## 2 Materials and Methods
### Geospatial Data Preparation
#### 2.2.7 Proportion of Buildings over 40 Years Old  
The aging of building structures introduces potential safety concerns, including aged wiring and material deterioration, which may escalate the likelihood of a fire. The proportion of buildings over 40 years old is defined as Equation (7). \[F_{7}=\frac{N_{bo}}{A}, \tag{7}\]  
where \(F_{7}\) denotes the proportion of buildings over 40 years old, and \(N_{bo}\) denotes the number of buildings aged 40 years and above in each village. Figure 2g illustrates the proportion of buildings aged 40 years and above. 2.2.8. Proportion of Non-Reinforced Concrete (RC) Buildings  
Non-RC buildings refers to structures constructed with unreinforced concrete, lacking the addition of steel bars or mesh. In construction, reinforcement is commonly integrated into concrete structures to augment their strength and longevity. It signifies that the mentioned buildings do not possess this supplementary reinforcement and have been in existence for four decades. In this study, non-RC buildings are considered one of the factors influencing fire, with its formula expressed as Equation (8). \[F_{8}=\frac{N_{brc}}{A}, \tag{8}\]  
where \(F_{8}\) denotes the proportion of buildings, and \(N_{brc}\) denotes the number of non-RC buildings in each village. Figure 2h presents the ratio of non-RC buildings in Keelung City. 2.2.9. Proportion of First, Secondary, and Tertiary Sectors of the Economy  
According to the Department of Economic Affairs, Keelung City Government [48], industries in Keelung City are classified into three levels: primary industry, secondary industry, and tertiary industry. The primary industry includes forestry, agriculture, animal husbandry, and fishing. The secondary industry comprises industrial activities, while the tertiary industry encompasses service-related sectors such as food and beverage, accommodation, and more. The proportion of the first, secondary, and tertiary sectors of the economy is evaluated by Equation (9). \[F_{9}=\frac{N_{fe}}{A},\ F_{10}=\frac{N_{se}}{A},\ \text{and}\ F_{11}=\frac{N_{ te}}{A} \tag{9}\]  
where \(F_{9}\), \(F_{10}\), and \(F_{11}\) denote the proportion of first, secondary and tertiary sectors of the economy, and \(N_{fe}\), \(N_{se}\), and \(N_{te}\) denote the number of first, secondary, and tertiary sectors of the economy in each village. Figure 2i-k illustrates the proportion of first, secondary, and tertiary sectors of the economy. 3. Dimensionality Reduction Techniques  
Dimensionality reduction methods in machine learning are employed to decrease the number of features or variables in a dataset while retaining essential information. The objective is to simplify the dataset by removing redundant or irrelevant information, thereby addressing the dimensionality reduction [22; 34]. In this study, we implemented dimensionality reduction to enhance data interpretability. While these techniques serve diverse purposes in machine learning, PCA, FA, and OOB predictor importance are interconnected with dimensionality reduction for feature extraction [41; 42], as utilized in this study. Additionally, OOB predictor importance was employed to identify influential predictors among the eleven variables and was compared to results obtained from PCA and FA. 3.1. Principal Component Analysis  
The primary goal of PCA is to transform the original variables into a new set of uncorrelated variables or principal components that capture the maximum variance in the data. In PCA, it assumes that all the variance in the variables is due to the underlying structure captured by the principal components [19; 20]. These components are linear combinations of the original variables. The principal components are linear combinations of the original variables, and each component is a weighted sum of all variables [21; 22]. These components capture the maximum variance in the data, allowing for the reduction of dimensions while preserving most of the information.