# Smart Grid Theft Detection Based on Hybrid Multi-Time Scale Neural Network
## 2 Analysis of the Characteristics of Customers
### Correlation Analysis of Customer's Characteristics  
To analyze the robust correlation of electricity load more effectively amongst legitimate customers versus the feeble correlation amongst electricity theft customers, the study conducted a correlation analysis on electricity consumption data using the Pearson's correlation coefficient (PCC). Figure 4 presents the correlation coefficient matrix heat map of the electricity consumption load data for a normal customer over 12 months in 2015, while Figure 5 displays the correlation coefficient matrix heat map of the electricity consumption load data for an electricity theft customer over the same period. Upon examination of the figures, it was evident that the majority of the PCC values for the normal customer exceeded 0.7, indicating a strong month-to-month correlation in their electricity consumption data.  
Figure 3: Daily electricity consumption curves of normal and electricity theft customers in August. (**a**) Normal customer; (**b**) Electricity theft customer.  
Figure 2: Monthly electricity consumption curves of normal and electricity theft customers. (**a**) Normal customer; (**b**) Electricity theft customer.  
Conversely, the PCC values for the electricity theft user were predominantly less than 0.3 or even negative, signifying very little correlation amongst their electricity consumption data.  
Similarly, a correlation analysis was performed on electricity consumption data from both a regular customer and one engaged in electricity theft over a four-week period in August, utilizing the Pearson's correlation coefficient (PCC). As depicted in Figure 6, the correlation coefficient matrix heat map for the electricity consumption load data of a regular customer over four weeks was examined, while Figure 7 displays the correlation coefficient  
Figure 4: Heat map of correlation coefficient matrix of monthly load data for a normal customer.  
Figure 5: Heat map of correlation coefficient matrix of monthly load data for an electricity theft customer.  
matrix heat map for the electricity consumption load data of an electricity theft customer over the same period. These maps revealed that there were distinct differences in the electricity consumption patterns between the two groups. The results showed that most of the PCC values of a normal customer were greater than 0.8, indicating that their electricity consumption data were highly correlated between different weeks. In contrast, most of the PCC values of an electricity theft customer were less than 0.3, indicating that their electricity consumption data had very low correlation with each other.  
In summary, the statistical and correlation analyses conducted on the electricity consumption data of regular and electricity theft customers indicated that the consumption data of an electricity theft customer generally exhibited lower correlation than that of a regular customer. This observation was consistent with the findings of a previously published study [26], and similar trends were observed in other electricity consumption datasets from  
Figure 6: Heat map of correlation coefficient matrix of weekly load data for a normal customer.  
Figure 7: Heat map of correlation coefficient matrix of weekly load data for an electricity theft customer.  
different regions and countries. Consequently, such data provided a more dependable foundation for the development of electricity theft detection models. Further examination of the data could reveal significant insight into electricity consumption patterns and inform the construction of more effective detection models.