# Improving Human Activity Recognition Performance by Data Fusion and Feature Engineering

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## Abstract

**:**

## 1. Introduction

## 2. Algorithm Description

#### 2.1. Calculation of the Joint Angle

#### 2.2. Features

#### 2.2.1. Feature Calculation

- TD Features

- FD Features

- TFD Features

#### 2.2.2. Resampling

#### 2.2.3. Feature Evaluation

#### 2.3. Feature Selection

- Initialization

- 2.
- Fitness evaluation function

- 3.
- Genetic operators

- COFAN: Firstly, the gene bits activated in each parent individual are extracted to form an intermediate individual of length ${N}_{init}$, each of whose gene bits represents the sequence number of an activated gene bits in the parent. Then, the same genes were selected from the intermediate individuals of the two parents to form the homogeneous gene pair, and remaining gens of each intermediate individuals are made into the heterogeneous gene pairs. The two-point crossover operation is performed on the two heterogeneous gene pairs to produce the progeny heterogeneous gene pairs, which are then combined with the homogeneous gene pair to form progeny intermedia individuals. Finally, each of the children is produced by setting the corresponding gene bits of an unactivated individual to “1” according to the progeny intermedia individual.
- MOFAN: Mutation operation is performed on each activated gene bits of the parent individual according to the mutation probability and the actual number of mutations is recorded firstly. Subsequently, the same number of unactivated bits are randomly selected to perform the mutation operation and the child individual is finally generated.

## 3. Experiments Description

#### 3.1. Participants

#### 3.2. Data Collection

#### 3.2.1. Activities and Procedure

#### 3.2.2. Sensors Configuration and Data Acquisition

#### 3.3. Preprocessing and Segmentation

## 4. Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 5.**The selected ADLs: (

**a**) standing, (

**b**) sitting, (

**c**) squatting, (

**d**) lying, (

**e**) walking, (

**f**) ascending stairs, (

**g**) descending stairs, (

**h**) ascending ramps, and (

**i**) descending ramps.

**Figure 7.**(

**a**) SFI of all features with different window parameter pairs with and without calibration of IMUs. (

**b**) Enlarge details of the black box in (

**a**) at the window length of 400 ms. Where red means calibrated and blue means uncalibrated.

**Figure 8.**(

**a**) F-measure per activity for dataset with calibration and without calibration. (

**b**) F-measure per feature subset for dataset with calibration and without calibration. (

**c**) F-measure per classification algorithm for dataset with calibration and without calibration. (

**d**) F-measure per sensor combination for dataset with calibration and without calibration.

**Figure 9.**Mean F-Measure of all feature subsets per sensor combination and classification algorithms (KNN, RF and SVM).

**Figure 10.**Mean F-Measure per activity and multiple sensors combination with different classification algorithms: (

**a**) KNN; (

**b**) RF; (

**c**) SVM.

Feature | Mathematical Definition | Feature | Mathematical Definition |
---|---|---|---|

Mean Value (MV) | $\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}{x}_{i}$ | Standard Deviation (SD) | $\sqrt{\frac{1}{N-1}{\displaystyle \sum _{i=1}^{N}}{\left({x}_{i}-\overline{x}\right)}^{2}}$ |

Variance (VAR) | $\frac{1}{N-1}{\displaystyle \sum _{i=1}^{N}}{x}_{i}{}^{2}$ | Root Mean Square (RMS) | $\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}{x}_{i}{}^{2}}$ |

Skewness (SKE) | $\frac{1}{N{\sigma}^{3}}{\displaystyle \sum _{i=1}^{N}}{\left({x}_{i}-\overline{x}\right)}^{3}$ | Kurtosis (KUR) | $\frac{1}{N{\sigma}^{4}}{\displaystyle \sum _{i=1}^{N}}{\left({x}_{i}-\overline{x}\right)}^{4}$ |

Interquartile Range (IQR) | ${Q}_{3}-{Q}_{1}$ | Peak to Peak(P2P) | ${x}_{max}-{x}_{min}$ |

Mean Absolute Value (MAV) | $\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}\left|{x}_{i}\right|$ | Waveform Length (WL) | $\sum _{i=1}^{N-1}}\left|{x}_{i+1}-{x}_{i}\right|$ |

