## 3 Research Framework and Methodology
### Accurate Identification of Industrial Clusters Based on MDBSCAN  
Patents involve the latest and most active technical information in almost all related technical fields. Effectively analyzing and utilizing the complex correlations between patents can not only provide direction for future research but also help organizations such as enterprises and institutions to identify the best partners. At present, academics generally believe that the relationship between patents is mainly divided into four kinds: competing, blocking, complementary, and unrelated [60]. Among them, the first two relationships mainly reflect the similarity between patents when conducting patent relevance analysis. The research on patent technology complementarity appears relatively weak, and few studies at home and abroad have synthesized the theory, method, and application related to patent technology complementarity. In fact, major technological innovation generally relies on the introduction of complementary technologies, and through technological cooperation between enterprises or organizations with complementary patents, they can absorb each other's advantageous technologies to make up for their own technological deficiencies while maintaining their own core technological strengths so as to improve the success rate of innovation, reduce the costs and risks of technological innovation, and obtain a more desirable investment value. In order to determine the complementarity between applicants within a cluster, we propose the following definition of technical distance: when two patents belong to two different subfields in the same technical field, it means that they belong to the same field in terms of technical content and can realize complementary advantages through their differences. Scholars have emphasized that spatial concentration is a key feature of industrial clusters [61; 62]. In essence, clusters reflect proximity, i.e., the spatial concentration of firms from a micro-geographic perspective. In order to identify the clusters, it is necessary to consider both spatial and technological distances based on the calculation needs of the applicant. An algorithm compatible with both distances needs to be introduced due to the variations in how different distances are represented. One such similarity calculation method is the Euclidean distance, which calculates similarity by cumulatively calculating the difference between different variables of the nodes [63]. Compared with similarity calculation methods such as cosine similarity and Jaccard similarity, the Euclidean distance is well suited for numerical similarity calculation. It imposes no constraints on the value range, with larger values indicating greater distances. Moreover, it provides an absolute distance measure that effectively captures the differences between different variables of the nodes, making it suitable for both spatial and technological distance calculations. If there exists a set of variables \(x\) = {\(x_{1}\), \(x_{2}\),..., \(x_{n}\)} and \(y\) = {\(y_{1}\), \(y_{2}\),..., \(y_{n}\)}, the Euclidean distance of the two variables is computed as follows:  
\[d_{ij}=\sqrt{\sum_{n=1}^{N}\left(x_{in}-x_{jn}\right)^{2}} \tag{2}\]  
The calculation of the distance between various applicants can establish a geographical foundation for subsequent cluster identification. Currently, the methods of calculating spatial distance are divided into linear distance and spherical distance [64]. \[sd_{ij}=d_{s}\times\sqrt{\left(ln_{i}-ln_{j}\right)^{2}+\left(la_{i}-la_{j} \right)^{2}} \tag{3}\]  
where \(d_{s}\) refers to the plane distance of the unit longitude and latitude and is determined uniformly based on the node's location. The spatial distance increases as the difference between the longitude and latitude of different nodes becomes greater, as indicated by Formula (3). This relationship aligns with real-world geographical scenarios.