## 3 Research Methodology
### Artificial Neural Network: Multilayer Perceptron (MPL)  
In this analysis, the input systems are covariances which are trained to produce an output. The QS and CPM are the primary custodians of post-contract cost controlling techniques decision making and therefore the output of the analysis. ANN will be used to predict the most effective post-contract cost controlling technique through a pseudo-probability classification of the construction professionals in this study. The first step of this methodology extracted factors from literature sources for Likert scale data collection. The next step is level 1 ANN which adopted the standardised rescaling of the factors for the purposes of pseudo-probability. This was done to ensure that the final output is not just between the scale of 1 to 5. The standardised rescaling used the formula:  
\[(x-mean)/s \tag{1}\]  
where x represents each value, which are subtracted from the mean of all the samples under each factor; and s is the standard deviation. The partitioning of the data set for input was divided into training and testing. 50% of the variables were trained, and 50% were tested. The training samples served as an independent set of samples used to test the model for errors [70]. The profit and loss technique was selected as a partitioning variation in the first level because they are influenced by the remaining variables. Hence, the overall number of levels 1 training will be 17 samples instead of 18. The hyperbolic tangent was selected as the activation function, which links the total units in one layer to another [71]. This function has the formula:  
\[\gamma(c)=tanh(c)=(ec-e-c)/(ec+e-c) \tag{2}\]  
\(\gamma(c)\) represents the hyperbolic tangent, and \((ec-e-c)/(ec+e-c)\) connotes the direction of the synaptics. The hyperbolic tangent collates the real-valued arguments and converts them to the range of \(-1\) and 1. When automatic architecture selection is used, this is the activation function for all units in the hidden layers. The hyperbolic tangent is used for the output, hidden and input layers. In stage 3 of the research framework as indicated in Figure 1, a second iteration of level 1 normalised the standardised variables using all the post-contract cost controlling factors. The multilayer perceptron output for level one was used as the new partitioning instead of profit and loss factor. Figure 1: Research framework for ANN prediction of post-contract cost controlling techniques in building construction (Source: Authors’ compilation, 2020). Normalisation formula involves subtracting the minimum value and then dividing it by the range, (x\(-\)min)/(max\(-\)min). Normalized values fall between 0 and 1. The learning rate for the training is given as 0.4; momentum 0.9; and offset interval is + or \(-\)0.5. The outputs of levels 1 and 2 were the pseudo-probability, classification, and normalised importance of the variables. These were all transferred to the final stage for validation using the holdout sample. A set of holdout samples of 25% was used to validate the existing multi-trained network. In the validation stage, 50% of samples went into training and 25% was tested. The holdout samples provided an honest estimate of the predictability of the model. Therefore, identifying errors which were inconsistent in building the model. The results accruing from levels 1, 2 and the validation stage have been presented in the form of tables and graphs for clarity in the subsequent sections. Synaptic weights represent the strength of the connections between neurons [52; 70; 71; 72]. [PERSON] et al. [73] simplified synaptic weights as:  
\[y_{j}=\sum\
olimits_{i}w_{ij}\ x_{i}\ or\ y=wx \tag{3}\]  
where \(x\) is the input variable, \(y\) is the output, and the synaptic matrix represents the vector of synaptic weights for the output indexed by \(y_{j}\). The post-contract cost control variables are the neurons in this study, and the links between them are the neurons. The general rule of thumb associated neurons that fire together as wiring together.