# Graph Convolutional Spectral Clustering for Electricity Market Data Clustering
## 3 Experiment
### Deep Mining of End-User Electricity Consumption Information Big Data  
For residential users, the time interval for collecting load power is 20 min, resulting in 72 data points within a day's load curve. Figure 6 shows the load curve for a user on a given day. It can be seen from the figure that the user's load curve has many features and high dimension, which affects the accuracy and efficiency of clustering and extracting typical load curves for end users. To address this issue, the information entropy-based classification aggregation approximation algorithm mentioned earlier was utilized to reduce the dimensionality of load curves and achieve feature extraction. Combining with the user power curve shown in Figure 6, the process of entropy-based segmented aggregation approximation is described. Initially, the maximum time resolution of the user time-series is 20 min, and the time-series has a period of 24 h. Based on the span of the user dataset sequence, the data dimension is determined to be 72 nodes. The initial number of segments is set to \(k=12\), with each segment containing 6 data points, and each segment's time-series span is \(T=120\) min. Subsequently, for each segmented time-series, values are calculated, and a judgment of \(\rho<\sigma\) is made. If this condition holds true, it indicates that the fluctuation level of the data sequence in that segment meets the requirements. The formula for segmented aggregation approximation is then applied to reduce the dimensionality and re-express the data in that segment. If it does not hold true, for segmented time-series where \(\rho<\sigma\), if the length of the time-series can still be evenly divided by 2, a 2-segment division is performed, and the judgment is reevaluated. Otherwise, the time-series is output directly, and the result of the re-expression of each segmented time-series is saved. Figure 7a shows the symbolic representation of the user curve using the typical segmented aggregation approximation algorithm [35], while Figure 7b presents the symbolic representation of the user curve using the proposed segmented aggregation approximation based on information entropy. By comparing the results in Figure 7a and Figure 7b, it can be observed that the proposed segmented aggregation approximation based on information entropy not only extracts features accurately but also preserves the original shape of the user load curve in detail. The algorithm uses different time resolutions for segmented aggregation approximation in regions with significant fluctuation trends, retaining central features and better re-expression the load curve. Following the feature extraction of load curves using the information entropy-based segmented symbolic aggregation approximation method, an algorithm combining GCN and spectral clustering was employed for the unsupervised classification of end-user load curves. This process extracts typical daily load curves, and the clustering results are shown in Figure 8a-e.  
Figure 6: The load curve for a user on a given day. From Figure 8, it can be observed that the spectral clustering algorithm successfully achieves the unsupervised classification of users. In Figure 8a, the power curve for cluster one reaches its lowest point from 8:00 to 18:00 and peaks during 0:00-8:00 and 18:00-24:00, reflecting the nighttime electricity consumption characteristics of clustered users. This indicates that high-energy-consuming users adjust their production activities in response to time-of-use electricity prices. In Figure 8b, cluster two's power curve peaks from 8:00 to 18:00, while maintaining low consumption at other times, revealing the daytime production-oriented characteristics of users, primarily businesses, technology companies, and material processing factories operating during the day. Figure 8c,d show that users in clusters three and four exhibit a bimodal pattern.