# Hybrid Binary Particle Swarm Optimization Differential Evolution-Based Feature Selection for EMG Signals Classification

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## Abstract

**:**

## 1. Introduction

## 2. Preliminary

#### 2.1. Binary Particle Swarm Optimization

_{i1}, v

_{i2}, …, v

_{iD}) and the position of the particle is denoted as X = (x

_{i1}, x

_{i2}, …, x

_{iD}), where i represents the order of the particle in the population. In BPSO, the optimal location of each particle is known as Pbest and the global best solution in the population is called Gbest. For each iteration t, the particle updates its velocity as follow:

_{1}and c

_{2}are the acceleration coefficients, and r

_{1}and r

_{2}are the two independent random numbers uniformly distributed between 0 and 1. Then, the velocity is converted into a probability value using the sigmoid function as follow:

_{max}and w

_{min}are the bounds on the inertia weight, t is the current iteration, and T is the maximum number of iterations. In this study, w

_{max}and w

_{min}were set to 0.9 and 0.4, respectively.

#### 2.2. Binary Differential Evolution

_{r1}, x

_{r2}, and x

_{r3}are randomly selected from the population for vector x

_{i}. Note that r

_{1}≠ r

_{2}≠ r

_{3}≠ i. Then, the difference vector is computed as follow:

_{r1}is equal to x

_{r2}, then the difference vector will become 0. Otherwise, the differential vector will become the same as x

_{r1}. Next, the mutation is performed as shown in Equation (6).

_{rand}is a random feature index distributed between 1 and D, and δ is a random number distributed between 0 and 1.

## 3. Materials and Methods

#### 3.1. EMG Data

#### 3.2. Discrete Wavelet Transform-Based Feature Extraction

_{high}(k) and y

_{low}(k) represent the detail and approximation, respectively. In wavelet decomposition, detail (D) exhibits the signal at high frequency, whereas the low-frequency component is represented by the approximation (A) [26]. Previous works indicated that the selection of the mother wavelet and decomposition level were the main factors that can strongly affect the performance of DWT in EMG pattern recognition. According to the finding of Reference [27], DWT at the fourth decomposition level was employed in this work. An illustration of DWT is displayed in Figure 2.

#### 3.3. Proposed Hybrid Binary Particle Swarm Optimization Differential Evolution

#### 3.3.1. Dynamic Inertia Weight

_{3}is a random number distributed between 0 and 1. Figure 3a illustrates an example of dynamic inertia weight. As can be seen, the inertia weight was generated uniformly between 0.5 and 1. Since it is difficult to estimate the exploration and exploitation stage, a random inertia weight is more appropriate to be used in this dynamic environment [31].

#### 3.3.2. Dynamic Crossover Rate

Algorithm 1. Hybrid Binary Particle Swarm Optimization Differential Evolution |

Input Parameters:N, T, c_{1}, and c_{2} |

(1) Randomly initialize a population of particles, x |

(2) Evaluate the fitness of particles, F(x) |

(3) Set Pbest and Gbest |

(4) for t = 1 to maximum number of iterations, T |

// BPSO Algorithm // |

(5) if mod(t,2) = 1 |

(6) $w=0.5+\frac{rand\left(0,1\right)}{2}$ |

(7) for i = 1 to number of particles, N |

(8) for d = 1 to number of dimension, D |

(9) ${v}_{i}^{d}\left(t+1\right)=w\times {v}_{i}^{d}\left(t\right)+{c}_{1}\times {r}_{1}\times \left(Pbes{t}_{i}^{d}\left(t\right)-{x}_{i}^{d}\left(t\right)\right)+{c}_{2}\times {r}_{2}\times \left(Gbes{t}^{d}\left(t\right)-{x}_{i}^{d}\left(t\right)\right)$ |

(10) $S\left({v}_{i}^{d}\left(t+1\right)\right)=\frac{1}{1+exp\left(-{v}_{i}^{d}\left(t+1\right)\right)}$ |

(11) if $rand\left(0,1\right)\le S\left({v}_{i}^{d}\left(t+1\right)\right)$ |

(12) ${x}_{i}^{d}\left(t+1\right)=1$ |

(13) else |

(14) ${x}_{i}^{d}\left(t+1\right)=0$ |

(15) end if |

(16) end for |

(17) Evaluate the fitness of new particle, $F\left({x}_{i}\left(t+1\right)\right)$ |

(18) end for |

// BDE Algorithm // |

(19) else |

(20) $CR=1-\left(\frac{t}{T}\right)$ |

(21) for i = 1 to number of particles, N |

(22) Random select vectors ${x}_{r1},{x}_{r2},{x}_{r3}$ and ${d}_{rand}=rand\left(1,D\right)$ |

