## 3 Results
### Reduced Dimension Clustering to Identify Demand Patterns
The analysis aims to find a set of new variables in order to extract the most important information from the data set and analyze the structure of the observations and variables. The results can be seen in Table 5. The analysis gives the following variables as most important factors for clustering households; number of household occupants, building size, building type and terrain type. We evaluate the appropriate cluster solution, by examining the absolute differences between the original and random sum of squared errors (SSE) against the chosen cluster solutions. The appropriate cluster solution is given by the solution where the actual SSE differs the most from the mean of the random SSE. This process is shown in Figure 4, giving evidence for selecting 5 as the appropriate number of clusters. We thus proceed with the five strongest variables, of which the first two components explain more than 80% of the point variability of the entire data set. The visualization of the k-means clustering is given in Figure 5 against the two strongest principal components, segmenting the data set into clearly distinguishable clusters. The k-means clustering analysis resulted in a cluster sum-of-squares of 84.31. The two strongest principal components explain 78.17% of the point variability within our sample. Each of the five identified clusters of this study should be seen as an archetype that categorizes the households across our sample, with the respective individual within-cluster variance given within brackets: \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & **PC1** & **PC2** & **PC3** & **PC4** & **PC5** & **PC6** & **PC7** & **PC8** & **PC9** \\ \hline Standard deviation & 1.74 & 1.22 & 1.10 & 1.00 & 0.96 & 0.84 & 0.63 & 0.51 & 0.00 \\ Proportion of & 0.33 & 0.17 & 0.13 & 0.11 & 0.10 & 0.08 & 0.04 & 0.03 & 0.00 \\ Variance & & & & & & & & & \\ Cumulative & 0.33 & 0.50 & 0.64 & 0.75 & 0.85 & 0.93 & 0.97 & 1.00 & 1.00 \\ Proportion & 0.29 & \(-0.19\) & \(-0.43\) & \(-0.17\) & \(-0.47\) & \(-0.53\) & 0.27 & \(-0.04\) & 0.29 \\ Building Size & \(-0.56\) & 0.15 & 0.05 & 0.09 & \(-0.07\) & 0.01 & \(-0.12\) & \(-0.06\) & 0.79 \\ Building Type & 0.28 & \(-0.53\) & 0.11 & 0.25 & 0.43 & 0.23 & 0.39 & \(-0.21\) & 0.38 \\ Solar Panels & \(-0.03\) & \(-0.24\) & 0.37 & \(-0.80\) & 0.25 & \(-0.24\) & \(-0.18\) & \(-0.09\) & 0.10 \\ Terrain Type & 0.45 & \(-0.04\) & \(-0.04\) & 0.29 & 0.16 & \(-0.22\) & \(-0.77\) & \(-0.04\) & 0.20 \\ Persons & 0.42 & 0.39 & 0.04 & \(-0.22\) & 0.15 & 0.19 & \(-0.22\) & \(-0.68\) & 0.24 \\ Solar Heating & \(-0.04\) & \(-0.05\) & \(-0.73\) & \(-0.35\) & 0.17 & 0.49 & \(-0.21\) & \(-0.14\) & 0.05 \\ Ventilation Type & 0.27 & 0.15 & 0.09 & \(-0.06\) & 0.08 & \(-0.01\) & 0.12 & \(-0.67\) & 0.14 \\ Roof Insulation & 0.25 & \(-0.16\) & 0.33 & \(-0.11\) & \(-0.67\) & 0.54 & \(-0.18\) & \(-0.10\) & 0.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Principal component analysis of all available household variables. * 'Cluster 1' (18.09) represents 17% of the participating households. The group of households consists of large groups of people, that are only residing in urban or suburban areas. The majority of this group resides in semi-detached and row-houses. The group represents higher-end urban workers with families. * 'Cluster 2' (15.75) represents the largest group of households with 36%. This group represents households living in urban areas, in row or semi-detached houses. The group represents lower-end urban workers. * 'Cluster 3' (14.07) represents 21% of the participating households. The cluster primarily contains three-person households, which live mostly in detached houses, in the city or rural areas. We identify young starters to be present in this group. * 'Cluster 4' (4.59) is characterized by a small group composition of 2 persons on average. They are represented in all classes of building type and terrain, but with a relatively large size of building. We find this group to consist of mainly seniors.