## 3 Cost Estimation Methodology by Multioutput Regression
### Scaling and Regularization  
A machine learning model learns through feature data and the output data to be predicted. In this case, if the deviation of the data used in the model increases, the data learning process is not constant, and thus the accuracy of the output value may decrease. The problem of increasing the deviation of the data may be improved by scaling of the \begin{table}
\begin{tabular}{c c} \hline \hline
**Influence Factor** & **Description** \\ \hline Total Area & The total area of each floor of the building. \\ Building Area & The area occupied by the building. \\ Total Height & The total height of the building. \\ Super Structure Floor & The number of floors on the ground. \\ Basement Floor & The number of basement floors. \\ Site Total Area & The entire land area. \\ Landscape Area & Landscape area. \\ Typical Floor Height & Height of the base floor. \\ Parking Lot & The number of cars parked. \\ Building Year & Construction year. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Factors influencing construction costs selected. learning data. Scaling is a method of making data used in machine learning models uniform, typically with methods such as minimum-max normalization and Z-score. In this study, there was a very large deviation in input/output data used to predict construction costs, and construction cost prediction is common. For example, the number of floors in a building has a value of about 10, but the output data has a value of up to 30,000,000 won. Deviations inside these data are also very large, so when machine learning is performed on these data, the learning process or results can be very unstable. To solve this problem, by performing the scaling preprocessing on input/output data, the data deviation can be reduced as much as possible and stable machine learning can be performed. Min-Max Normalization is a method of adjusting input data to a value between 0 and 1 according to the ratio based on the smallest and largest values of all data used in the model; the value x is scaled as in Equation (4). The input data modified by min-max normalization has a value between 0 and 1, thereby reducing the input deviation of the input data and improving the learning performance. \[x_{min-max}=\frac{x-x_{min}}{x_{max}-x_{min}} \tag{4}\]  
In Z-score normalization, the value \(x\) can be converted to a Z-score using Equation (5). It can be seen that some data converts to a standard normal distribution (Gaussian distribution). If the data x is equal to the average value, it is scaled to 0, but if it is less than the average value, it is negative, and if it is greater than the average, it is positive. At this time, the size of the negative and positive numbers calculated is determined by the standard deviation of the data. As the standard deviation of the input data increases, the scaled value approaches zero. Z-score and min-max normalization are the same in that they improve learning performance by reducing the deviation of input data, but there is a difference in the distribution of the converted values of input data, which can lead to a difference in learning performance. \[z_{z-score}=\frac{\mathrm{x-\mu}}{\sigma} \tag{5}\]  
where x represents the original data, \(\mu\) represents the mean value, and \(\sigma\) represents the standard deviation. When performing machine learning on a particular dataset, poor predictive performance for general data, which is only suitable for learning data, is called overfitting. Conversely, underfitting is a case in which even a given dataset is not properly learned. Although a model with good performance is important, a model that is overfitted may have poor versatility. Regularization is a technique that partially modifies the learning algorithm so that the model becomes more generalized. Even if scaling of input/output data is performed through preprocessing for predictive stability of construction costs, there might be a problem that predictive performance could be degraded due to deviation in the machine learning process.