# A New Competitive Binary Grey Wolf Optimizer to Solve the Feature Selection Problem in EMG Signals Classification

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{D}, where D is the dimension of features [13]. For example, if we have 100 features, then, the possible combination of features is 2

^{100}, which is impractical for conducting an exhaustive search.

## 2. Materials and Methods

#### 2.1. EMG Data

#### 2.2. Feature Extraction Using STFT

#### 2.2.1. Renyi Entropy

#### 2.2.2. Spectral Entropy

#### 2.2.3. Shannon Entropy

#### 2.2.4. Singular Value Decomposition-Based Entropy

_{SVD}) is an entropy estimated from singular value decomposition (SVD). Initially, SVD is applied to decompose the time-frequency amplitude into signal subspace and orthogonal alternate subspace. The entropy based on singular values offers the time-frequency information related to the complexity and magnitude of STFT [9]. Mathematically, E

_{SVD}can be formulated as

_{k}is the singular value of matrix S[n,m] that obtained from the singular value decomposition.

#### 2.2.5. Concentration Measure

#### 2.2.6. Mean Frequency

_{m}is the frequency value at frequency bin m, and M is the total number of the frequency bin. In this work, the averaged MNF across multiple instants of time sample is calculated.

#### 2.2.7. Median Frequency

#### 2.2.8. Two-Dimensional Mean, Variance, and Coefficient of Variation

#### 2.3. Grey Wolf Optimizer

_{p}is the position of prey, A is the coefficient vector, and D is defined as

_{1}and r

_{2}are two independent random numbers uniformly distributed between [0, 1], and a is the encircling coefficient that is used to balance the tradeoff between exploration and exploitation. In GWO, parameter a is linearly decreasing, from 2 to 0, according to Equation (17).

_{1}, X

_{2}, and X

_{3}are calculated as follows:

_{α}, X

_{β}, and X

_{δ}are the position of alpha, beta, and delta at iteration t; A

_{1}, A

_{2}, and A

_{3}are calculated as in Equation (15); and D

_{α}, D

_{β}and D

_{δ}are defined as in Equations (22)–(24), respectively.

_{1}, C

_{2}, and C

_{3}are calculated as in Equation (16).

#### 2.3.1. Binary Grey Wolf Optimization Model 1 (BGWO1)

_{1}, Y

_{2}, and Y

_{3}) is the crossover operation between solutions, and Y

_{1}, Y

_{2}, and Y

_{3}are the binary vectors affected by the movement of alpha, beta, and delta wolves, respectively. In BGWO1, Y

_{1}, Y

_{2}, and Y

_{3}are defined using Equations (26), (29) and (32), respectively.

_{3}is a random vector in [0, 1], and $cste{p}_{\alpha}^{d}$ denotes the continuous valued step size that can be calculated as in Equation (28).

_{4}is a random vector in [0, 1], and $cste{p}_{\beta}^{d}$ denotes the continuous valued step size that can be calculated as in Equation (31).

_{5}is a random vector in [0, 1], and $cste{p}_{\delta}^{d}$ denotes the continuous valued step size that can be calculated as in Equation (34).

_{1}, Y

_{2}, and Y

_{3}, the new position of the wolf is updated using the crossover operation, as follows:

_{6}is a random number uniformly distributed between [0, 1].

_{1}, Y

_{2}, and Y

_{3}are computed using Equations (26), (29), and (32), respectively. Then, the position of wolf is updated by applying the crossover between Y

_{1}, Y

_{2}, and Y

_{3}. Next, the fitness of each wolf is evaluated. Iteratively, the positions of alpha, beta, and delta are updated. The algorithm is repeated until the terminated criterion is satisfied. At last, the alpha solution is selected as the optimal feature subset.

#### 2.3.2. Binary Grey Wolf Optimization Model 2 (BGWO2)

_{7}is a random vector in [0, 1], d is the dimension of search space, and S is the sigmoid function, and it can be expressed as

_{1}, X

_{2}, and X

_{3}are computed using Equations (19)–(21), respectively. Next, the new position of grey wolf is updated by applying Equation (36). Afterward, the fitness of wolves is evaluated, and the position of alpha, beta, and delta are updated. The algorithm is repeated until the terminated criterion is satisfied. Finally, the alpha solution is selected as the optimal feature subset.