(23) for d = 1 to number of dimension, D |

(24) if ${x}_{r1}^{d}={x}_{r2}^{d}$ |

(25) $differencevecto{r}_{i}^{d}=0$ |

(26) else |

(27) $differencevecto{r}_{i}^{d}={x}_{r1}^{d}$ |

(28) end if |

(29) if $differencevecto{r}_{i}^{d}=1$ |

(30) $mutantvecto{r}_{i}^{d}=1$ |

(31) else |

(32) $mutantvecto{r}_{i}^{d}={x}_{r3}^{d}$ |

(33) end if |

(34) if $rand\left(0,1\right)\le CRord={d}_{rand}$ |

(35) ${u}_{i}^{d}=mutantvecto{r}_{i}^{d}$ |

(36) else |

(37) ${u}_{i}^{d}={x}_{i}^{d}\left(t\right)$ |

(38) end if |

(39) end for |

(40) Evaluate the fitness of trial vector, $F\left({u}_{i}\right)$ |

(41) Perform greedy selection between current particle and trial vector |

(42) end for |

(43) end if |

// Pbest and Gbest Update // |

(44) for i = 1 to number of particles, N |

(45) Update Pbest and _{i}Gbest |

(46) end for |

(47) end for |

Output: Global best solution |

#### 3.4. Application of BPSODE for Feature Selection

_{R}is the error rate computed by a learning algorithm, |R| is the length of the feature subset, |S| is the total number of features, and α is the parameter that control the weight between error rate and ratio of selected features. Considering the classification performance to be the most important measurement, the α was set to 0.9 in this work.

## 4. Results and Discussions

#### 4.1. Comparison Algorithms and Evaluation Metrics

#### 4.2. Experimental Results and Analysis

#### 4.2.1. Effect of Population Size

#### 4.2.2. Comparison Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Table 1.**Parameter settings of the hybrid binary particle swarm optimization differential evolution (BPSODE), binary bat algorithm (BBA), binary differential evolution (BDE), binary particle swarm optimization (BPSO) and binary flower pollination algorithm (BFPA).

Algorithm | Parameter | Value |
---|---|---|

BPSODE | Acceleration coefficient, c_{1} and c_{2} | 2 |

Bound on velocity | (−6,6) | |

BDE | Crossover rate, CR | 1 |

BPSO | Acceleration coefficient, c_{1} and c_{2} | 2 |

Inertia weight, w | 0.9–0.4 | |

Bound on velocity | (−6,6) | |

BFPA | Switch probability, P | 0.8 |

Levy component, λ | 1.5 | |

BBA | Maximum frequency, f_{max} | 2 |

Minimum frequency, f_{min} | 0 | |

Control coefficient, α and γ | 0.9 | |

Loudness, A | (1,2) | |

Pulse rate, r | (0,1) |

**Table 2.**Experimental results of five different feature selection methods on 10 subjects. The best result of each metric is highlighted in bold text.

Subject | Metrics | Feature Selection Method | ||||
---|---|---|---|---|---|---|

BPSODE | BBA | BDE | BFPA | BPSO | ||

1 | Accuracy (%) | 88.29 ± 1.58 | 88.64 ± 1.64 | 87.14 ± 1.67 | 87.79 ± 1.70 | 88.21 ± 1.60 |

Feature selection ratio (FSR) | 0.4196 ± 0.0283 | 0.4462 ± 0.0260 | 0.4926 ± 0.0329 | 0.5525 ± 0.0420 | 0.4486 ± 0.0250 | |

Precision | 0.9034 ± 0.0108 | 0.9049 ± 0.0128 | 0.8941 ± 0.0156 | 0.9001 ± 0.0130 | 0.9023 ± 0.0120 | |

F-measure | 0.8852 ± 0.0148 | 0.8880 ± 0.0165 | 0.8732 ± 0.0180 | 0.8798 ± 0.0169 | 0.8843 ± 0.0152 | |

2 | Accuracy (%) | 89.93 ± 1.35 | 90.43 ± 1.54 | 90.43 ± 1.24 | 90.50 ± 1.25 | 90.21 ± 1.16 |

FSR | 0.4079 ± 0.0324 | 0.4424 ± 0.0167 | 0.4920 ± 0.0342 | 0.5594 ± 0.0550 | 0.4467 ± 0.0184 | |

Precision | 0.9143 ± 0.0098 | 0.9182 ± 0.0132 | 0.9169 ± 0.0101 | 0.9190 ± 0.0106 | 0.9153 ± 0.0108 | |

F-measure | 0.9018 ± 0.0120 | 0.9063 ± 0.0146 | 0.9061 ± 0.0111 | 0.9069 ± 0.0115 | 0.9042 ± 0.0105 | |

