Research on the Collaborative Innovation Relationship of Artificial Intelligence Technology in Yangtze River Delta of China: A Complex Network Perspective

Abstract

Artificial intelligence (AI), as a rapidly developing interdisciplinary field, is a key driver of future economic development. The Yangtze River Delta (YRD) is one of the most significant economic regions of China, which also has a leading role in the AI industry. In this study, based on the patent cooperation data of YRD in the past decade, we focus on studying the collaborative innovation relationship in the AI field of the YRD from the perspective of complex networks. In order to investigate the interprovincial, intra-city and inter-city collaborative innovation relationships, we construct the Yangtze River Delta AI collaborative innovation (YRD-AICI) network. Subsequently, to analyze the development status and collaborative innovation relationship of innovation bodies in the AI field of YRD, we construct the Yangtze River Delta AI patent cooperation (YRD-AIPC) network. Next, the basic characteristics and spatio-temporal evolution of these two networks are explored, and the research results are presented that: (1) Shanghai, Jiangsu Province, and Zhejiang Province have obvious leading advantages in the AI field of the YRD, and the development gap between cities is significant; (2) the pioneering innovation bodies in the AI industry of the YRD are identified using centrality measures, and their cooperative innovation relationship is revealed; (3) based on link prediction methods, future partnerships between cities and innovation bodies are predicted to provide the future development trend of the YRD. The results provide theoretical support for exploring the cooperation mechanism of collaborative innovation in the AI field of YRD and inspire future development planning.

1. Introduction

With the acceleration of the global digitalization process, artificial intelligence (AI) has gradually become a frontier and strategic technology to lead the future development of the world [1]. AI is an important driving force in the new round of technological revolution and industrial transformation [2]. Here, AI refers to technology that simulates and possesses human-like cognitive functions on various machine carriers, and the related computing technologies include natural language processing, cloud computing, big data, and deep learning, such as intelligent robots, virtual personal assistants, autonomous driving, and voice recognition [3,4,5,6,7]. In the late 1990s, with the improvement of computer technology, AI technology also achieved rapid development. The potential benefit of AI is the automation of cognitive tasks, including classification and perception, and its application has penetrated many fields, such as mathematics, physics, medicine, and financial trade [8,9,10,11,12].

With the rapid development of the AI industry, the global regional industrial competition pattern is changing. China, as one of the important economies in the world, has attracted the attention of the world. In recent years, China has been committed to promoting the development of the AI industry and has important AI industry clusters [13]. In addition, the Yangtze River Delta, Beijing-Tianjin-Hebei, Pearl River Delta, and Sichuan-Chongqing are four major economic circles in China, whose progress drives the development of China [14]. The Yangtze River Delta (YRD), as the active economic center of China, has a leading position in the AI field, while the regional integration of the YRD has been elevated to a national strategy. Meanwhile, as a knowledge-intensive industry, AI requires more collaborative innovation development in different regions of the country [15]. Therefore, it is necessary to improve the collaborative innovation capabilities in the YRD, which will contribute to the development of the AI industry and some related industries in China and other regions in the world.

AI patent innovation is a critical technical indicator to measure the development of AI in a country and region, which is also a key force to promote the research and development (R&D) of AI technology [16]. The number of granted patents is rapidly increasing in the context of accelerated global development of AI technology, which can be obtained through quantitative analysis of patent applications. In addition, patents are a demonstration of regional collaborative innovation, and collaborative patent applications can effectively represent the collaborative innovation process between companies, universities and individuals. During the patent application, patent documents are expressed in the form of the applicant’s co-signature, so they can reflect the trend of spatial aggregation and the evolutionary characteristics of innovation output, and we can analyze their complex collaborative relationships through the established patent collaboration networks.

With the continuous development of science and technology, scientific research presents the characteristics of synthesis and complexity. Thus, cooperative research among disciplines, regions and units is a ubiquitous social phenomenon in modern science, and it is encouraged all over the world. It is obvious that cooperative research significantly improves the quality of the results and accelerates research progress to great extent. For citation cooperation networks or patent cooperation networks, predicting future collaborations or potential parters is a hot research issue in the field of citation cooperation networks and patent cooperation networks, which can help promote new collaborations and resource sharing [17].

