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We observed that by applying ensemble method of type majority voting on the algorithms Decision tree, Random Forest, Naive Bayes, and K means, we could achieve an accuracy of 91.56%. To additionally improve the precision, we proposed the following algorithm. The design of the proposed method is as given in Figure 1.12.

Figure 1.12 Proposed architecture.

Algorithm 1.1 Probabilistic optimization.

 initialization

 d ← dataset

 a1 ← Naive_Bayes_output ← ApplyNaiveBayes(d)

 a2 ← Decision_tree_output ← ApplyDesisionTree(d)

 a3 ← Random_tree_output ← ApplyRandomForest(d)

 a4 ← K_Means_output ← ApplyKmeans(d)

 winner(0, 1) ← Voting(a1, a2, a3, a4)

 op ← winner_of_max_count(0,1)

 if op ≠ desired_output then

 Probability_calculation of each column with output 0 or 1

end

For each value in c_i

count ← c_i/2

For k to count

 Add the probability (Find the max column with which probability matches)

 Number of columns selected as ti

 wi ← Weightage of selected columns

 αi ← Append the weightage with the input of data

Find mean square error with the training and find lowest (MSE) parameter. Calculate the Euclidean distance

Find the minimum distance using this formula.

If probability of data > 0.5 and MSE < 0.5 and ED < 0.2

Classify as 1

else

Classify as 0

The following block diagram explains the flow of Algorithm 1.1.

The working of the algorithm is explained briefly as follows.

1 1. The ensemble method of the four algorithms (Decision Tree, Random Forest, Naive Bayes, and K Means) is applied by majority voting and classification is obtained on presence or absence of cardiopathy.

2 2. The wrongly classified records are stored in a separate dataset.

3 3. The probability of each column with output is calculated and stored. For example, considering age, the probability of heart disease for age greater than 45 is more than otherwise.

4 4. We calculate those columns for which probability is maximum.

5 5. Only select these columns for further analysis.

6 6. Calculate the weights of these columns using formula y = mx + c for linear data using Multiple linear regression.

7 7. For non-linear data wherein the chances of misclassification are more, more complex functions such as tanh, sigmoid, and relu are used for calculating the weights.

8 8. Append the weights to the column at the time of classification.

9 9. Calculate the mean square error and Euclidean distance.

10 10. Finally, based on probability, mean square error and Euclidean distance, we classify the records as 1 or 0 which indicates presence/absence of heart disease.

11 11. Hence, accuracy achieved is higher than using the classical ensemble method.

Hence, our proposed methodology achieves a precision that not only surpasses the individual methods but also overshoots the combination method and the precision achieved thus is quite competitive.