | 0.59 |

3 | 2nd winner | 0.42 | 0.21 | 0.14 | 0.94 | 0.71 | 0.62 | 0.61 | 0.84 | 0.78 | 0.59 |

5 | 3rd winner | 0.19 | 0.12 | 0.12 | 0.77 | 0.57 | 0.49 | 0.37 | 0.85 | 0.61 | 0.45 |

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**MDPI and ACS Style**

Lee, D.; Park, S.-H.; Lee, S.-G.
Improving the Accuracy and Training Speed of Motor Imagery Brain–Computer Interfaces Using Wavelet-Based Combined Feature Vectors and Gaussian Mixture Model-Supervectors. *Sensors* **2017**, *17*, 2282.
https://doi.org/10.3390/s17102282

**AMA Style**

Lee D, Park S-H, Lee S-G.
Improving the Accuracy and Training Speed of Motor Imagery Brain–Computer Interfaces Using Wavelet-Based Combined Feature Vectors and Gaussian Mixture Model-Supervectors. *Sensors*. 2017; 17(10):2282.
https://doi.org/10.3390/s17102282

**Chicago/Turabian Style**

Lee, David, Sang-Hoon Park, and Sang-Goog Lee.
2017. "Improving the Accuracy and Training Speed of Motor Imagery Brain–Computer Interfaces Using Wavelet-Based Combined Feature Vectors and Gaussian Mixture Model-Supervectors" *Sensors* 17, no. 10: 2282.
https://doi.org/10.3390/s17102282