# Classification of MRI Brain Images Using DNA Genetic Algorithms Optimized Tsallis Entropy and Support Vector Machine

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Feature Extraction with DWT and Tsallis Entropy

#### 2.1. Feature Extraction

#### 2.2. Discrete Wavelet Transform

#### 2.3. Tsallis Entropy

## 3. SVMs and Parameters

#### 3.1. Support Vector Machine

_{n}represents a p-dimensional data point, y

_{n}stands for category (y

_{n}can be 1 or −1, respectively, which represents two different classes). The target of a classifier is to find a hyperplane in the p-dimensional data space. Assuming that one dataset is nonlinear, we need to create a nonlinear classification function:

#### 3.2. Kernel Functions

## 4. DNA-GA for Optimal Parameters

#### 4.1. The Proposed Algorithm

#### 4.2. DNA Encoding and Decoding

#### 4.3. DNA Genetic Operators

#### 4.3.1. The Selection Operation

#### 4.3.2. The Crossover Operations

#### 4.3.3. The Mutation Operations

#### 4.4. Fitness Function

## 5. Experimental Study

#### 5.1. Database

#### 5.2. Feature Extraction

#### 5.3. Results on SBD

#### 5.4. Results on AANLIB

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Table 1.**Comprehensive results of 100 accuracy evaluations of SBD image classification using DNA-GA-TE + SVM.

SNR = 5 db | SNR = 10 db | SNR = 15 db | SNR = 20 db | |
---|---|---|---|---|

Average | 0.8341 | 0.937 | 0.9567 | 0.9684 |

Best | 0.8671 | 0.948 | 0.9723 | 0.9795 |

Worst | 0.7128 | 0.8844 | 0.8919 | 0.932 |

**Table 2.**Parameters of comparison by random selection method (the final row corresponds to our proposed method) on AANLIB.

$\mathit{C}$ | $\mathit{\sigma}$ | $\mathit{q}$ | Success Cases | Classification Rate (%) | |
---|---|---|---|---|---|

Random 1 | 124.71 | 0.625 | 0.1 | 410 | 91.11 |

Random 2 | 185.13 | 1.439 | 0.2 | 412 | 91.56 |

Random 3 | 136.2 | 1.491 | 0.3 | 423 | 94 |

Random 4 | 176.78 | 1.595 | 0.4 | 409 | 90.89 |

Random 5 | 160.8 | 1.836 | 0.5 | 401 | 89.11 |

Random 6 | 137.9 | 1.973 | 0.6 | 401 | 89.11 |

Random 7 | 87.01 | 1.654 | 0.7 | 396 | 88 |

Random 8 DNAGA-TE+KSVM | 149.96 143.3 | 1.372 1.132 | 0.9 0.8 | 427 440 | 94.89 97.78 |

Method | Confusion Matrix | Success Cases | Sensitivity | Specificity | Classification Accuracy |
---|---|---|---|---|---|

BP-NN | 374 11 51 14 | 388 | 88% | 56% | 86.22% |

RBF-NN | 393 7 32 18 | 411 | 92.47% | 72% | 91.33% |

DNAGA-TE+KSVM | 417 2 8 23 | 440 | 98.12% | 92% | 97.78% |

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**MDPI and ACS Style**

Zang, W.; Wang, Z.; Jiang, D.; Liu, X.; Jiang, Z.
Classification of MRI Brain Images Using DNA Genetic Algorithms Optimized Tsallis Entropy and Support Vector Machine. *Entropy* **2018**, *20*, 964.
https://doi.org/10.3390/e20120964

**AMA Style**

Zang W, Wang Z, Jiang D, Liu X, Jiang Z.
Classification of MRI Brain Images Using DNA Genetic Algorithms Optimized Tsallis Entropy and Support Vector Machine. *Entropy*. 2018; 20(12):964.
https://doi.org/10.3390/e20120964

**Chicago/Turabian Style**

Zang, Wenke, Zehua Wang, Dong Jiang, Xiyu Liu, and Zhenni Jiang.
2018. "Classification of MRI Brain Images Using DNA Genetic Algorithms Optimized Tsallis Entropy and Support Vector Machine" *Entropy* 20, no. 12: 964.
https://doi.org/10.3390/e20120964