## 4 Performance Evaluation
### Classification Prediction Accuracy  
For the purpose of obtaining classification prediction accuracies, we used six ML algorithms to present the performance of best classification algorithm for our dataset. It is worth mentioning that we used MATLAB (R2020b, MathWorks, United Kingdom) libraries for all six ML classifiers. The KNN classifier from Equations (1) and (2) with several values of \(K\) as the distance metric of nearest neighbours that is discussed in Section 2 where \(K=1\) belongs to the distance metric called _Mahalanobis_ outperforms compared to other metrics, as shown in the Figure 4. This proves the simplicity of the algorithm in classifying new data points based on similarity measures. Similar to \(K=1\), when \(K=2,3,4,\dots\), the output value stays closer to the \(K=1\) result, meaning the test points from the training dataset. The classifier has memorised the last movement to the correct label and the classifier achieves minimal error rate response. Section 2.2 provides a brief explanation of _Mahalanobis_ distance metric. However, for a detailed analysis, _Mahalanobis_ distance metric is based on correlations between a set of variables of a multivariate analysis, i.e., daily bus passengers in peak and off-peak times in our case. It is based on correlations between different class passengers where different patterns can be identified and analysed. Unlike the Euclidean distance, which is the commonly used straight line distance between two points, _Mahalanobis_ distance is suitable for determining multivariate similarity of a set of independent variables in dispersed directions, i.e., multidimensional position of each case of the sample class. In Figure 4, the number of uncorrelated neighbours are shown on the x-axis, the distance metrics are shown on the y-axis and the estimated values of objective function are shown on the z-axis. The total functional evaluations performed for all the distance metrics are 30 along with the total elapsed time 63.65 s and total objective function evaluation time as 5.24 s. After application of all the distance metrics, _Mahalanobis_ distance provided best classification accuracy based on our dataset of two uncorrelated classes, peak and off-peak time travels. The objective function value is the real-valued function whose value is to be either minimised or maximised over the set of feasible alternatives dependant on the best performing distance in the outliers. For optimisation purposes where the value of the objective function is to be maximised, the optimal value is the least upper bound of the objective function values over the entire feasible region. Conversely, when minimising the objective function values, the optimal value is the greatest lower bound of the objective function values over the entire feasible region. For the best observed feasible points, observed objective function value is 0 which is based on the estimated objective function value 1.024 \(\times\) 10\({}^{-6}\) and the function evaluation time is 0.89 s.  
Figure 4: KNN Functional Model with the observed optimal values and next point classification. The second classifier was DA with the linear function being used. The third classifier was SVM with default RBF kernel parameters settings but the kernel size used was 200. The fourth classifier was DT with maximum splits set to 50. The fifth classifier was NB with its normal function used. The sixth classifier was ANN with neurons set to multiple values to train weights and layers in each \(k\) intervals while the rest of the values were set to default. In total, 840 observations were used for peak and off-peak time travel for the performance metric mobility prediction accuracies using the six ML classifiers, as shown in Table 2. It can be seen that the ANN algorithm failed to provide good accuracy of classification and is listed at the bottom of the table with only 73.09%.