## 4 Empirical Research
### FEI Clusters  
Referring to the criteria for the identification of industrial clusters of SMEs in China [13] and existing literature [79; 80; 81], the range of the distance for the applicants is set between 25 km and 250 km, with 25 km being one unit of measurement, and the range for the number of patent application enterprises is set between 10 and 100, with 5 as a measurement unit; the range of technological distance is set between 20 and 1200, with 20 as a measurement unit. Through the partial DBI results, the index floor of the joint DBI is set to 10. By employing the python program to develop the MDBSCAN algorithm and incorporating a matplotlib plug-in to display the algorithm results, the calculation results are shown in Figure 5. In this figure, the darker color of the ball signifies a lower DBI value, indicating a superior clustering effect, whereas a lighter color corresponds to a higher DBI value. Through the joint analysis of the three input indicators, it can be found that some of the indicators within the value range are significantly better than those in other regions. For the number of patent application enterprises, when the number of applicants within \(x_{min}=(5,10)\), the DBI index will be significantly lower than the indexes in other intervals. In terms of spatial distance, the DBI indicator is significantly lower than that in the other zones when the spatial distance is equal to 25, 200, and 225 values. For example, when the number of applicants is less than 20 and the spatial distance is equal to 25 and 225, an interesting observation emerges: as the technological distance tends to approach 1200, the DBI decreases. Conversely, in other indicators, there seems to be no significant disparity in the technological distance; in fact, larger distances correspond to larger indicators. This example underscores the notable influence of the technological distance, spatial distance, and number of participating enterprises on the cluster evaluation effect yielded by the MDBSCAN algorithm. If only the number of participating enterprises and spatial distance are employed as constraints, it becomes apparent that the approach does not align with the actual situation. The selection of clusters considered the number of clusters in the evaluation of DBI. To further obtain the optimal parameters in this case, considering the range of the obtained DBI values (0.397533376, 1.222981034) and the number of distributions, combinations lower than 0.45 are selected as secondary screening objects, and a total of 13 groups are obtained, as shown in Table 2. In this table, the ranks of 1, 2, and 3 variable combinations have low DBI values, but the numbers of clusters are all small, making the granularity of cluster division too large, resulting in too many participating enterprises within the cluster, which is not conducive to the implementation of cluster policy. \(sd_{min}=25\), \(td_{min}=350\), and \(x_{min}=10\) are selected as cluster identification indicators, and a total of 44 clusters are obtained. Figure 4: Perplexity calculation results. The application of the MDBSCAN algorithm under specific constraints of a minimum technological distance, spatial distance, and number of nodes results in the identification of a total of 44 clusters. These clusters are then assigned numerical labels based on their cluster sizes, as illustrated in Figure 6. The dominant clusters in China's flexible electronics industry are primarily concentrated in three key regions: the Yangtze River Delta (c1), the Pearl River Delta (c2), and Beijing (c3). These clusters not only have the characteristics of many participating enterprises but also tend to span multiple administrative regions. For example, the flexible electronics industry cluster in Shenzhen extends to the adjacent Guangzhou and Dongguan, and the industry cluster in Shanghai extends to its adjacent Suzhou.