In conclusion, based on the patent cooperation data from 2012 to 2021, this paper aims to explore the collaborative innovation relationship in the AI field of China’s YRD from the perspective of complex networks. Specifically, this study intends to analyze the current development status and evolutionary trend of AI collaborative innovation in China’s YRD. For this purpose, we first construct the Yangtze River Delta AI collaborative innovation (YRD-AICI) network with urban agglomerations as nodes and investigate the interprovincial, intra-city and inter-city collaborative innovation relationships. Subsequently, we construct the Yangtze River Delta AI patent cooperation (YRD-AIPC) network with innovative bodies as nodes. For the YRD-AIPC network, the topological properties and spatio-temporal evolution are investigated for the two developing stages. Moreover, the core cities and pioneering innovative bodies of AI industry in China’s YRD are identified by some classic centrality measures, and the future partnership between cities and innovation bodies is predicted to guide the future development direction of the YRD.

The framework of this paper is as follows. Section 2 reviews the related research work. Section 3 introduces the research methods. Section 4 presents the data sources. Section 5 and Section 6 focus on the analysis of patent collaboration networks and potential collaborator prediction. Finally, some conclusions and suggestions are given in Section 7.

2. Literature Review

Patent data are an open and available data source. In the past decades, a great number of studies have utilized patent data to evaluate technology transfer [18] and university-industry collaboration achievements [19,20]. Several scholars have confirmed from different perspectives that patents are vital factors for national innovation performance and industrial technology development. Furthermore, patent analysis is an important indicator or tool to measure innovation in many industries [21]. The evaluation of collaborative patents helps researchers understand the collaborative relationships of partners and the innovation patterns of cooperation. At present, a large number of studies have applied the methods of patent network analysis to practical problems and provided support for theoretical research on technology development trends [22,23,24,25]. Patent cooperation networks are an important form of collaborative innovation, and several scholars have focused on related studies from different perspectives, including collaboration patterns, collaboration scales, and collaboration characteristics [26,27,28,29]. To fill the gaps in the current research on AI collaborative innovation networks and patent cooperation networks, this paper evaluates patent data on cooperation among innovation bodies such as universities, enterprises, and research institutions to measure the development trends of AI technologies in the YRD of China.

Collaboration refers to the joint completion of tasks between partners to achieve common goals, and evaluating and selecting suitable partners is critical for successful cooperation. In the existing research, a series of approaches have been proposed for studying on partner selection in cooperation networks, which can be mainly classified into two families: location-based collaboration and competency-based collaboration. In the early years, limited by undeveloped communication technology and expensive transportation costs, the geographical locations of cooperators is crucial for the selection of partners [30]. Evolution analysis of cooperation networks is very beneficial for the prediction of potential partners. Maggioni and his coworkers [31] constructed an original framework to interpret the innovative activity among European regions, which investigated the factors that determine patenting activity, including geographical distance, topological structure and relational spillovers. Burhop and Wolf [32] concluded that the geographic distance between cooperators is an important factor for patent assignments. Capaldo et al. [33] argued that collaboration with remote partners will weaken the relationship between one another and suggested selecting partners at close range if the cooperative organizations worked in different cities. Geerts et al. [34] confirmed that technology exploration and exploitation activities display a various level of technological performance in different geographical regions. Gattringer et al. [35] supposed that geographical proximity promotes the occurrence of cooperation and the exchange of tacit knowledge, and the verification results show that trust and commitment are of little relevance in cooperation. In addition, based on the patent database from the national institute of intellectual property, Mejdalani et al. [36] constructed a network of inter-regional co-patenting from 2000 to 2011 in Brazil, and indicated that geographical distance plays an important role in network construction.

In recent years, a growing number of studies have focused on the complementarity of cooperator capabilities. Shah and Swaminathan [37] introduced a framework to address the problem of partner selection with specific characteristics, which concluded that partners should have complementary rather than overlapped resources. Furthermore, considering that knowledge complementarity plays a significant role in the partner selection process, Baum et al. [38] developed a dynamic model of alliance formation to evaluate the probability of two organizations being cooperative partners. Savin and Egbetokun [39] presented an innovation network with endogenous absorptive capacity for analyzing the cooperation relationship between firms in different locations. In order to achieve collaborative innovation, Lü and Qi [40] designed a novel partner selection method in a supply chain system. According to three existing cases, Wei et al. [41] proposed a two-stage partner selection framework in the innovation ecosystem that guided manufacturing firm strategies. Jee and Sohn [42] constructed a patent-based framework to select suitable partners for technology-based entrepreneurial firms, which comprehensively considered their complementary capabilities, potential for learning, and risk of knowledge spillovers.

