# A Data-Driven Model for the Energy and Economic Assessment of Building Renovations
## 3 Results
### Clustering Analysis for Building Digital Representative Building  
The clustering analysis phase plays a pivotal role in this methodology, enabling the classification of high-energy-consuming buildings into distinct, data-driven digital representative buildings that support tailored retrofit interventions. Various clustering techniques have been explored in the literature, generally categorized into four main types: partitional, hierarchical, density-based, and grid-based methods [31]. Among these, k-means  
Figure 3: Feature importance derived from the Random Forest model. clustering (a partitional approach) and agglomerative hierarchical clustering (AHC) are the most widely adopted for building energy analysis. [PERSON] et al. [32] conducted a comprehensive comparison of clustering algorithms, testing different normalization techniques and validation indices to identify representative residential multifamily buildings. Their results showed that k-means consistently outperformed other methods, including AHC, particularly for applications involving energy use segmentation [33], thermal zoning, and load pattern classification in office buildings [34]. Furthermore, k-means has proven effective in identifying homogeneous subgroups based on energy consumption characteristics, reinforcing its utility for clustering tasks in the built environment [35]. In this study, clustering was employed as an unsupervised technique to segment the building dataset into groups with similar energy performance and physical characteristics. The k-means algorithm was used, a computationally efficient and scalable method well-suited to high-dimensional numerical data. Despite its simplicity, k-means may be less effective for detecting arbitrarily shaped clusters, as it relies on Euclidean distance to define cluster boundaries [36]. The input features for clustering included normalized values of energy consumption per square meter, wall and glass U-values, glazing percentage, building volume, and occupancy density--selected for their demonstrated relevance to energy use. The optimal number of clusters (k = 3) was determined using the elbow method, which identified a clear inflection point in the within-cluster sum of squares curve, and validated through silhouette analysis, which yielded a score of 0.64--indicating well-differentiated and cohesive clusters. This outcome is also consistent with the findings of [PERSON] et al. [37], who reported that k = 3 offered the best cluster quality for electricity usage profiles in residential buildings. To visualize the cluster structure and further assess validity, principal component analysis (PCA) was applied to project the high-dimensional feature space onto two principal components. The resulting segmentation--Critical, High, and Moderate-High clusters--captures distinct patterns in building energy behavior, supporting strategic retrofit prioritization. As shown in Figure 4, this data-driven segmentation reveals that nearly 75% of buildings fall into the Critical and High categories, emphasizing the value of clustering for guiding resource allocation and targeted intervention in the energy transition process. The identification of these distinct high-consumption digital representative buildings directly supports the research objective of developing a data-driven model for cost-benefit assessment of retrofit interventions. Each consumption level cluster exhibits a unique combination of influential factors--with Critical-level buildings showing the highest wall and glass U-values (0.87 and 0.76 normalized) and earliest construction years (0.25 normalized), while Moderate-High buildings demonstrate better envelope performance but still require substantial improvements. These differentiated profiles enable the prioritization of retrofit measures based on cluster-specific characteristics rather than applying generic solutions across the entire building stock.