# Hand Movement Classification Using Burg Reflection Coefficients

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Selection and Preprocessing

#### 2.2. Standard Time Domain Features

#### 2.3. Autoregressive Model Features

^{th}autocorrelation coefficient of the model of order m, which implies a combination of previous values and the reflection coefficients ${K}_{m}$ [37]:

#### 2.4. Dataset Construction

#### 2.5. Proposed Classification Methodology by Applying Burg Reflection Coefficients

#### 2.5.1. Classification Model Training

- Time domain datasets (Equations (1)–(11)): TD= [IEMG MAV SSI VAR RMS WL WAMP SSC ZC MYOP]
- Reflection coefficients: K = [K${}_{1}$ K${}_{2}$ … K${}_{n}$]

#### 2.5.2. Features Selection and Reduction Methods

## 3. Results

#### 3.1. Classification

#### 3.2. Feature Selection Classification Performance

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Table 1.**Time-domain and frequency-domain features used in sEMG data processing and classification tasks.

Feature | Abbreviation | |
---|---|---|

1 | Root mean squared value | RMS |

2 | Mean average value | MAV |

3 | Variance | VAR |

4 | Willison amplitude | WAMP |

5 | Wavelength | WL |

6 | Auto-regressive | AR |

7 | Difference absolute mean value | DAMV |

8 | Difference absolute standard deviation value | DASDV |

9 | Difference absolute variance | DVARV |

10 | Difference absolute standard deviation | DASDV |

11 | Second order moment | M2 |

12 | Integrated EMG | IEMG |

13 | Simple squared integration | SSI |

14 | Myopulse percentage rate | MYOP |

15 | Cepstral coefficients | CC |

16 | Log detector | LOG |

17 | Temporal moment | TK |

18 | V order | V |

19 | Zero crossings | ZC |

20 | Slope sign change | SSC |

**Table 2.**Feature extraction techniques for hand movement classification applied to the EMG dataset from the University of California at Irvine (UCI) machine learning repository.

Research Group | Algorithm | Accuracy |
---|---|---|

[32] | Neural Network after Empirical Mode Decomposition (EDM) | 85% |

[32] | Adaptive Boosting after EMD | 55% |

[32] | Linear Discriminant Analysis after EMD | 65% |

[32] | Random Forest after EMD | 91% |

[32] | Random Forest + PCA after EMD | 94% |

[29] | Singular-Value Decomposition with SVM | 98.22% |

[29] | k-Nearest Neighbor | 94.77% |

[29] | Naive Bayes | 91.66% |

[29] | Radial Basis Function Network | 94% |

**Table 3.**Feature reduction process. MAV, mean average value; SSI, simple squared integration; WL, wavelength; WAMP, Willison amplitude; MYOP, myopulse percentage rate.

l | r | Remaining Features |
---|---|---|

29 | 1 | [MAV, SSI, VAR, RMS, WL, WAMP, SSC, ZC, MYOP, Arb${}_{1}$:Arb${}_{10}$, K${}_{1}$:K${}_{10}$] |

28 | 2 | [SSI, VAR, RMS, WL, WAMP, SSC, ZC, MYOP, Arb${}_{1}$:Arb${}_{10}$, K${}_{1}$:K${}_{10}$ |

27 | 3 | [VAR, RMS, WL, WAMP, SSC, ZC, MYOP, Arb${}_{1}$:Arb${}_{10}$, K${}_{1}$:K${}_{10}$] |

⋮ | ⋮ | ⋮ |

10 | 20 | [ZC, MYOP, Arb${}_{1}$, Arb${}_{2}$, Arb${}_{7}$, Arb${}_{8}$, Arb${}_{10}$, K${}_{1}$, K${}_{2}$, K${}_{10}$] |

**Table 4.**Classification results of the time domain (TD), Arb, and K datasets separately. P3, third order polynomial.

N | Dataset | Bayes | IBk | MLP | Tree | SVM | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

− | − | $Naive$ | $net$ | ${k}_{1}$ | ${k}_{7}$ | − | $J48$ | $Random$ | $radial$ | $linear$ | $P3$ |

20 | TD | $46.55$ | $68.33$ | $93.22$ | $91.22$ | $86.55$ | $83.33$ | $92.88$ | $27.33$ | $76.33$ | $93.11$ |

20 | Arb | $59.11$ | $63.33$ | $90.77$ | $91.66$ | $86.33$ | $78.00$ | $90.55$ | $47.00$ | $61.11$ | $37.77$ |

20 | k | $57.44$ | $71.11$ | $93.55$ | $93.33$ | $86.44$ | $74.77$ | $92.00$ | $45.55$ | $65.44$ | $29.77$ |

