A Robust Algorithm for Classification and Diagnosis of Brain Disease Using Local Linear Approximation and Generalized Autoregressive Conditional Heteroscedasticity Model
Abstract
:1. Introduction
2. Methods and Materials
2.1. Image Processing
2.2. Discrete Wavelet Transform (DWT)
2.3. Generalized Autoregressive Conditional Heteroscedasticity
Algorithm 1. GARCH |
1: Input: 2: Output: 3: Step 1: Estimate AR(q): 4: 5: 6: Step 2: Compute and plot the autocorrelations of by: 7: 8: Step 3: null hypothesis states that there are no ARCH or GARCH errors |
2.4. Local Linear Approximation
2.5. K-Nearest Neighbour Algorithm
2.6. Proposed Method
Algorithm 2. Presented |
1: Input: 2: Switch: 3: Case 1: WGK 4: Step 1: Wavelet decomposition for all images 5: Step 2: Calculate GARCH parameters for sub-bands of high-frequency detail of (HH1, HL1, LH1, HL2, LH2) 6: Step 3: Normalization of features 7: Step 4: Feature reduction using PCA and PCA+LDA 8: Step 5: Classification of Features using KNN 9: Case 2: D-WGK 10: Step 1: Apply homomorphic filtering for all images 11: Step 2: Wavelet decomposition for all images 12: Step 2: Calculate GARCH parameters for all sub-bands of high-frequency detail of (HH1, HL1, LH1, HL2, LH2, LL2) 13: Step 3: Normalization of features 14: Step 4: Feature reduction using PCA and PCA+LDA 15: Step 5: Classification of Features using KNN 16: Case 3: WLK 17: Step 1: Wavelet decomposition for all images 18: Step 2: Calculate LLA parameters 19: Step 3: Normalization of features 20: Step 4: Feature reduction using PCA and PCA+LDA 21: Step 5: Classification of Features using KNN 22: Comparison and analysis |
3. Results and Discussion
3.1. Datasets
3.2. Two-dimensional Discrete Wavelet Transforms (2D-DWT)
3.3. Feature Reduction
- WGK: Using GARCH without LL2 + PCA
- WGK: Using GARCH without LL2 + PCA + LDA
- D-WGK: Using Homomorphic filtering + GARCH with LL2 + PCA
- WLK: Using LLA + PCA
- WLK: Using LLA + PCA + LDA
3.4. The Classification Results
4. The Complexity Analysis
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Ethical Approval
References
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Method | Class | Images | Features | Accuracy |
---|---|---|---|---|
Ref. * | 6 | 56 | 6 | 91.5 |
PCA + LDA (WGK) ** | 8 | 80 | 10 | 89.4 |
PCA (WGK) ** | 8 | 80 | 22 | 90.1 |
Proposed PCA + LDA (D-WGK) | 8 | 240 | 10 | 90.2 |
Proposed PCA (D-WGK) | 8 | 240 | 20 | 89.3 |
Proposed PCA + LDA (WLK) | 8 | 240 | 3 | 92.5 |
Proposed PCA (WLK) | 8 | 240 | 7 | 91.3 |
Diseases | TPR | TNR | PPV | ACC | FPR |
---|---|---|---|---|---|
Alzheimer | 0.933 | 1 | 0.903 | 0.967 | 0 |
Alzheimer+ | 0.933 | 1 | 0.875 | 0.967 | 0 |
Glioma | 0.900 | 1 | 1 | 0.950 | 0 |
Huntington | 0.967 | 1 | 0.906 | 0.983 | 0 |
Meningioma | 0.967 | 1 | 1 | 0.983 | 0 |
Pick | 0.867 | 1 | 0.839 | 0.933 | 0 |
Sarcoma | 0.833 | 1 | 0.926 | 0.917 | 0 |
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Hamzenejad, A.; Jafarzadeh Ghoushchi, S.; Baradaran, V.; Mardani, A. A Robust Algorithm for Classification and Diagnosis of Brain Disease Using Local Linear Approximation and Generalized Autoregressive Conditional Heteroscedasticity Model. Mathematics 2020, 8, 1268. https://doi.org/10.3390/math8081268
Hamzenejad A, Jafarzadeh Ghoushchi S, Baradaran V, Mardani A. A Robust Algorithm for Classification and Diagnosis of Brain Disease Using Local Linear Approximation and Generalized Autoregressive Conditional Heteroscedasticity Model. Mathematics. 2020; 8(8):1268. https://doi.org/10.3390/math8081268
Chicago/Turabian StyleHamzenejad, Ali, Saeid Jafarzadeh Ghoushchi, Vahid Baradaran, and Abbas Mardani. 2020. "A Robust Algorithm for Classification and Diagnosis of Brain Disease Using Local Linear Approximation and Generalized Autoregressive Conditional Heteroscedasticity Model" Mathematics 8, no. 8: 1268. https://doi.org/10.3390/math8081268
APA StyleHamzenejad, A., Jafarzadeh Ghoushchi, S., Baradaran, V., & Mardani, A. (2020). A Robust Algorithm for Classification and Diagnosis of Brain Disease Using Local Linear Approximation and Generalized Autoregressive Conditional Heteroscedasticity Model. Mathematics, 8(8), 1268. https://doi.org/10.3390/math8081268