#### 2.4. Competitive Binary Grey Wolf Optimizer

#### 2.4.1. New Position Update

_{8}is a random vector in [0, 1], X

_{1}, X

_{2}, and X

_{3}are defined as follows:

_{α}, X

_{β}, and X

_{δ}are the positions of alpha, beta, and delta at iteration t; A

_{1}, A

_{2}, and A

_{3}are computed as in Equation (15); and ${\overline{D}}_{\alpha}$, ${\overline{D}}_{\beta}$, and ${\overline{D}}_{\delta}$ are calculated as in Equations (42)–(44), respectively.

_{w}is the winner wolf, X

_{l}is the loser wolf, C

_{1}, C

_{2}, and C

_{3}are calculated as in Equation (16). As can be seen in Equations (42)–(44), the losers update their positions by learning from the winners. This means that losers are not only instructed by the alpha, beta, and delta wolves, but also guided by the winners to move toward the best prey position. In this way, CBGWO can explore the search region effectively.

#### 2.4.2. Leader Enhancement

_{L}is the leader (either alpha, beta or delta), rand (0,1) is a random number generated—either 1 or 0, and r

_{9}is a random number uniformly distributed between [0, 1]. In CBGWO, the R is linearly decreasing from 0.9 to 0, as shown in Equation (46).

- In CBGWO, only the positions of N/2 (half of the population) wolves are updated. This means that the processing speed of CBGWO is extremely fast.
- CBGWO applies leader enhancement, which has the capability to avoid the leaders (alpha, beta, and delta) from being trapped in the local optimum.
- CBGWO includes the role of winner and loser in the position update. This indicates that the process of hunting and searching prey of wolves, is not only guided by the leaders, but also the winner wolf in each couple.
- CBGWO employs the dynamic change rate, R, in the random walk strategy, which aims to balance the exploration and exploitation in the leader enhancement process.

#### 2.5. Proposed CBGWO for Feature Selection

## 3. Results

_{1}and C

_{2}, are set at 2, and the maximum and minimum velocity are set at 6 and −6, respectively. For GA, the crossover rate, CR, is set at 0.6, the mutation rate, MR, is set at 0.01, the roulette wheel selection is applied for parent selection, and the single point crossover is implemented.

#### Experimental Results

^{−4}), CBGWO versus BGWO1 (p = 9.2063 × 10

^{−4}), CBGWO versus BGWO2 (p = 0.0023), and CBGWO versus BPSO (p = 0.011). This shows that the performance of CBGWO is significantly better than GA, BGWO1, BGWO2, and BPSO. The statistical results revealed the superiority of CBGWO over other algorithms in feature selection.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Classification accuracy of five different feature selection methods for individual subjects.

**Figure 8.**The mean class-wise accuracy of five different feature selection methods across 10 subjects.

**Figure 9.**The average computation time of five different feature selection methods across 10 subjects.

Subject | Number of Selected Features (Original = 120) | Precision | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

GA | BGWO1 | BGWO2 | BPSO | CBGWO | GA | BGWO1 | BGWO2 | BPSO | CBGWO | ||

1 | 59.15 | 61.15 | 57.70 | 42.15 | 40.75 | 0.9427 | 0.9500 | 0.9755 | 0.9500 | 0.9794 | |

2 | 62.85 | 61.80 | 56.05 | 43.05 | 37.85 | 0.9569 | 0.9583 | 0.9716 | 0.9613 | 0.9784 | |

3 | 61.75 | 61.85 | 58.05 | 48.20 | 46.35 | 0.8993 | 0.9022 | 0.9120 | 0.9103 | 0.9412 | |

4 | 62.25 | 61.60 | 58.20 | 44.90 | 42.25 | 0.8863 | 0.8878 | 0.9037 | 0.8936 | 0.9184 | |

5 | 59.45 | 60.00 | 58.15 | 46.85 | 46.55 | 0.8708 | 0.8751 | 0.8775 | 0.8710 | 0.9073 | |

6 | 62.75 | 62.85 | 59.85 | 48.20 | 44.30 | 0.8962 | 0.9001 | 0.9134 | 0.8961 | 0.9165 | |

7 | 60.10 | 60.80 | 56.85 | 46.75 | 42.85 | 0.9466 | 0.9637 | 0.9677 | 0.9628 | 0.9971 | |

