## 3 Study Area and Research Method
### Research Method
#### 3.2.2 Data Analysis  
(1) Spatial concentration and colocation analysis  
Determining the degree of spatial concentration and dispersion of patents, this research employs the Lorenz curve and calculates the Gini coefficient of the 35 fields. The Gini index is traditionally used to measure wealth inequality. [PERSON] [64] as well as [PERSON] and [PERSON] [65] were the earliest to propose the application of a Ginicoefficient to the comparison of the spatial variation of industries. Later on, the coefficient is widely used in innovation space studies [10; 33]. It is denoted by  
\[\text{Gini}=\frac{\sum_{i}\sum_{j}\abs{x_{i}-x_{j}}}{2n\sum_{i}x_{i}}\]  
where \(n\) represents the number of cities. Gini ranges from 0 to 1, with 0 indicating a complete dispersion of patent activities and 1 denoting complete concentration. The higher the value, the more concentrated the innovative activities, and vice versa. To identify how technological fields are potentially correlated with one another, principal component analysis (PCA) is conducted to group subcategories of patents with analogous geographical distribution and convenient exchange of knowledge across technologies. The PCA approach is powerful for the dimensionality reduction of data and sorting subclassified patents into a composite \"technology group\". The loading values suggest the extent of how technologies associate with one another: the greater the value, the more prominent the colocation effects of the classified patents. Figure 3: Number and ratio of three types of (valid) patents. Cross-classification and spatial autocorrelation  
Spatial concentration analysis and component analysis are combined to identify the relative characteristics of technologies. Each field is located into a four-quadrant diagram (Figure 4), based on its relative values of Gini coefficient and principal component loading to the average values of those in all fields. The horizontal axis represents the principal component loading value, the lower value (L) the left, the higher value (H) the right; the vertical axis represents the values of Gini coefficient, the lower value (L) the bottom, the higher value (H) the top. Those falling into the lower-left grid with lower values in both Gini and PCA are extensive technologies characterized by vast knowledge flows across multiple technology fields; the rest are as claimed in the figure. For more, please refer to Section 2.2. Spatial autocorrelation allows the measurement of to what extent these technologies spatially depend and empowers the visualization of such dependence. Global Moran's I assesses the overall spatial dependency, with I = 0 indicating an equally spatial pattern, I > 0 indicating a clustered pattern of similar values, and I < 0 indicating proximity of dissimilar values. Local Moran's I differentiates five types of technological spatial clusters: high-high indicates levels of similar tech outputs of place and its neighbours are all high; low-low indicates levels of similar tech outputs of place and its neighbours are all low; high-low indicates a place where tech outputs are high neighbouring places where similar tech outputs are low; low-high indicates a place where tech outputs are low neighbouring places where similar tech outputs are high; a not significant area indicates a place that does not significantly differ nor resemble its neighbours. Relation with cities  
Regression is applied to analyse the relational factors of technological innovation outputs. Subcategories of patents from 2010 to 2018 are aggregated, as dependent variables. The nine indicators include residential population, GDP, GDP per capita, public budget expenditure, building construction area, green park area per capital, road mileage, actual utilized FDI, and number of students in universities, and are collated as independent variables (Table 1). Figure 4: Cross-classification of technological innovation by extant of concentration and colocation.