## 3 Materials and Methods
### Feature Selection  
Improving the performance of machine learning algorithms necessitates the selection of relevant, trustworthy, and reliable features. The process of selecting an optimal subset of attributes from which to build a machine learning model is known as feature selection. Correlation-based Feature Selection (CFS) is a primary filter method that uses a correlation-based heuristic evaluation function to rank feature subsets. The evaluation function is biased in favor of subsets with attributes that are substantially correlated with the target class but uncorrelated with one another. A higher score is given to subsets with a strong association with the target class label but a poor correlation with other features. Irrelevant attributes should be eliminated because they have no or minimum correlation with the target class. As redundant features are heavily correlated to one or more of the remaining features, they should be eliminated. The CFS feature subset evaluation function is given by  
\[M_{S}=\frac{K\overline{r}_{cf}}{\sqrt{K+K(K-1)\overline{r}_{ff}}} \tag{1}\]  
where \(M_{S}\) is the heuristic'merit' of a feature subset \(S\) containing \(K\) features, \(\overline{r}_{cf}\) is the average of class-attribute correlations \((f\in S)\), and \(\overline{r}_{ff}\) is the average of attribute-attribute intercorrelations. The numerator of Equation (1) reflects how well a group of features predicts the class and the denominator represents how much redundancy exists among the features. CFS has a modest level of time complexity. The pairwise feature correlation matrix is computed using \(m\big{(}\big{(}n^{2}-n\big{)}/2\big{)}\) operations, where \(n\) is the starting number of \begin{table}
\begin{tabular}{l l} \hline \hline
**No.** & **Principal Components** \\ \hline
1. & \(-0.317\)slope = \(1-0.317\)thal = \(3-0.302\)thalach + \(0.297\)oldpeak + \(0.292\)cp = \(4\ldots\) \\ \hline
2. & \(-0.54\)restecg = \(0+0.526\)restecg = \(2-0.28\)thal = \(7+0.278\)thal = \(3-0.24\)sex = \(1\ldots\) \\ \hline
3. & \(0.476\)ca = \(0-0.422\)ca = \(1-0.364\)slope = \(1+0.338\)slope = \(3+0.295\)oldpeak \(\ldots\) \\ \hline
4. & \(0.37\)sex = \(1-0.347\)slope = \(2+0.247\)thal = \(7-0.27\)thal = \(3+0.267\)thalach \(\ldots\) \\ \hline
5. & \(-0.395\)fbs = \(1-0.386\)cp = \(3+0.345\)cp = \(4-0.289\)restbps \(-0.278\)age... \\ \hline
6. & \(-0.438\)ca = \(2+0.368\)ca = \(1+0.352\)cp = \(3+0.323\)sex = \(1-0.253\)cp = \(4\ldots\) \\ \hline
7. & \(0.523\)thal = \(6+0.364\)cp = \(1-0.333\)thal = \(7-0.315\)cp = \(3-0.279\)chol... \\ \hline
8. & \(-0.488\)slope = \(3+0.414\)slope = \(2-0.273\)restecg = \(1-0.271\)ca = \(1-0.242\)cp = \(4\ldots\) \\ \hline
9. & \(0.593\)ca = \(3+0.423\)cp = \(2-0.337\)ca = \(2+0.303\)thal = \(6-0.295\)cp = \(1\ldots\) \\ \hline
10. & \(0.381\)cp = \(2+0.367\)ca = \(1-0.33\)ca = \(2-0.285\)thal = \(6+0.272\)cp = \(1\ldots\) \\ \hline
11. & \(-0.376\)slope = \(3+0.355\)restbps \(-0.344\)cp = \(2+0.324\)thal = \(6-0.308\)oldpeak... \\ \hline
12. & \(-0.494\)cp = \(1-0.423\)ca = \(3+0.382\)fbs = \(1+0.313\)cp = \(2-0.233\)restecg = \(1\ldots\) \\ \hline
13. & \(0.642\)restecg = \(1+0.36\)ca = \(2-0.221\)fbs = \(1+0.214\)thalach \(-0.209\)exang = \(1\ldots\) \\ \hline
14. & \(-0.625\)fbs = \(1+0.429\)thal = \(6-0.382\)restecg = \(1+0.309\)chol \(-0.217\)exang = \(1\ldots\) \\ \hline
15. & \(-0.577\)chol + \(0.425\)age \(-0.305\)thalach + \(0.268\)restbps \(-0.234\)cp = \(1\ldots\) \\ \hline
16. & \(-0.607\)restbps + \(0.396\)age \(-0.383\)thalach + \(0.294\)chol + \(0.211\)ca = \(0\ldots\) \\ \hline
17. & \(0.592\)exang = \(1+0.448\)sex = \(1-0.286\)cp = \(4+0.225\)cp = \(3-0.209\)fbs = \(1\ldots\) \\ \hline
18. & \(0.616\)sex = \(1-0.439\)exang = \(1+0.256\)cp = \(4+0.237\)thal = \(3-0.209\)cp = \(1\ldots\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Principal components of the combined dataset. features and \(m\) is the number of observations. Equation (1) is the basis of CFS that provides rank on attribute subsets in the search area of all feasible attribute subsets [50; 51].