N | Features | Bayes | IBk | MLP | Tree | SVM | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

− | − | $Naive$ | $net$ | ${k}_{1}$ | ${k}_{7}$ | − | $J48$ | $Random$ | $radial$ | $linear$ | $P3$ |

40 | $k+TD$ | $61.44$ | $83.22$ | $99.88$ | $99.55$ | $98.44$ | $87.11$ | $98.33$ | $18.33$ | $83.11$ | $93.22$ |

40 | $k+Arb$ | $78.22$ | $82.33$ | $99.66$ | $99.33$ | $98.44$ | $84.77$ | $98.66$ | $64.00$ | $90.00$ | $54.66$ |

60 | X | $76.00$ | $83.33$ | $100.0$ | $99.77$ | $99.11$ | $85.55$ | $95.55$ | $17.77$ | $83.00$ | $93.22$ |

**Table 6.**Classification performances using different feature vectors after feature selection: SE = [$C{h}_{1}$Arb(1,2,5,9,10), $c{h}_{1}$k(1,2,3,4,9), $C{h}_{1}$WL, $C{h}_{1}$SSC, $C{h}_{1}$ZC, $C{h}_{1}$MYOP, $C{h}_{2}$Arb(1,2,4,5,10), $C{h}_{2}k$(1,5,7), $C{h}_{2}$WL, $C{h}_{2}$MYOP], $F{S}_{1}$ = [Arb(1,2,7,8,10), K(1,2,10), ZCC, MYOP], $F{S}_{2}$ = [Arb1, K1, ZCC, RMS], $F{S}_{3}$ = [$Ar{b}_{1}$, ${K}_{1}$, ZCC, MAV], $F{S}_{4}$ = [$Ar{b}_{1}$, ${K}_{1}$, MYOP, RMS] $F{S}_{5}$ = [$Ar{b}_{1}$, ${K}_{1}$, MYOP, MAV].

N | Features | Bayes | IBk | MLP | Tree | SVM | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

− | − | $Naive$ | $net$ | ${k}_{1}$ | ${k}_{7}$ | − | $J48$ | $Random$ | $radial$ | $linear$ | $P3$ |

26 | $SE$ | $82.55$ | $91.55$ | $99.88$ | $99.88$ | $99.11$ | $87.77$ | $99.55$ | $18.00$ | $74.33$ | $82.00$ |

26 | $PC$ | $88.11$ | $88.66$ | $99.66$ | $98.88$ | $97.55$ | $84.11$ | $98.44$ | $100.0$ | $96.11$ | $99.55$ |

20 | $F{S}_{1}$ | $79.88$ | $86.88$ | $100.0$ | $99.66$ | $97.66$ | $86.33$ | $98.77$ | $24.88$ | $68.88$ | $57.77$ |

8 | $F{S}_{2}$ | $64.88$ | $84.22$ | $99.22$ | $99.22$ | $88.55$ | $88.66$ | $97.88$ | $22.33$ | $55.11$ | $49.88$ |

8 | $F{S}_{3}$ | $65.00$ | $83.22$ | $99.22$ | $98.77$ | $89.22$ | $89.55$ | $97.88$ | $22.33$ | $54.33$ | $45.88$ |

8 | $F{S}_{4}$ | $66.77$ | $84.66$ | $98.22$ | $97.77$ | $87.55$ | $88.77$ | $89.88$ | $66.11$ | $70.77$ | $28.66$ |

8 | $F{S}_{5}$ | $67.33$ | $83.00$ | $98.22$ | $97.77$ | $88.55$ | $88.55$ | $98.33$ | $61.44$ | $68.66$ | $32.55$ |

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**MDPI and ACS Style**

Ramírez-Martínez, D.; Alfaro-Ponce, M.; Pogrebnyak, O.; Aldape-Pérez, M.; Argüelles-Cruz, A.-J. Hand Movement Classification Using Burg Reflection Coefficients. *Sensors* **2019**, *19*, 475.
https://doi.org/10.3390/s19030475

**AMA Style**

Ramírez-Martínez D, Alfaro-Ponce M, Pogrebnyak O, Aldape-Pérez M, Argüelles-Cruz A-J. Hand Movement Classification Using Burg Reflection Coefficients. *Sensors*. 2019; 19(3):475.
https://doi.org/10.3390/s19030475

**Chicago/Turabian Style**

Ramírez-Martínez, Daniel, Mariel Alfaro-Ponce, Oleksiy Pogrebnyak, Mario Aldape-Pérez, and Amadeo-José Argüelles-Cruz. 2019. "Hand Movement Classification Using Burg Reflection Coefficients" *Sensors* 19, no. 3: 475.
https://doi.org/10.3390/s19030475