3. Research Methodology

To analyze the collaborative innovation relationship in the AI field of the YRD, we explore the topological characteristics and evolution trend of the YRD-AICI and YRD-AIPC networks from the perspective of complex networks. In this section, some classical methods of complex networks are introduced, including centrality measures and link prediction methods. On the one hand, centrality measures are widely used to assess the importance of nodes and find influential nodes in complex networks. The identification of influential nodes is one of the most hot and important research issues in network science, which is very beneficial in addressing numerous problems such as improving the robustness of networks [43], preventing epidemic outbreaks [44] as well as accelerating the spread of information [45]. In this study, we will employ four classical centrality measures to find the leading innovation bodies in the AI field of China’s YRD during the past decade. On the other hand, the link prediction methods can predict the nodes that may generate edges in the future, which lays a theoretical foundation for the identification of potential cooperation opportunities between urban agglomerations and innovative bodies in the AI field of the YRD and the revealing of the formation mechanism of cooperation relationships.

3.1. Centrality Measures

Degree of centrality (DC) [46] is a simple and classical indicator that can measure the importance of nodes directly. In an undirect and unweighted network, the degree of a node is expressed as the sum of the number of its direct neighbors, which reads

$$DC\left(i\right)=\sum _{j=1}^N{a}_{ij}$$

(1)

where $a_{ij}$ represents the element of the adjacency matrix. If node i and node j are adjacent, $a_{ij}=1$; otherwise $a_{ij}=0$.

In an undirect and weighted network, the weighted degree of centrality (WDC) of a node is expressed as the sum of the edge weights between the node and its direct neighbors, which is defined as

$$WDC\left(i\right)=\sum _{j=1}^N{w}_{ij}$$

(2)

where $w_{ij}$ represents the weight of edge $e_{ij}$.

Betweenness centrality (BC) [47] is a classical path-based index for measuring the importance of nodes in a network. The main idea is that the more numbers a node exists on in the shortest path of all pairs of nodes, the more important the role of the node is in the process of information propagation. The betweenness centrality of node i can be computed as follows.

$$BC\left(i\right)=\sum _{i\ne u\ne v}\frac{s_{uv}^i}{s_{uv}}$$

(3)

where nodes u and v are any two nodes in the network other than node i, $s_{uv}$ is the number of shortest paths between node u and node v, and $s_{uv}^i$ represents the number of these paths that pass through node i.

Similarly closeness centrality (CC) [47] takes into account the average shortest distance between a node and all other nodes in a network to measure the importance of the nodes in a network. More concretely, the smaller the average distance between a node and all other nodes in the network, the faster the node can spread information to others, i.e., the more important the node is. The closeness centrality of node i can be calculated as follows.

$$CC\left(i\right)=\sum _{j=1}^N\frac{1}{d_{ij}}$$

(4)

where $d_{ij}$ indicates the shortest distance between nodes i and j. $d_{ij}=\infty$ if there is no reachable path between these two nodes.

3.2. Link Prediction

Link prediction is one of the fundamental problems that aims at predicting whether two disconnected nodes in a network are likely to have a link. It is important for understanding the topological characteristics and network evolution. In social networks, link prediction can help marketers find potential brand spokesmen and future partners [48]. In biological networks, link prediction is commonly employed to identify protein-protein interactions [49]. In cooperative networks, link prediction can predict potential partners and provide references for future decision-making [50]. This study will discover hidden information and investigate the evolution of the constructed networks by using link prediction algorithms. Thus far, numerous techniques have been established for link prediction [51,52]. With the increasing size of complex networks, a number of local-based methods have been widely employed due to their low time complexity, which are listed in

Table 1. Some classic link prediction methods.

