## 5 Modeling Details
### Advanced Preprocessing and Hybrid DI Approach
One of these patterns is shown in Figure 5. As can be seen, most residential and commercial buildings' cluster number vary between 5 and 25, which is an acceptable cluster size considering individual consumption level [35]. Moreover, different percentages of anomalous days for all customers in the dataset are shown in Figure 6. This range also varied between 8-12% in general, and the white regions are not considered at this stage because these customers' data sets consist of very small consumption values. Another hypothesis can be obtained from clustering results represented in a chronological manner. A commercial building's clustering calendar is shown in Figure 7. The days shown in gray and red on the calendar correspond to the situations where consumption values cannot be obtained and anomalous days that are represented as black stars in Figure 4b, respectively. The anomalous days on the calendar are a good example of [PERSON] definition of outlier _\"generated by a different mechanism\"_ in [36]. Although these days cannot be included in any cluster, when examined carefully, it can be concluded that some of these days coincided with the religious holidays celebrated in Turkey. Other situations indicate three  
Figure 5: The relation between epsilon values versus number of clusters in dataset. Figure 6: Percentage of different categories in dataset. clusters with different colors in Figure 4b. It can be seen from Figure 7 that transition from one consumption behavior to another has generally an ordered structure. Although cluster changes are not observed in transition months (such as spring to summer or from autumn to winter) for this commercial building due to schedule or workload, an increase in the number of clusters is observed in almost half of the households in transition months (e.g., April to May or September to October). The normalization process helps to limit the input values of all features within the 0 to 1 interval in order to avoid excessive feature values during the learning process as follows:  
\[x_{i}^{\prime}=\frac{x_{i}-x_{min}}{x_{max}-x_{min}} \tag{14}\]  
where \(x_{i}\) is the original value of the input dataset, \(x_{i}^{\prime}\) is the normalized value scaled to the range \([0,1]\), and \(x_{max}\) and \(x_{min}\) indicate the maximum value and minimum value of the features in \(\mathbf{x}\), respectively. Normalizing the dataset features eliminates the large deviation of instances, maps the data vector \(\mathbf{x}\) to a small range vector \(\mathbf{x}^{\prime}\), and helps the learning algorithm to perform accurately. The supervised learning form supports the learning in the training process by providing example pairs of the input to output prediction as follows:  
\[\mathbf{y}^{\prime}=H_{SL}(\mathbf{x}^{\prime}) \tag{15}\]  
where \(\mathbf{y}^{\prime}\) is the normalized predicted energy load profile of the time series and \(H_{SL}\) is the function of the supervised learning and the normalized output vector is defined as follows:  
Figure 4:0  
where \(y_{i_{n}}^{\prime}\) is the mapped predicted load profile at a time \(i_{n}\) and \(i_{n}\in\{m+1,m+2,...,m+n\}\) and \(n\) is the number of future time prediction elements in the set \(\mathbf{y}^{\prime}\). To evaluate the performance of the proposed prediction model properly, the testing set examines the trained and validated model independently. Therefore, we split the normalized supervised dataset into three sub-datasets (the training set 70%, validation set 20%, and the testing set 10%) in order to maintain the fairness of performance evaluation. The learning in the prediction model segment is unlike the learning of traditional CNN or BLSTM models hybridized to improve the learning process. The first half of the prediction segment is the 1-D CNN, which is utilized to extract the input features and to  
Figure 4:1 Clustering calendar of a commercial building in 2018 (customer ID: y3).