## 3 Research Framework and Methodology
### Accurate Identification of Industrial Clusters Based on MDBSCAN
To calculate the technological distance between different applicants who are involved in multiple technologies simultaneously, a combination of the Euclidean distance method and the bipartite network algorithm can be employed. The technological distance is computed as follows:  
\[td_{ij}=\sqrt{\sum_{t=1}^{T}\left(e_{it}-e_{it}\right)^{2}} \tag{4}\]  
where \(td_{ij}\) represents the technological distance between the applicant nodes \(e_{i}\) and \(e_{j}\), and \(t\) represents the presence or absence of technology in the same field identified by the LDA method, with applicants having two or more patents in technology \(t\) recorded as 1 and those with none recorded as 0. The process of identifying industrial clusters involves clustering and evaluating clusters, and it directly impacts relevant industrial policies and the economic interests of those clusters. To minimize artificial intervention, this paper utilizes an unsupervised identification method based on machine learning. The DBSCAN algorithm, a classical density-based clustering algorithm, is employed. Unlike the KM algorithm, DBSCAN has the advantage of automatically determining the number of clusters and identifying clusters with arbitrary shapes. This characteristic makes it well suited for clustering nodes located at various positions within a spatial network [65]. In addition to massive data, DBSCAN can find outliers while clustering and is insensitive to outliers in the dataset. However, the traditional DBSCAN only considers the maximum distance \(sd_{min}\) between nodes within a cluster and the minimum number of nodes \(x_{min}\) as clustering constraints, i.e., it requires the need to satisfy (\((td\leq dt_{min})\cap(x\leq x_{min})\)) among cluster members, without considering the complementarity or dissimilarity between technologies within a cluster. Consequently, this limitation fails to meet the requirements of actual industrial clusters. To address this issue, we propose an enhancement to the existing DBSCAN algorithm, with the name MDBSCAN by adding the minimum technology distance variate \(td_{min}\). This enhancement ensures that during the clustering process, cluster members must satisfy the condition (\((td\leq td_{min})\cap(x\leq x_{min})\cap(sd\leq sd_{min})\)). In this regard, the MDBSCAN algorithm is employed in this study to facilitate the fusion of multiple variables. By doing so, it enables the identification of clusters with both a high spatial density and significant technological complementarity. The flow algorithm of the whole algorithm and its pseudo-code can be found in Appendix A. It is worth stating that various studies have employed KM, HC, and SC methods to combine multiple variables during the clustering process. However, the underlying principle primarily involves computing the Euclidean distances of multiple variables concurrently during the initial clustering stage; these distances are then consolidated into a unified distance value using weights. Subsequently, different elements are clustered based on a distance threshold [66; 67; 68]. Since different weights can have a significant impact on the final clustering effect, the determination of the weights often relies on manual assignment, making such algorithms susceptible to subjective experiences. In contrast, MDBSCAN uses technological distance and spatial distance to filter and classify elements separately, thereby avoiding these issues. Industrial clusters are formed by utilizing big data and require the evaluation of their effectiveness with different combinations of input variables. The evaluation methods for clusters can be mainly classified into internal and external evaluation techniques [69]. Internal evaluation involves calculating metrics that measure the intra-cluster and inter-cluster elements, supplying an assessment of clustering effectiveness without the use of real labels. This method is applicable for evaluating clusters without real labels.