Methods	Equations
Common Neighbors (CN) index [53]	$|{\mathsf{\Gamma }}_x\cap {\mathsf{\Gamma }}_y|$
Jaccard index [54]	$|{\mathsf{\Gamma }}_x\cap {\mathsf{\Gamma }}_y|/|{\mathsf{\Gamma }}_x\cup {\mathsf{\Gamma }}_y|$
Hub Promoted (HP) index [55]	$|{\mathsf{\Gamma }}_x\cap {\mathsf{\Gamma }}_y|/min(k_x,k_y)$
Preferential Attachment (PA) index [56]	$k_x\times k_y$
Adamic/Adar (AA) index [57]	$\sum _{z\in {\mathsf{\Gamma }}_x\cap {\mathsf{\Gamma }}_y}1/log{k}_z$
Resource-Allocation (RA) index [58]	$\sum _{z\in {\mathsf{\Gamma }}_x\cap {\mathsf{\Gamma }}_y}1/k_z$
Local Path (LP) index [59]	$A^2+\alpha A^3$

.

Note that these classical link prediction methods only consider partial information between node pairs, which has some limitations. Based on this, this paper applies our proposed novel link prediction algorithm SCL-WTNS [60] to predict the possible links in the network, which combines the local structure between nodes and the links between community structure information. It is defined as follows.

$$SCL-WTNS\left(i\right)=\left\{\begin{array}{ccc}\hfill WTN{S}_{ij}& \hfill ,\hfill & \hfill C_i=C_j,\\ \hfill SCL(C_i,C_j)\times WTN{S}_{ij}& \hfill ,\hfill & \hfill C_i\ne C_j\end{array}\right.$$

(5)

where the weighted two-level neighborhoods similarity index $WTN{S}_{ij}$ is calculated as

$${WTNS}_{ij}=\lambda \times \sum _{z\in {\mathsf{\Gamma }}_i\cap {\mathsf{\Gamma }}_j}\frac{1}{k_z}+(1-\lambda )\times \sum _{x\in {\mathsf{\Gamma }}_i,y\in {\mathsf{\Gamma }}_j}\frac{a_{xy}}{\sqrt{k_x\times k_y}}$$

(6)

where $k_x$, $k_y$ and $k_z$ are the degree of nodes x, y and z respectively. Meanwhile, $SCL(C_i,C_j)$ can well depict the strength of connectivity between the communities $C_i$ and $C_j$, which can be computed using Equations (7) or (8).

(i): If $x\in C_i,y\in C_j,C_i=C_j$,

$$SCL(C_i,C_j)=1.$$

(7)

(ii): If $x\in C_i,y\in C_j,C_i\ne C_j,$

$$SCL(C_i,C_j)=\frac{|(\mathrm{E}\left(C_i\right)\cup \overline{\mathrm{E}}\left(C_i\right))\cap (\mathrm{E}\left(C_j\right)\cup \overline{\mathrm{E}}\left(C_j\right))|}{|\overline{\mathrm{E}}\left(C_i\right)|+|\overline{\mathrm{E}}\left(C_j\right)|+1}$$

(8)

where $\mathrm{E}\left(C_i\right)=\left\{(x,y)\right|x\in C_i,y\in C_i,(x,y)\in E\}$ is the set of edges between node pairs in community $C_i$. $\overline{\mathrm{E}}\left(C_i\right)=\left\{(x,y)\right|x\in C_i,y\notin C_i,(x,y)\in E\}$ is the set of connected edges between community $C_i$ and other communities.

In addition, the area under the receiver operating characteristic curve (AUC) [51] is a classical evaluation metric, and it is widely used in link prediction to measure the accuracy of methods, which reads

$$AUC=\frac{n_1+0.5n_2}{n}$$

(9)

where among the n independent comparisons, $n_1$ is the number of times a missing link has a higher similarity score than a nonexistent link, and $n_2$ is the number of times they have the same score.

4. Data Sources

Considering the availability of data, we chose the China National Intellectual Property Admin and the incoPat technology innovation intelligence platform as the data sources (https://www.incopat.com, accessed on 20 September 2021). Meanwhile, the patent grant years are limited from January 2012 to August 2021. Based on the American Association for Artificial Intelligence, Association for Computing Machinery, the Institute of Electrical and Electronics Engineers and the Library of Congress Subject Headings (LCSH), main keywords and patent classification numbers are listed in

Table 2. Main keywords and classification numbers related to artificial intelligence.

