## 2 Literature Review
### Identification Algorithms  
The process of identifying industrial clusters involves collecting data and clustering them according to geographical or technological factors. Such data are typically characterized by a large volume, multiple dimensions, and a low density, requiring accurate and reliable algorithms to effectively classify it. According to the indicators considered, the current commonly used clustering algorithms mainly include Local Moran's I (LMI) [42], K-Means (KM) [43], Spectral Cluster (SC) [44], Hierarchical Cluster (HC) [45] and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) [46]. The LMI algorithm is utilized to determine the existence of industrial clusters by examining the performance of indicators in a specific target area and its geographical adjacent areas. This algorithm assesses whether these indicators surpass the overall average value and subsequently verifies the forecasted results with a \(p\)-value and \(Z\)-score. LMI comprises two subgroups: bivariate [47] and multivariable local Moran index [48]. These two subgroups calculate the performance of two or more indicators within a region. By using this method, it is possible to geographically analyze the agglomeration of high or low indicators simultaneously. However, fundamentally, this approach involves separately calculating the values of the elements within the cluster and gathering individuals who meet all the conditions at the same time. Hence, this method cuts off the relationship between different elements and fails to comprehensively analyze the overall indicator performance of the cluster from a macro perspective [49]. Other methods that share similar limitations include the location entropy method [50] and principal component analysis method [51], both of which will not be included in this research. The KM algorithm is an iterative and unsupervised clustering analysis algorithm and begins by randomly selecting k cluster centers and calculating the distance between the sample data nodes and each cluster center. A threshold value for cluster classification is then applied, and the algorithm proceeds to calculate the average value of each cluster datum to obtain a new cluster center. The process is repeated through several iterations to guide the cluster towards convergence and complete the clustering analysis. The KM algorithm has strong readability and quick iteration. However, there are several concerns regarding its application in industrial clusters identification. First, the number of clusters and threshold must be predetermined, which is challenging, as it is difficult to accurately determine the required number of groups in advance. Second, the KM algorithm primarily focuses on the spatial distance for clustering nodes in the research of industrial clusters and often neglects the clustering of industrial aspects. Lastly, the KM algorithm can only be used for cluster samples with regular shapes. In industrial clusters, clustering may encompass multiple regions and irregular shapes. Thus, the KM algorithm is unable to meet all requirements. The SC algorithm is a node clustering method based on graphic information. It needs to preset the number of clusters to be divided, construct the adjacency matrix of different nodes, use the distance algorithm to calculate the connection strength of different nodes, and cut the graph to form multiple subgraphs. The cutting standard is that the distance between nodes in the subgraph is the smallest and the distance between nodes in the subgraph is the largest. Although the SC algorithm can process and obtain clusters of different shapes, it can be learned from the clustering principle that the SC algorithm and the KM algorithm both need to be presented with the number of clusters in advance and set the minimum number of clusters, which obviously cannot meet the requirements of the actual spatial cluster clustering [52]. The HC algorithm is divided into top-down and bottom-up according to the clustering method.