3 | Accuracy (%) | 87.86 ± 3.09 | 85.71 ± 2.22 | 83.43 ± 1.70 | 85.36 ± 1.60 | 86.14 ± 1.68 |

FSR | 0.4386 ± 0.0289 | 0.4528 ± 0.0210 | 0.4981 ± 0.0489 | 0.5811 ± 0.0488 | 0.4636 ± 0.0185 | |

Precision | 0.8949 ± 0.0303 | 0.8727 ± 0.0245 | 0.8519 ± 0.0181 | 0.8709 ± 0.0188 | 0.8779 ± 0.0186 | |

F-measure | 0.8810 ± 0.0326 | 0.8588 ± 0.0227 | 0.8359 ± 0.0168 | 0.8555 ± 0.0160 | 0.8632 ± 0.0182 | |

4 | Accuracy (%) | 87.93 ± 1.35 | 87.79 ± 1.43 | 86.86 ± 1.89 | 87.79 ± 1.35 | 87.43 ± 1.36 |

FSR | 0.4196 ± 0.0343 | 0.4393 ± 0.0207 | 0.4859 ± 0.0233 | 0.5581 ± 0.0523 | 0.4444 ± 0.0179 | |

Precision | 0.8891 ± 0.0139 | 0.8870 ± 0.0146 | 0.8782 ± 0.0205 | 0.8880 ± 0.0136 | 0.8854 ± 0.0136 | |

F-measure | 0.8754 ± 0.0135 | 0.8736 ± 0.0146 | 0.8653 ± 0.0194 | 0.8742 ± 0.0140 | 0.8705 ± 0.0136 | |

5 | Accuracy (%) | 95.93 ± 1.41 | 95.43 ± 1.19 | 94.07 ± 1.49 | 95.43 ± 0.99 | 95.29 ± 1.32 |

FSR | 0.4157 ± 0.0318 | 0.4333 ± 0.0189 | 0.4820 ± 0.0168 | 0.5546 ± 0.0402 | 0.4426 ± 0.0221 | |

Precision | 0.9654 ± 0.0103 | 0.9603 ± 0.0101 | 0.9505 ± 0.0121 | 0.9607 ± 0.0086 | 0.9593 ± 0.0111 | |

F-measure | 0.9593 ± 0.0141 | 0.9544 ± 0.0119 | 0.9411 ± 0.0144 | 0.9546 ± 0.0099 | 0.9525 ± 0.0134 | |

6 | Accuracy (%) | 92.29 ± 1.42 | 92.64 ± 1.56 | 90.71 ± 1.50 | 91.86 ± 1.24 | 92.21 ± 1.57 |

FSR | 0.4225 ± 0.0295 | 0.4436 ± 0.0216 | 0.4876 ± 0.0176 | 0.5663 ± 0.0434 | 0.4507 ± 0.0158 | |

Precision | 0.9355 ± 0.0113 | 0.9389 ± 0.0121 | 0.9234 ± 0.0098 | 0.9338 ± 0.0087 | 0.9351 ± 0.0121 | |

F-measure | 0.9258 ± 0.0136 | 0.9289 ± 0.0147 | 0.9111 ± 0.0152 | 0.9215 ± 0.0123 | 0.9251 ± 0.0151 | |

7 | Accuracy (%) | 97.71 ± 0.97 | 97.86 ± 0.87 | 97.86 ± 0.98 | 97.86 ± 0.98 | 97.71 ± 1.17 |

FSR | 0.3824 ± 0.0361 | 0.4031 ± 0.0165 | 0.4627 ± 0.0111 | 0.4717 ± 0.0348 | 0.4149 ± 0.0200 | |

Precision | 0.9788 ± 0.0087 | 0.9798 ± 0.0079 | 0.9799 ± 0.0092 | 0.9799 ± 0.0092 | 0.9789 ± 0.0102 | |

F-measure | 0.9774 ± 0.0098 | 0.9785 ± 0.0092 | 0.9786 ± 0.0104 | 0.9786 ± 0.0104 | 0.9772 ± 0.0121 | |

8 | Accuracy (%) | 93.00 ± 1.60 | 92.36 ± 1.33 | 91.14 ± 1.44 | 92.29 ± 1.34 | 92.93 ± 1.43 |

FSR | 0.4426 ± 0.0285 | 0.4536 ± 0.0272 | 0.5169 ± 0.0522 | 0.5676 ± 0.0485 | 0.4593 ± 0.0202 | |

Precision | 0.9338 ± 0.0143 | 0.9278 ± 0.0125 | 0.9164 ± 0.0132 | 0.9268 ± 0.0121 | 0.9323 ± 0.0131 | |

F-measure | 0.9295 ± 0.0160 | 0.9229 ± 0.0133 | 0.9110 ± 0.0143 | 0.9225 ± 0.0135 | 0.9287 ± 0.0141 | |

