# Towards a Predictive Analytics-Based Intelligent Malaria Outbreak Warning System+
## 3 Intelligent Malaria Outbreak Warning System
### Data Preprocessing  
It was a tradition, prior to the application of machine learning algorithms, that datasets need to be pre-processed to enable a faster and more accurate learning process. The heuristic approach involves the discretization techniques most often used in data mining. This involves transforming continuous-valued datasets to discrete datasets by creating a set of contiguous intervals [43]. In this paper, we are making use of a dataset on climate variables as the input while the output variable is malaria incidence data. Our concern is the development of a predictive model using supervised machine learning algorithms that will predict the likelihood of malaria incidence. The output variable appeared to have high-magnitude in-terms of reported number of malaria cases; hence using it directly may cause over-fitting to the predictive model. Therefore, it is pertinent to transform the dataset using some techniques for discretization to enable us to build efficient models. We have therefore discretized the output variable to form a target variable using the k-means clustering algorithm [44]. This methodology is chosen over equal width (EW) and equal frequency (EF) because it is less sensitive to outliers and also the number of clusters (partitions) can be optimized by analysis rather than pre-determination. In general, the choice of discretization method and choice of k can be guided by the objectives of the discretization task. By invoking R software, we can determine the optimum number of clusters to enable us to partition the output variable. From the analysis, the optimum number of clusters obtained is k = 4 and the algorithm converges after nine iterations with 89.9% variation. Also, we observed that for k = 5, the number of iterations exceeded the maximum number of tolerable iterations supposed to achieve convergence and in this case it diverges even though the percentage of variation is still good at 93%. For k = 2 and 3, the algorithm converges after three and four iterations with 66.4% and 82% variation, respectively. This gives sufficient evidence to choose the optimum number of clusters as k = 4. Similarly, we have also tried the \"NbClust\" package in R software for determining the optimal number of clusters. Using the values \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Measurement/Structural Model** & **Parameter** & **Estimate** & **Bias** & **Standard Error** & **Lower** & **Upper** \\ \hline Minimum \(\longleftarrow\) FactorI & \(\lambda_{1,1}\) & 0.9479 & \(-0.0057\) & 0.0467 & 0.8240 & 0.9890 \\ Relative humidity \(\longleftarrow\) FactorI & \(\lambda_{1,2}\) & 0.9910 & \(-0.0055\) & 0.0347 & 0.9823 & 1.0000 \\ Maximum temperature \(\longleftarrow\) FactorII & \(\lambda_{2,1}\) & 0.8816 & \(-0.0329\) & 0.1289 & 0.4769 & 0.9810 \\ Solar radiation \(\longleftarrow\) FactorII & \(\lambda_{2,2}\) & 0.8735 & \(-0.0343\) & 0.1748 & \(-0.0705\) & 0.9550 \\ Precipitation \(\longleftarrow\) FactorIII & \(\lambda_{3,1}\) & 0.9849 & \(-0.1748\) & 0.4044 & 0.7666 & 1.0000 \\ Wind speed \(\longleftarrow\) FactorIII & \(\lambda_{3,2}\) & 0.0017 & 0.1356 & 0.4059 & \(-0.6593\) & 0.7300 \\ FactorI \(\longrightarrow\) FactorII & \(\beta_{1,2}\) & \(-0.3248\) & \(-0.0333\) & 0.1692 & \(-0.4974\) & 0.4260 \\ FactorII \(\longrightarrow\) FactorIII & \(\beta_{2,3}\) & \(-0.2774\) & \(-0.0264\) & 0.2191 & \(-0.4963\) & 0.3810 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Bootstrapping test of the outer loadings and path coefficients in the PLS-PM with a 95% confidence interval. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Factor** & **Reflective Variables** & **Communality** & **Dillon–Goldstein’s \(\rho\)** \\ \hline I & 2 & 0.94 \({}^{c}\) (94\%) & 0.97 \({}^{c}\) (97\%) \\ II & 2 & 0.77 (77\%) & 0.87 (87\%) \\ III & 2 & 0.49 (49\%) & 0.49 (49\%) \\ \hline \hline \end{tabular} \({}^{c}\) the most significant hidden factor.  
\end{table} 
Table 5: Indices for selecting the ecological hidden factor of high malaria incidence in the study area.