8 | 61.80 | 61.80 | 60.40 | 44.40 | 43.20 | 0.8885 | 0.9000 | 0.9027 | 0.9340 | 0.9040 | |

9 | 61.45 | 60.65 | 59.40 | 44.60 | 41.70 | 0.9740 | 0.9775 | 0.9765 | 0.9784 | 0.9804 | |

10 | 62.30 | 62.40 | 56.60 | 46.40 | 38.75 | 0.9414 | 0.9456 | 0.9574 | 0.9461 | 0.9701 | |

Mean | 61.39 | 61.49 | 58.13 | 45.55 | 42.46 | 0.9203 | 0.9260 | 0.9358 | 0.9304 | 0.9493 |

**Table 2.**Result of F-measure and Matthew correlation coefficient (MCC) of five different feature selection methods.

Subject | F-Measure | Matthew Correlation Coefficient (MCC) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

GA | BGWO1 | BGWO2 | BPSO | CBGWO | GA | BGWO1 | BGWO2 | BPSO | CBGWO | ||

1 | 0.9175 | 0.9273 | 0.9589 | 0.9324 | 0.9671 | 0.9253 | 0.9325 | 0.9641 | 0.9340 | 0.9691 | |

2 | 0.9345 | 0.9363 | 0.9533 | 0.9389 | 0.9655 | 0.9379 | 0.9396 | 0.9563 | 0.9426 | 0.9676 | |

3 | 0.8322 | 0.8398 | 0.8779 | 0.8452 | 0.9273 | 0.8812 | 0.8803 | 0.8922 | 0.8941 | 0.9278 | |

4 | 0.8395 | 0.8432 | 0.8581 | 0.8542 | 0.8746 | 0.8512 | 0.8525 | 0.8658 | 0.8561 | 0.8828 | |

5 | 0.8029 | 0.8075 | 0.8131 | 0.8178 | 0.8540 | 0.8500 | 0.8548 | 0.8527 | 0.8551 | 0.8663 | |

6 | 0.8416 | 0.8444 | 0.8479 | 0.8611 | 0.8554 | 0.8566 | 0.8599 | 0.8761 | 0.8618 | 0.8735 | |

7 | 0.9210 | 0.9425 | 0.9529 | 0.9479 | 0.9953 | 0.9273 | 0.9486 | 0.9551 | 0.9500 | 0.9956 | |

8 | 0.8527 | 0.8658 | 0.8604 | 0.8876 | 0.8746 | 0.8676 | 0.8811 | 0.8851 | 0.9082 | 0.8886 | |

9 | 0.9574 | 0.9629 | 0.9604 | 0.9635 | 0.9686 | 0.9652 | 0.9680 | 0.9683 | 0.9712 | 0.9706 | |

10 | 0.9130 | 0.9151 | 0.9344 | 0.9218 | 0.9516 | 0.9165 | 0.9196 | 0.9380 | 0.9247 | 0.9546 | |

Mean | 0.8812 | 0.8885 | 0.9017 | 0.8970 | 0.9234 | 0.8979 | 0.9037 | 0.9154 | 0.9098 | 0.9297 |

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**MDPI and ACS Style**

Too, J.; Abdullah, A.R.; Mohd Saad, N.; Mohd Ali, N.; Tee, W. A New Competitive Binary Grey Wolf Optimizer to Solve the Feature Selection Problem in EMG Signals Classification. *Computers* **2018**, *7*, 58.
https://doi.org/10.3390/computers7040058

**AMA Style**

Too J, Abdullah AR, Mohd Saad N, Mohd Ali N, Tee W. A New Competitive Binary Grey Wolf Optimizer to Solve the Feature Selection Problem in EMG Signals Classification. *Computers*. 2018; 7(4):58.
https://doi.org/10.3390/computers7040058

**Chicago/Turabian Style**

Too, Jingwei, Abdul Rahim Abdullah, Norhashimah Mohd Saad, Nursabillilah Mohd Ali, and Weihown Tee. 2018. "A New Competitive Binary Grey Wolf Optimizer to Solve the Feature Selection Problem in EMG Signals Classification" *Computers* 7, no. 4: 58.
https://doi.org/10.3390/computers7040058