## 5 Evaluation and Findings
### Experimental Findings
#### 5.2.2 Analysis of the Correlation Heat Map (CHM)  
This section presents the CHM, illustrating the relationships between different variables within the cardiovascular data for both the Cleveland and Statlog datasets. Figures 8 and 9 display these CHMs, where each column signifies a specific variable, and each row visualizes its correlations with other variables. The numerical values within the tables convey the strength and direction of these correlations, which can span from \(-1\), indicating a perfect inverse correlation, to 1, representing a perfect positive correlation. This visual representation offers valuable insights into the interplay among the dataset variables and their potential impacts on heart disease prediction. In Figure 8, the CHM of the Cleveland dataset illustrates the comparisons among various variables. These variables include age, gender, blood pressure (trestbps), cholesterol level (chol), fasting blood sugar (fbs), electrocardiogram results (restecg), maximum heart rate achieved (thalach), exercise-induced angina (exang), ST depression induced by exercise relative to rest (oldpeak), the number of major vessels colored by fluoroscopy (ca), type of chest pain (cp), and slope of the peak exercise ST segment (slope). Additionally, the presence of two types of thalassemia, indicated as thal and thal2, are considered. The values within the matrix fall within the \(-1\) to \(1\) range, where positive values signify a positive correlation, negative values indicate a negative correlation, and a value of \(0\) denotes no discernible correlation between the variables. Analysis of the CHM for the Cleveland dataset reveals the following insights:  
* The first section of the matrix compares age, sex, and blood pressure. The correlation between age and blood pressure is weakly positive (\(0.28\)), while the correlation between sex and blood pressure is weakly negative (\(-0.098\));
* The second section compares cholesterol and blood sugar. Cholesterol and blood sugar have a weakly negative correlation (\(-0.057\));
* The third section compares restecg, thalach, exang, and oldpeak. The resting electrocardiogram results (restecg) and exercise-induced angina (exang) have a weakly positive correlation (\(0.14\)), while the maximum heart rate achieved during exercise (thalach) has a weakly negative correlation (\(-0.044\)) with ST depression induced by exercise relative to rest (oldpeak);* The fourth section compares the number of major vessels colored by fluoroscopy (ca) with the other variables. There is a weakly positive correlation between ca and age (0.12), and a weakly positive correlation between ca and cholesterol (0.097);
* The fifth section compares the different types of chest pain (cp) and their correlations with the other variables. Chest pain type 0 (cp_0) has a weakly positive correlation with ca (0.14), while chest pain type 1 (cp_1) has a weakly negative correlation with thal2 (\(-\)0.15). Chest pain type 2 (cp_2) has a weakly positive correlation with fbs (0.084), and chest pain type 3 (cp_3) has a weakly positive correlation with age (0.048);
* The final section of the matrix compares the slope of the peak exercise ST segment (slope) and the two types of thalassemia (thal and thal2). There is a weakly positive correlation between slope and thal2 (0.18), and a weakly negative correlation between slope and thal (\(-\)0.42). Also, according to the results of the CHM analysis for the Statlog dataset in Figure 9, it can be understood that:  
* The values in the matrix represent the correlations between each pair of variables. A positive value indicates a positive correlation (as one variable increases, so does the other), while a negative value indicates a negative correlation (as one variable increases, the other decreases);
* For example, we can see that age is highly negatively correlated with itself (correlation coefficient of \(-\)1.00), since it is impossible for someone's age to be negatively correlated with their own age.