Keywords

Classification Numbers

Information retrieval & recommendation, Machine learning, Computational theory, Computer system, Database, Security & privacy, Knowledge engineering, Natural language processing, Data mining, Computer vision, Chip technology, Robotics, Computer graphics, Computer networks, Human-computer interaction, Cloud computing, Autonomous intelligent system, Deep learning, Transportation big data, Knowledge graph technology, Expert systems, Knowledge acquisition, Adaptive learning, Planning & optimization, Industrial internet, Mixed reality, Quantum computing, Blockchain, Edge computing, Neural network, Genetic algorithm, Intensive Learning, Random forest, Linear algorithm, Support vector machine, Spectral clustering, Logistic regression, Intelligent manufacturing, Decision tree, Naive Bayes, Probabilistic reasoning, Back propagation, Nuclear machine, Inverse deduction algorithm, Intelligent search, Intelligent finance, Intelligent education, Intelligent healthcare, Intelligent digital government, Driverless, Speech recognition, Image processing, Pattern classification, Personal assistant, Intelligent recommendation

H04N, G06F, G06T, G10L, H04L, H04M, G06K, H03M, G09G, H04Q, G01B, G06N, G05B, G01N, B65G, G05D, H01L, H04W, G06Q, H04B, G01B, G08B, G07C, G02B, G01R, G10L, A81B, B60W, G01S, B25J, A61K, G01C, G08K, A61B, H04R, G11B

as the search fields for the database.

AI innovations in China’s YRD have rapidly increased in number over the past decade. In this study, the information retrieval expression includes the names of 41 city in China’s YRD, the beginning and ending time, and the keywords and classification numbers given in Table 2. It was found that there are 19,929 granted cooperative patents and 73,914 pending cooperative patents in the YRD from 2012 to 2021. Figure 1 shows the number of patent applications per year in the YRD. The number of pending patents and granted patents in the YRD has been steadily increasing since 2012, with the number of pending patents in this region exceeding 5000 in 2014 and 10,000 in 2018, until reaching the peak of 11,548 in 2020. As for the granted patents, the number of collective granted patents in the YRD exceeded 1000 in 2014 and 2000 by 2016, while the number of collective granted patents from 2020 onwards has exceeded 3000. As of August 2021, the current number of collective granted patents has reached 2970. As shown in Figure 1, the AI technology in China’s YRD region has grown rapidly.

In 2011, the State Council of China issued the “Twelfth Five-Year Plan for National Informatization”, which listed AI technology as a strategic frontier technology. Thereafter, AI patent applications have entered a rapid growth phase in the YRD. From 2012 to 2016, the scale of collaborative innovation in the AI field continued to expand, and the number of nodes and edges continued to increase. Since 2017, the number of patent applications in the AI industry has been in a period of high growth, and an increasing number technology companies and units have paid attention to the AI field. The rapid development of research technology has laid the foundation for the development of the AI industry. Thus, according to the development characteristics of the AI industry, the collaboration innovation in China’s YRD could be divided into two stages. The first stage is the technological embryonic stage from 2012 to 2016, and the second stage is the high-speed technological development stage from 2017 to 2021.

5. Spatio-Temporal Evolution Analysis of the YRD-AICI Network

In this section, in order to analyze the AI cooperative innovation between and within the 41 cities in the YRD of China, we construct two YRD-AICI networks of urban agglomerations. In the following, the research tool of complex network is employed to analyze the basic characteristics and spatio-temporal evolution process of these two networks and to explore the current situation of AI collaborative innovation development in the YRD urban agglomerations. Subsequently, the future partners of the YRD urban agglomerations are predicted based on the link prediction to explore the development trends of the AI field.

5.1. Construction of the YRD-AICI Network

According to keywords and search strategies in the AI field, we obtained patent cooperation data in the AI field of the YRD from 2012 to 2021. If there are multiple applicants in these patent cooperation data, it means that they have a cooperation relationship. Here, we focus on the cooperation relationship between patent applicants and the urban agglomerations and then explore the collaborative innovation relationships of intra-city and inter-city areas in the YRD. For the sake of simplicity, we choose two joint AI patents in China’s YRD as examples. It is assumed that the applications of a given patent include three innovative bodies, Shanghai Jiao Tong University, Magang Holding Co., Ltd, and Nanjing University of Aeronautics and Astronautics. They are located in Shanghai, Maanshan, and Nanjing, respectively. Thus, three cooperative relationships are generated between Shanghai and Maanshan, Shanghai and Nanjing, and Maanshan and Nanjing. In addition, if the applications of a given patent include two innovative bodies, Shanghai University and State Grid Shanghai Electric Power Company, there is a cooperative relationship within Shanghai.