9 | Accuracy (%) | 94.79 ± 1.25 | 94.93 ± 1.57 | 94.57 ± 1.94 | 94.86 ± 2.24 | 94.36 ± 1.64 |

FSR | 0.4065 ± 0.0411 | 0.4139 ± 0.0203 | 0.4813 ± 0.0270 | 0.5217 ± 0.0557 | 0.4332 ± 0.0207 | |

Precision | 0.9563 ± 0.0097 | 0.9575 ± 0.0115 | 0.9543 ± 0.0161 | 0.9566 ± 0.0180 | 0.9518 ± 0.0143 | |

F-measure | 0.9472 ± 0.0132 | 0.9483 ± 0.0165 | 0.9453 ± 0.0197 | 0.9478 ± 0.0235 | 0.9428 ± 0.0172 | |

10 | Accuracy (%) | 97.29 ± 1.13 | 96.5 ± 1.64 | 95.57 ± 1.38 | 97.00 ± 0.92 | 95.64 ± 1.35 |

FSR | 0.4214 ± 0.0380 | 0.4343 ± 0.0177 | 0.4985 ± 0.0433 | 0.5785 ± 0.0314 | 0.4408 ± 0.0199 | |

Precision | 0.9758 ± 0.0101 | 0.9680 ± 0.0154 | 0.9598 ± 0.0132 | 0.9731 ± 0.0087 | 0.9612 ± 0.0117 | |

F-measure | 0.9731 ± 0.0114 | 0.9652 ± 0.0167 | 0.9561 ± 0.0142 | 0.9705 ± 0.0094 | 0.9570 ± 0.0129 |

Subject | p-Value | |||
---|---|---|---|---|

BBA | BDE | BFPA | BPSO | |

1 | 0.506287 | 0.056945 | 0.413356 | 0.847362 |

2 | 0.217023 | 0.109897 | 0.088031 | 0.384724 |

3 | 0.010163 | 2.00 × 10^{−5} | 0.018040 | 0.001725 |

4 | 0.629456 | 0.031698 | 0.666264 | 0.049260 |

5 | 0.109897 | 0.000358 | 0.129670 | 0.058264 |

6 | 0.425133 | 0.000462 | 0.249168 | 0.870789 |

7 | 0.605826 | 0.605826 | 0.605826 | 1.000000 |

8 | 0.131348 | 0.000265 | 0.135088 | 0.803685 |

9 | 0.693922 | 0.651311 | 0.894854 | 0.186411 |

10 | 0.085574 | 0.000499 | 0.329877 | 0.000490 |

Win (w)/tie (t)/lose(l) | 1/9/0 | 6/4/0 | 1/9/0 | 3/7/0 |

Subject | Average Computational Time(s) | ||||
---|---|---|---|---|---|

BPSODE | BBA | BDE | BFPA | BPSO | |

1 | 11.2170 | 9.6904 | 11.0745 | 10.9240 | 13.9385 |

2 | 11.4169 | 9.5965 | 11.3315 | 10.9586 | 13.6228 |

3 | 11.5064 | 9.7207 | 11.0580 | 11.4189 | 13.6346 |

4 | 11.6714 | 9.3344 | 11.2869 | 10.6936 | 13.4868 |

5 | 11.3360 | 9.3501 | 11.5490 | 11.0549 | 13.3068 |

6 | 11.5847 | 9.3415 | 11.2253 | 11.3795 | 13.2607 |

7 | 11.5799 | 9.2611 | 11.5731 | 11.1553 | 13.0535 |

8 | 11.8117 | 9.2501 | 11.9112 | 11.3934 | 13.3610 |

9 | 11.5575 | 9.1336 | 11.8026 | 11.2800 | 13.4043 |

10 | 11.7899 | 9.2060 | 11.7631 | 11.4669 | 13.3526 |

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**MDPI and ACS Style**

Too, J.; Abdullah, A.R.; Mohd Saad, N.
Hybrid Binary Particle Swarm Optimization Differential Evolution-Based Feature Selection for EMG Signals Classification. *Axioms* **2019**, *8*, 79.
https://doi.org/10.3390/axioms8030079

**AMA Style**

Too J, Abdullah AR, Mohd Saad N.
Hybrid Binary Particle Swarm Optimization Differential Evolution-Based Feature Selection for EMG Signals Classification. *Axioms*. 2019; 8(3):79.
https://doi.org/10.3390/axioms8030079

**Chicago/Turabian Style**

Too, Jingwei, Abdul Rahim Abdullah, and Norhashimah Mohd Saad.
2019. "Hybrid Binary Particle Swarm Optimization Differential Evolution-Based Feature Selection for EMG Signals Classification" *Axioms* 8, no. 3: 79.
https://doi.org/10.3390/axioms8030079