Zero Crossing (ZC) | $\{\begin{array}{c}ZC={\displaystyle \sum _{i=1}^{N}}{z}_{i}\times z{c}_{i}\\ z{c}_{i}=sgn\left(-{x}_{i}{x}_{i+1}\right)\\ {z}_{i}=\{\begin{array}{l}1,\left|{x}_{i}-{x}_{i+1}\right|{\delta}_{z}\\ 0,else\end{array}\end{array}$ | Slope Sign Change (SSC) | $\{\begin{array}{c}SSC={\displaystyle \sum _{i=2}^{N-1}}{s}_{i}\times ss{c}_{i}\\ ss{c}_{i}=sgn\left[\left({x}_{i}-{x}_{i-1}\right)\left({x}_{i}-{x}_{i+1}\right)\right]\\ {s}_{i}=\{\begin{array}{l}1,\left|{x}_{i}-{x}_{i+1}\right|{\delta}_{s}\cap \left|{x}_{i}-{x}_{i-1}\right|{\delta}_{s}\\ 0,else\end{array}\end{array}$ |

Wilson Amplitude (WAMP) | $\sum _{i=1}^{N-1}}sgn\left(\left|{x}_{i+1}-{x}_{i}\right|-{\delta}_{\mathrm{w}}\right)$ | Log Detector (LD) | $\mathrm{exp}\left(\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}log\left(\left|{x}_{i}\right|\right)\right)$ |

Auto Regressive Coefficient (ARC) | ${x}_{k}={\displaystyle \sum _{i=1}^{4}}{a}_{i}{x}_{k-i}+{e}_{k}$ | Energy | $\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}{\left|{x}_{i}\right|}^{2}$ |

Modified Mean Absolute Value (MMAV) | $\{\begin{array}{c}\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}{\omega}_{i}\left|{x}_{i}\right|\\ {\omega}_{i}=\{\begin{array}{l}1,0.25N\le i\le 0.75N\\ 0,else\end{array}\end{array}$ | Correlation Coefficient (CC) | $\frac{{{\displaystyle \sum}}_{i=1}^{N}\left(cc{a}_{i}-\overline{cca}\right)\left(cc{b}_{i}-\overline{ccb}\right)}{\sqrt{{{\displaystyle \sum}}_{i=1}^{N}{\left(cc{a}_{i}-\overline{cca}\right)}^{2}{{\displaystyle \sum}}_{i=1}^{N}{\left(cc{b}_{i}-\overline{ccb}\right)}^{2}}}$ |

Jerk | $\frac{1}{2}{\displaystyle \sum _{i=2}^{N}}{\displaystyle \sum _{j=1}^{3}}{\left(AC{C}_{j}\left(i\right)-AC{C}_{j}\left(i-1\right)\right)}^{2}$ | Signal Magnitude Area (SMA) | $\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}\left(\left|sma{x}_{i}\right|+\left|sma{y}_{i}\right|+\left|sma{z}_{i}\right|\right)$ |

Mean Power Frequency (MPF) | $\frac{{{\displaystyle \sum}}_{i=1}^{n}{p}_{i}{f}_{i}}{{{\displaystyle \sum}}_{i=1}^{n}{p}_{i}}$ | Entropy | $-{\displaystyle \sum _{i=1}^{n}}\left(\frac{{p}_{i}}{{{\displaystyle \sum}}_{i=1}^{n}{p}_{i}}ln\left(\frac{{p}_{i}}{{{\displaystyle \sum}}_{i=1}^{n}{p}_{i}}\right)\right)$ |

Median Frequency (MDF) | $\sum _{i={f}_{min}}^{MDF}}{p}_{i}={\displaystyle \sum _{i=MDF}^{{f}_{max}}}{p}_{i$ | One Quarter of Frequency (F25) | $3{\displaystyle \sum _{i={f}_{min}}^{F25}}{p}_{i}={\displaystyle \sum _{i=F25}^{{f}_{max}}}{p}_{i}$ |

Three Quarters of Frequency (F75) | $\sum _{i={f}_{min}}^{F75}}{p}_{i}=3{\displaystyle \sum _{i=F75}^{{f}_{max}}}{p}_{i$ |

