# Graph Convolutional Spectral Clustering for Electricity Market Data Clustering
## 1 Introduction
[PERSON] et al. [14] proposed a curve smoothing and dimensionality reduction method for power user time-series based on information entropy segment aggregation and slope event processing. Traditional Euclidean distance in spectral clustering algorithms was replaced with dual-scale similarity measurement, enabling the unsupervised clustering of power users. This contributes to the formulation of strategies for power companies in response to user electricity behavior in the electricity market. [PERSON] et al. [15] addressed the complexity and decentralization of electricity consumption data resulting from the widespread use of smart meters. They introduced an adaptive K-means distributed clustering algorithm, locally clustering smart meter data for physically proximate power users, obtaining typical local user curves. Weighted values were assigned to each local user curve, and traditional clustering methods were employed for global secondary clustering, revealing typical user electricity behaviors. [PERSON] et al. [16] tackled the issue of load data category imbalance and large dataset sizes in power systems. They utilized a feedback-corrected back propagation neural network on the Spark parallel computing platform for global clustering. Local clustering of load data was accomplished using the K-medoids clustering method for each training sample. To address imbalances in local samples, oversampling methods were applied, achieving data classification. The aforementioned studies illustrate an increasingly profound global understanding of the value of power big data. Research on supporting the production, operation, decision making, forecasting, management, and services of power and grid enterprises has shown initial success. However, research on the value creation process, models, and mechanisms remains relatively nascent. Furthermore, researchers have identified that graph structures possess the capability to capture intrinsic relationships within data [17; 18], often exhibiting stronger expressive power than the original data. Consequently, graph learning emerges as a fundamental method of representing data within a graph structure, widely applied in hierarchical clustering and spectral clustering algorithms. [PERSON] et al. [19] pioneered the use of a sparse weakly connected graph to generate initial clusters. They measured the similarity between clusters using the product of the average in-degree and the average out-degree in the k-nearest neighbor graph, followed by agglomeration in hierarchical clustering. This approach effectively addresses density imbalance issues in high-dimensional spaces. [PERSON] et al. [20] introduced a novel graph structure hierarchical clustering method, utilizing path integral as the structural descriptor of clustering and incremental path integral as the similarity measure between clusters. [PERSON] et al. [21] proposed an enhanced graph-learning-based hierarchical clustering algorithm named Chameleon2. They modified the internal clustering quality measure, added an extra step to ensure algorithm robustness, and introduced an automatic cutoff selection method for producing high-quality clusters autonomously. The graph partitioning method based on adjacency matrix eigenvectors was initially proposed by [PERSON] and [PERSON] [22]. [PERSON] [23] later suggested using the second eigenvector of the Laplacian matrix for graph partitioning, demonstrating its close relationship to binary partitioning. [PERSON] and [PERSON] [24] subsequently identified the correlation between clustering, graph partitioning, and eigenvectors of similarity matrices, introducing a proportional cut model. Despite the successful applications of spectral clustering in various domains, there remain many challenges requiring further in-depth research, particularly in the clustering of high-dimensional complex feature data, which remains a current focal point in research.