In order to more intuitively depict the collaborative innovation relationship, we employed the ArcGIS software to display the spatial distribution of the Yangtze River Delta AI collaborative innovation (YRD-AICI) network of urban agglomerations from 2012 to 2016 and from 2017 to 2021, as shown in Figure 2 and Figure 3. Here, the node represents one city in a YRD urban agglomeration, and the connected edge represents the innovative bodies located in the cities connected by itself jointly applying for an AI patent. For the first stage in the past decade, the YRD-AICI network from 2012 to 2016 has 41 nodes and 151 edges. Additionally, the YRD-AICI network from 2017 to 2021 has 41 nodes and 216 edges. Moreover, the size of a city node is directly related to its degree of centrality, and the greater the intra-city cooperation, the larger the node. The edges between city nodes portray the intensity of cooperation between two cities, and the thicker an edge, the more inter-city cooperation there is. Note that the constructed YRD-AICI network is weighted, where the weight indicates the frequency of joint AI patent applications between different cities. In addition, since the original data are the information of the joint AI patent application, the direction of connected edges among city nodes is no longer distinguished.

5.2. Basic Characteristics of the YRD-AICI Network

To further investigate the intrinsic topology of the two YRD-AICI networks, we utilized the Matlab and Gephi software to calculate the basic topological characteristics of the YRD-AICI network of urban agglomerations, as listed in

Table 3. The basic properties of the YRD-ALCI network, including average degree of centrality ($\langle DC\rangle$), average weighted degree of centrality ($\langle WDC\rangle$), network diameter (D), graph density ($\rho$), connected components ($\sigma$), average clustering coefficient ($\langle C\rangle$) and average path length (L).

Year	$\langle \mathit{DC}\rangle$	$\langle \mathit{WDC}\rangle$	D	$\mathit{\rho }$	$\mathit{\sigma }$	$\langle \mathit{C}\rangle$	L
2012–2016	7.3659	131.2195	3	0.0841	0.9756	0.9612	1.8768
2017–2021	10.4878	138	3	0.2738	1	0.8831	1.8073

. The average degree of centrality and average weighted degree of centrality indicate the connection strength of nodes in the network, and the values in the second stage are significantly higher than those in the first stage. It can be seen that the frequency of intra-city and inter-city collaborative innovation in the YRD urban agglomerations is increasing, and the connections are getting stronger. In addition, the graph density shows that the second stage is 3.2556 times higher than the first stage, which indicates that the overall structure of the network is more compact and the trend of regional integration is more obvious. From the connected components of the network, the value being 0.9756 in the first stage indicates that most cities in the YRD urban agglomerations have joined the AI industry. The connected components of the second-stage network reach the highest value of 1, which also indicates that the development of the AI field in the YRD is gradually maturing, which is consistent with the integration process of the economic development of the urban agglomerations. The average path length decreases from 1.8768 to 1.8073. The smaller the value, the better the accessibility of the network, demonstrating that the connection cost between the YRD urban agglomerations gradually decreases, and the circulation of innovation resources and the efficiency of communication gradually increases. In general, the collaborative innovation capability of AI in the YRD urban agglomerations has gradually improved, and the whole network shows the characteristics of a small world network.

5.3. Evolution Analysis of the YRD-AICI Network

Figure 2 and Figure 3 present the visualization of the YRD-ALCI network in two stages. As shown in Figure 2, the three provinces in the YRD have core cities, which lead to the development of AI in each province from 2012 to 2016, including Nanjing, Suzhou and Wuxi in Jiangsu Province, Hangzhou, Ningbo and Taizhou in Zhejiang Province, and Hefei in Anhui Province. In addition, it can be seen that the frequency of patent cooperation between other cities is relatively small, and the differences between cities are more significant. This indicates that the development of the AI industry at this stage still needs to strengthen the driving and leading efforts of these core cities to the surrounding cities.

