## 2 Literature Review
### Cross-Classification and Spatial Dependence  
To better understand the intensity and interactivity of technologies, scholars proposed the cross-classification method to combine the results of concentration and colocation [16; 17]. Four quadrants are proposed to indicate the relative position of different technologies according to their concentration and colocation degrees: the assumption is that the higher the concentration degree, the more likely knowledge flows within the technology, and vice versa; the higher the colocation degree, the more likely knowledge flows across other technologies, and vice versa. The method responds to the argument of spatial proximity for local buzz and knowledge exchange [43; 44] across space: spatially dispersed technologies characterized by low colocation with other fields are extensive in nature, suggesting open and loose knowledge ties within and across technologies; spatially dispersed technologies characterized by high colocation with other fields are supportive in nature, implying weak internal knowledge flows but strong interaction with related fields; spatially concentered technologies characterized by low colocation with other fields are distinctive in nature, suggesting strong internal knowledge flows but dispersed knowledge ties with other fields; spatially concentrated technologies characterized by high colocation with other fields are intensive in nature, implying strong internal flows of knowledge and robust ties with associated technologies.  
Applying the method, researchers unveil that in U.S., the majority of technologies can be classified to extensive and distinctive types, with limited ones belonging to the supportive. In addition, as time went by, technologies once intensive are likely to become extensive as newly emerged technologies are often more intensive. This can be illustrated by computer technology which evolved relatively extensively after nanotechnology came into being [16; 17]. Though the method enables rapid classification of extensive, distinctive, supportive, and intensive technologies, it is too simplistic to identify the nuanced variations of knowledge exchange within and across technological fields. Understanding such variations is not insignificant because the ways knowledge has been shared are crucial for potential breakthroughs and radical innovation often occurs in knowledge-intensive industries [45; 46]. In this regard, this study improves the cross-classification method by visualizing the relative position of technologies and accurately maps them in the four-quadrant diagram. The quantities of each technology are further associated to reveal the actual innovative outputs in each field. The purpose is not for the identification of specialization, but to understand how technologies spatially agglomerate and coordinate with one and the other in reality.  
Spatial autocorrelation empowers the identification of where classified technologies locate and to what extent they are interdependent, thus reveals the inventive cities where knowledge flows are spatially dependent and reinforce innovative outputs [10; 47]. As noted in numerous studies, the exchange of tacit knowledge which inspires original innovations requires face-to-face communications, thus is distance-sensitive [43; 48]. Global and local Moran's I [49; 50] are valid coefficients in this regard and will be used in this research to reveal the overall spatial dependence of categorized technologies (Global Moran's I) as well as the association between technologies at a particular location and those at the neighboring areas (Local Moran's I). Disentangling patents' locational features and their spatial dependance helps the adjustment of a spatial plan, and necessitates inquiries of the question below:  
RQ2. Given its concentration and colocation features, how does technology vary from one to the other under the four-quadrant cross-classification system, and how do the cross-classified technologies spatially depend?