Figure 4: Diagrammatic illustration of the proposed

![0_image_0.png](0_image_0.png)

ensemble based approach for missing data For a classification task, the weight is assigned using the weighted majority scheme given by [16] as: 

$$\alpha_{i}={\frac{1-E_{i}}{\sum_{j=1}^{N}(1-E_{i})}}$$
α **(7)** 
$$(7)$$

where Ei is the estimate of model i**'s error on the** 
validation set. This kind of weight assignment has its roots in what is called boosting and is based on the fact that a set of networks that produces varying results can be combined to produce better results than each individual network in the ensemble [16]. The training algorithm is presented in *Algorithm 1* and the parameter *ntwk*i represents the ith **neural network in the ensemble.** 
The testing procedure is different for classification and regression. In classification, testing begins by selecting an elite classifier. This is chosen to be the classifier with the best classification rate on the validation set. To this *elite* classifier, two more classifiers are gradually added, ensuring that an odd number is maintained. Weighted majority voting is used at each instance until the performance does not improve or until all classifiers are utilised. In a case of regression, all networks are used all at once and their predictions, together with their weights are used to compute the final value. The final predicted value is computed as follows: 
regression value of an instance j**. As a result** ∑=≠
N**usable**
We try to solve this by recalculating the weights such that 

![0_image_1.png](0_image_1.png)

the sum of all weights corresponding to N*usable* **is 1.** 

## 6. **Experimental Results And Discussion**

$$({\boldsymbol{\delta}})$$

This section presents the results obtained in the experiments conducted using the two techniques presented above. Firstly, the results of the proposed technique in a classification problem will be presented and later the method will be tested in a regression problem. In both cases, the results are compared to those obtained after imputing the missing values using the neural network-genetic algorithm combination as discussed above. 

$$f(x)=y\equiv\sum_{i=1}^{N}\alpha_{i}f_{i}(x)$$

N
( ) α ( ) **(8)** 
where α **is the weight assigned during the validation** stage when no data were missing and N **is the total** number of regressors. The parameter α **is assigned such** 
that∑==
N
i i 1 α 1. **Considering that not all networks shall** 
be available during testing, we define N*usable* **as the** 
number of regressors that are usable in obtaining the 