# A Hybrid Artificial Intelligence Model for Detecting Keratoconus
## 5 Experiments and Results  
To evaluate the performance of the proposed method (FPA\(k\)-means) five quality assessment measures are calculated: namely recall, accuracy, purity, precision, f-measure. These measures are calculated using the following:  
* Accuracy: \[Acc=\frac{T_{a}+T_{r}}{T_{a}+F_{a}+T_{r}+F_{r}}\times 100\] (4) where \(T_{a}\), \(T_{r}\), \(F_{a}\), and \(F_{r}\) represent true acceptance, true reject, false acceptance, and false reject, respectively. * Precision: \[P(i,j)=\frac{L_{i,j}}{\left|C_{j}\right|},\] (5) where \(L_{i_{j}}\) is the number of tasks from class \(i\) correctly identified in cluster \(j\), and \(\left|C_{j}\right|\) is the numbers of tasks (samples) in cluster \(j\). * F-measure: \[F(i,j)=\frac{2\times P(i,j)\times R(i,j)}{P(i,j)+R(i,j)}\] (6)
* Purity: \[Purity=\frac{1}{n}\sum_{i=1}^{k}\max(i,j)\] (7) where \(\max(i,j)\) stands for the maximum number of correct label assignment (i.e., correct classification) from class \(i\) in cluster \(j\). * Recall: \[R(i,j)=\frac{\hat{L}_{i,j}}{T_{i}}\] (8)  
Figure 4: An example of the proposed method. where \(T_{i}\) is the total number of tasks (samples) from class \(i\). Figure 5 shows comparison of results between the proposed method (FPAK-means) and standard K-means, Kmedoids, and Spectral clustering approaches. Table 3 presents the experiment results with 25 runs concerning standard K-means, Kmedoids, and Spectral cluster. It is clear to notify that, the proposed hybrid method  
Figure 5: Comparison results of the proposed method. (FPAK-means) achieves almost the best results overall measures for all dataset with 2, 3, and 5 classes. The best results obtained with 2 classes dataset where the FPAK-means achieves 96.03, 96.29, 96.06, 96.17, and 96.03 for accuracy, Precision, Recall, F-measure, and Purity, respectively. Same scenario with 3 classes dataset the FPAK-means achieves 71.02, 53.53, 75.37, 64.64, and 80.85 for accuracy, Precision, Recall, F-measure, and Purity, respectively. With 5 classes dataset the FPAK-means almost achieves the best results except with Recall and Purity measures the proposed method obtained second ranked after the Spectral cluster. With such these results the FPAK-means suitable for keratoconus detection and can be improved to get the best results. Another evaluation measure is the plotting final the clustering Figure 6 shows a scattering plotting for the used datasets. Table 4 shows the comparison with previous machine learning-based studies for KCN detection. It should be noted that most of the previous studies used supervised machine \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Measures** & **Data Size** & **FPA-K-Means** & **K-Means** & **Kmedoids** & **Spectral Cluster** \\ \hline Accuracy & & **96.03** & 53.71 & 59.40 & 50.00 \\ Precision & & **96.29** & 50.12 & 62.34 & 50.00 \\ Recall & 2 classes & **96.06** & 76.83 & 80.76 & 79.82 \\ F-Score & & **96.17** & 60.66 & 65.94 & 60.94 \\ Purity & & **96.03** & 53.71 & 80.87 & 79.81 \\ \hline Accuracy & & **71.02** & 54.99 & 55.61 & 43.69 \\ Precision & & 53.53 & 33.72 & 41.04 & 34.59 \\ Recall & 3 classes & 75.37 & 36.23 & 69.03 & 70.36 \\ F-Score & & **64.64** & 35.43 & 39.98 & 33.32 \\ Purity & & **80.85** & 36.17 & 72.52 & 71.23 \\ \hline Accuracy & & **75.20** & 65.23 & 73.97 & 47.61 \\ Precision & & **35.01** & 20.65 & 33.80 & 20.23 \\ Recall & 5 classes & 47.70 & 26.63 & 40.60 & **55.33** \\ F-Score & & **48.97** & 26.63 & 46.22 & 37.10 \\ Purity & & 53.64 & 26.22 & 45.61 & **55.12** \\ \hline \hline \end{tabular} Bold value indicates the best value.  
\end{table} 
Table 3: Experimental results. Figure 6: Scattering plotting. learning classifiers [18; 20], apart from [28], where unsupervised machine leaning was used. The unsupervised machine learning used in [28], included PCA, manifold learning and t-SNE applied on 420 parameters obtained from CASIA corneal machine. Unlike [28], our study flower pollination algorithm (FPA) and the k-means algorithm and applied it on 50 features of the corneal shape.