# An Optimized Brain-Based Algorithm for Classifying Parkinson’s Disease

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## Abstract

**:**

## 1. Introduction

## 2. Background

## 3. Methodology

#### 3.1. Parkinson’s Disease

#### 3.2. Signal’s Transformation

#### 3.3. Experimental Design

## 4. Extreme Learning Machine

- Randomly generate input weight and bias $({w}_{i},{\beta}_{i})$, $i=\{1,2,\dots ,\tilde{N}\}$.
- Calculate the hidden layer output matrix H.
- Calculate the weight $\widehat{\beta}={H}^{\u2020}T$.

## 5. Proposed Approach

- It is assumed that all bats use echolocation to determine distances, and all of them are able to distinguish food, prey, and background barriers.
- A bat ${b}_{i}$ searches for prey with position ${x}_{i}$ that initially is random. Bats changes its frequency depending on the proximity of their target, then affecting velocity. Thus, to change their position, all bats used frequency ${f}_{i}$ calculated by Equation (4) and velocity ${v}_{i}$ computed by Equation (5). The new position is defined by Equation (6). The bat algorithm is considered a frequency-tuning algorithm that provides a balanced combination of exploration and exploitation. While more (positive) velocity, more exploration, less (positive) velocity, more exploitation.$${f}_{i}={f}_{min}+({f}_{max}-{f}_{min})\beta \hspace{1em}\beta \sim U(0,1)$$$${v}_{(i,t+1)}={v}_{(i,t)}+({x}_{best}-{x}_{(i,t)}){f}_{i}$$$${x}_{(i,t+1)}={x}_{(i,t)}+{v}_{(i,t+1)}$$
- Finally, the variability of solutions is given by loudness ${A}_{0}$ and a rate of pulse emission $r\in (0,1)$, determined by Equations (7) and (8), respectively. Although the loudness can vary in many ways, it is assumed that the loudness varies from a large (positive) ${A}_{0}$ to a minimum constant value ${A}_{min}$.$${A}_{(i,t+1)}=\alpha {A}_{0}\hspace{1em}0<\alpha <1$$$${r}_{(i,t+1)}={r}_{(i,0)}(1-ex{p}^{(-\gamma t)})\hspace{1em}\gamma >0$$

Algorithm 1: Bat algorithm. |

## 6. Computational Experiments

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Representation of the process used in the proposed BA-ELM. ELM starts by randomly initializing the input weights and hidden biases. Then, ELM is trained and generates a learning model. This model gives an accuracy and a loss, both are used by bat algorithm to be evaluated as the fitness. Finally, the bat algorithm computes new weights and biases for the ELM. This process operartes while a stop criteria is met.

Statistical Comparison | ||||
---|---|---|---|---|

Item | Accuracy | Loss | ||

ELM | BA-ELM | ELM | BA-ELM | |

Average | 90.70 | 96.34 | 6.35 | 3.72 |

Standard deviation | 0.59 | 0.27 | 0.58 | 0.27 |

Minimum | 89.76 | 95.81 | 5.36 | 3.27 |

1-IQR (25%) | 90.14 | 96.11 | 5.78 | 3.53 |

2-IQR (50%) | 90.87 | 96.41 | 6.42 | 3.77 |

3-IQR (75%) | 91.15 | 96.58 | 6.89 | 3.91 |

Maximum | 91.61 | 96.74 | 7.29 | 4.25 |

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**MDPI and ACS Style**

Olivares, R.; Munoz, R.; Soto, R.; Crawford, B.; Cárdenas, D.; Ponce, A.; Taramasco, C.
An Optimized Brain-Based Algorithm for Classifying Parkinson’s Disease. *Appl. Sci.* **2020**, *10*, 1827.
https://doi.org/10.3390/app10051827

**AMA Style**

Olivares R, Munoz R, Soto R, Crawford B, Cárdenas D, Ponce A, Taramasco C.
An Optimized Brain-Based Algorithm for Classifying Parkinson’s Disease. *Applied Sciences*. 2020; 10(5):1827.
https://doi.org/10.3390/app10051827

**Chicago/Turabian Style**

Olivares, Rodrigo, Roberto Munoz, Ricardo Soto, Broderick Crawford, Diego Cárdenas, Aarón Ponce, and Carla Taramasco.
2020. "An Optimized Brain-Based Algorithm for Classifying Parkinson’s Disease" *Applied Sciences* 10, no. 5: 1827.
https://doi.org/10.3390/app10051827