# Combined Regularized Discriminant Analysis and Swarm Intelligence Techniques for Gait Recognition

^{*}

## Abstract

**:**

## 1. Introduction

- proposing a combination of regularized discriminant analysis and particle swarm optimization for gait recognition,
- proposing a combination of regularized discriminant analysis and grey wolf optimization,
- proposing a combination of regularized discriminant analysis and whale optimization algorithm,
- comparing and improving the results obtained in the paper [21].

## 2. Material and Methods

#### 2.1. Gait Dataset

#### 2.2. Gait Recognition System

#### 2.3. Building Classification Model for Gait Recognition

#### 2.4. Regularized Discriminant Analysis

- dimensionality reduction and feature extraction before classification,
- a linear classifier (considered in this paper).

**I**is the identity matrix, and $\gamma \in [0,1]$ is the amount of regularization. The RDA introduces regularization into the covariance matrix estimate, enabling a solution to be obtained and allowing different influences of variables on the classification model. In addition to the parameter γ the RDA model uses the parameter δ that acts as a threshold: if a model coefficient has the magnitude smaller than δ the RDA sets this coefficient to zero, and the corresponding predictor can be eliminated from the model.

**M**is an N-by-K class membership matrix such that ${M}_{nk}=1$ if observation n is from class k, ${M}_{nk}=0$, otherwise. The estimate of the class mean for weighted data with positive weights w

_{n}is [30]

#### 2.5. Particle Swarm Optimization

**x**) and velocity (

**v**). The velocity

**v**

_{k}of the kth particle is determined using the following equation [31]:

**r**

_{1},

**r**

_{2}are vectors of random numbers in the range [0,1], c

_{1}is the cognitive coefficient, and c

_{2}is the social coefficient. It is seen that the update of the velocity is a weighted sum of the previous velocity ${\mathbf{v}}_{k}\left(t\right)$, the difference between the current position and the personal best position (

**pbest**), and the difference between the current position and the global best position (

**gbest**). The position

**x**

_{k}of the kth particle is updated according to the equation

#### 2.6. Grey Wolf Optimization

#### 2.6.1. Encircling Prey

#### 2.6.2. Hunting

#### 2.6.3. Attacking Prey (Exploitation) and Search for Prey (Exploration)

#### 2.7. Whale Optimization Algorithm

#### 2.7.1. Encircling Prey

#### 2.7.2. Bubble-Net Attacking (Exploitation Phase)

#### 2.7.3. Search for Prey (Exploration Phase)

#### 2.8. Integration of Swarm Intelligence Techniques with Regularized Discriminant Analysis

- ${w}_{1},{w}_{2},\dots ,{w}_{n}$ — the observation weights,
- $\delta $ — the linear coefficient threshold,
- $\gamma $ — the parameter for regularizing the covariance matrix of the predictors,

`fitcdiscr`from the Statistics and Machine Learning Toolbox [30], the RDA classifier model is created, while the function

`predict`from the same package is used to determine class predictions (Figure 3). The PSO method has been implemented using the function

`particleswarm`from the Global Optimization Toolbox [34] and the GWO and WOA methods using software developed by Mirjalili [32,33].

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Experiment | Subset | Classical Methods | Hybrid Methods |
---|---|---|---|

1: Set #1 | train | 169 | 137 |

validation | – | 32 | |

test | 156 | 156 | |

2: Set #2 | train | 325 | 261 |

validation | – | 64 | |

test | 58 | 58 | |

3: Set #3 | train | 325 | 261 |

validation | – | 64 | |

test | 31 | 31 | |

4: Set #4 | train | 90% ($\approx 293$) | 80% ($\approx 261$) |

validation | – | 10% ($\approx 32$) | |

test | 10% ($\approx 32$) | 10% ($\approx 32$) |

Experiment | kNN [21] | NB [21] | SMO [21] | MLP [21] | LDA | RDA-PSO | RDA-GWO | RDA-WOA |
---|---|---|---|---|---|---|---|---|

1: Set #1 | 47.44 | 55.77 | 67.95 | 80.13 | 45.51 | $\mathbf{87.05}$ | 86.28 | 86.92 |

2: Set #2 | 37.93 | 56.90 | 63.79 | 75.86 | 79.31 | $\mathbf{85.34}$ | 84.48 | 84.48 |

3: Set #3 | 38.71 | 70.97 | 67.74 | 77.42 | $\mathbf{93.55}$ | 88.39 | $\mathbf{93.55}$ | $\mathbf{93.55}$ |

4: Set #4 | 56.92 | 79.69 | 84.31 | 89.85 | 91.99 | 95.07 | $\mathbf{95.39}$ | 95.09 |

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Krzeszowski, T.; Wiktorowicz, K.
Combined Regularized Discriminant Analysis and Swarm Intelligence Techniques for Gait Recognition. *Sensors* **2020**, *20*, 6794.
https://doi.org/10.3390/s20236794

**AMA Style**

Krzeszowski T, Wiktorowicz K.
Combined Regularized Discriminant Analysis and Swarm Intelligence Techniques for Gait Recognition. *Sensors*. 2020; 20(23):6794.
https://doi.org/10.3390/s20236794

**Chicago/Turabian Style**

Krzeszowski, Tomasz, and Krzysztof Wiktorowicz.
2020. "Combined Regularized Discriminant Analysis and Swarm Intelligence Techniques for Gait Recognition" *Sensors* 20, no. 23: 6794.
https://doi.org/10.3390/s20236794