Feature | sEMG | ACC | GYR | Joint |
---|---|---|---|---|

MV | ● | ● | ● | ● |

SD | ● | ● | ● | ● |

VAR | ● | ● | ● | ● |

RMS | ● | ● | ● | ● |

SKE | ● | ● | ● | ● |

KUR | ● | ● | ● | ● |

IQR | ● | ● | ● | ● |

P2P | ● | ● | ● | ● |

MAV | ● | ● | ● | ● |

WL | ● | ● | ● | ● |

ZC | ● | ● | ||

SSC | ● | ● | ||

WAMP | ● | ● | ||

LD | ● | ● | ● | ● |

ARC | ● | ● | ● | ● |

Energy | ● | ● | ● | ● |

MMAV | ● | ● | ● | ● |

CC | ● | ● | ||

Jerk | ● | |||

SMA | ● | ● | ||

MPF | ● | ● | ● | ● |

MDF | ● | ● | ● | ● |

Entropy | ● | ● | ● | ● |

F25 | ● | ● | ● | ● |

F75 | ● | ● | ● | ● |

Top 3 Largest Value of DFT (3LVD) | ● | ● | ● | ● |

Energy of Wavelet Coefficient (EWC) | ● | ● | ● |

Gender | Number | Age (Year) | Weight (kg) | Height (cm) |
---|---|---|---|---|

Male | 13 | 27.5 $\pm $ 2.53 | 69.8 $\pm $ 7.65 | 176.5 $\pm $ 6.23 |

Female | 4 | 29.3 $\pm $ 4.79 | 59.6 $\pm $ 4.03 | 159.8 $\pm $ 2.75 |

All | 17 | 27.6 $\pm $ 3.10 | 66.8 $\pm $ 7.95 | 172.5 $\pm $ 9.17 |

**Table 4.**The classification performance of different sensor combinations and different feature subsets with KNN, RF and SVM.

GFSFAN 10 Features | Filter | SFS | All Features | ||||||
---|---|---|---|---|---|---|---|---|---|

Sensor Comb. | Algo. | FN | FM | FN | FM | FN | FM | FN | FM |

sEMG | KNN | 10 | 0.977 | 59 | 0.98 | 19 | 0.981 | 132 | 0.973 |

RF | 0.977 | 0.98 | 0.981 | 0.973 | |||||

SVM | 0.933 | 0.957 | 0.984 | 0.960 | |||||

ACC | KNN | 10 | 0.985 | 114 | 0.984 | 36 | 0.986 | 285 | 0.985 |

RF | 0.985 | 0.984 | 0.986 | 0.985 | |||||

SVM | 0.980 | 0.981 | 0.985 | 0.984 | |||||

GYR | KNN | 10 | 0.945 | 121 | 0.948 | 55 | 0.965 | 309 | 0.977 |

RF | 0.946 | 0.948 | 0.965 | 0.977 | |||||

SVM | 0.943 | 0.949 | 0.978 | 0.977 | |||||

Joint Ang. | KNN | 10 | 0.993 | 20 | 0.993 | 34 | 0.994 | 50 | 0.934 |

RF | 0.993 | 0.993 | 0.994 | 0.934 | |||||

SVM | 0.983 | 0.988 | 0.986 | 0.881 | |||||

IMU (ACC+GYR) | KNN | 10 | 0.987 | 231 | 0.991 | 31 | 0.992 | 594 | 0.991 |

RF | 0.989 | 0.991 | 0.992 | 0.991 | |||||

SVM | 0.987 | 0.988 | 0.991 | 0.989 | |||||

sEMG+IMU | KNN | 10 | 0.993 | 289 | 0.994 | 37 | 0.994 | 726 | 0.988 |

RF | 0.993 | 0.994 | 0.994 | 0.988 | |||||

SVM | 0.989 | 0.991 | 0.993 | 0.992 | |||||

sEMG+IMU+Joint Ang. | KNN | 10 | 0.994 | 307 | 0.994 | 36 | 0.995 | 776 | 0.988 |

RF | 0.994 | 0.994 | 0.995 | 0.988 | |||||

SVM | 0.983 | 0.991 | 0.994 | 0.983 | |||||

Mean Value | KNN | 10 | 0.982 | 163 | 0.986 | 35.4 | 0.987 | 410 | 0.977 |

RF | 0.982 | 0.986 | 0.987 | 0.977 | |||||

SVM | 0.971 | 0.977 | 0.987 | 0.966 |

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Chen, J.; Sun, Y.; Sun, S.
Improving Human Activity Recognition Performance by Data Fusion and Feature Engineering. *Sensors* **2021**, *21*, 692.
https://doi.org/10.3390/s21030692

**AMA Style**

Chen J, Sun Y, Sun S.
Improving Human Activity Recognition Performance by Data Fusion and Feature Engineering. *Sensors*. 2021; 21(3):692.
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**Chicago/Turabian Style**

Chen, Jingcheng, Yining Sun, and Shaoming Sun.
2021. "Improving Human Activity Recognition Performance by Data Fusion and Feature Engineering" *Sensors* 21, no. 3: 692.
https://doi.org/10.3390/s21030692