Figure 3 shows the development of the YRD urban agglomerations in the AI field from 2017 to 2021, and the core cities of each province have not changed significantly. Compared with the first stage, the frequency of intra-city and inter-city cooperation generally increases in the second stage, and more new cooperative relationships arise between cities, with more obvious development in Shanghai, Jiangsu Province and Zhejiang Province. It can be seen that AI patent cooperation in the YRD is becoming more and more closely connected, and knowledge circulation and interaction among cities are enhanced. In addition, from the perspective of the overall development layout, there exist differences in development between the east district and the west district. In the east, cities located in the Nanjing, Hangzhou, and Suzhou-Wuxi-Changzhou metropolitan area have relatively high cooperative relations; in particular, Shanghai to Nanjing is the most concentrated. Meanwhile, the core area of AI development in the YRD extends from Nanjing, Hangzhou, and Shanghai to the north and south sides, and the differences in development levels between cities are gradually narrowing. In the YRD of China, the overall development speed in Anhui Province is relatively slow. Compared with the other three provinces in the YRD, there is much less intra-provincial and inter-provincial cooperation in the AI field.

With respect to cooperative innovation at the provincial level, Zhejiang Province, Jiangsu Province, and Shanghai have close internal patent cooperation. However, the frequency of internal patent cooperation in Anhui Province is low, which is consistent with the development status of Anhui Province in the AI industry. In the second phase, the inter-provincial cooperation frequency between Shanghai and Zhejiang is reduced to some extent. The frequency of cooperation in Jiangsu Province is increased significantly, which indicates that the cities in Jiangsu Province are accelerating their growth and promoting the development of Jiangsu Province in the AI field. In addition, from the perspective of inter-provincial cooperation, the cooperation between Jiangsu, Zhejiang, and Shanghai is closer, while the frequency of cooperation between Anhui and other provinces is relatively low. It is worth noting that the frequency of intra-provincial cooperation is significantly higher than inter-provincial cooperation, which indicates that the cooperative relationship between the provinces in the Yangtze River Delta still needs to be strengthened. Nevertheless, the connections between provinces are gradually increasing with time, which also indicates that the AI industry in the YRD is steadily developing.

5.4. Cooperation Prediction between YRD Urban Agglomerations

Link prediction utilizes the known information of network structure to predict the connection possibility of two non-connected nodes, which is widely used in the prediction of cooperative relationships. Based on the YRD-AICI network, we employ several classical link prediction methods to predict the potential cooperation opportunities among YRD urban agglomerations so as to provide guiding suggestions for future partner trends and policy formulation among cities. The prediction accuracy of different link prediction methods are obtained, and the AUC values are shown in Figure 4.

It can be seen that the AUC values of Jaccard and HPI metrics are less than 0.8, indicating that they have poor prediction accuracy and are not suitable for link prediction in the YRD-AICI network. Among the remaining four indicators, the proposed SCL-WTNS algorithm has the highest AUC value, which may be due to the fact that the constructed network has a distinct community structure and the cooperation between urban agglomerations considers collaborators of collaborators besides direct collaborators. Therefore, on the basis of the SCL-WTNS algorithm, one can predict the potential cooperation between cities. The top 10 potential cooperation cities in the AI field of China’s YRD are shown in

Table 4. Top 10 potential cooperation cities in the AI field of China’s YRD.

Ranking	City-City	Similarity Score
1	Wenzhou-Wuxi	1.4725
2	Hangzhou-Huaian	1.4235
3	Huaian-Suzhou	1.2992
4	Taizhou-Suzhou	1.2765
5	Jiaxing-Changzhou	1.2626
6	Jiaxing-Xuzhou	1.1717
7	Ningbo-Yancheng	1.1642
8	Maanshan-Nangjing	1.1451
9	Lianyungang-Zhenjiang	1.1339
10	Wenzhou-Changzhou	1.0719

.

As displayed in Table 4, the top three are Wenzhou and Wuxi, Hangzhou and Huaian, as well as Huaian and Suzhou, respectively. Wenzhou, Huaian, Suzhou, and Jiaxing appear in the top 10 twice, indicating that these cities are more likely to collaborate on AI technologies in the future. Moreover, the bottom ten regions in the similarity score are mainly cooperation between Anhui Province and other provinces, which suggests that the development of AI technology is more uneven and there is more room for development in the AI field in Anhui Province. Furthermore, close cooperation already exists between core cities such as Shanghai, Nanjing and Hangzhou among all city node pairs, and core cities are more likely to cooperate with edge cities in the future. For example, the top 3 cities where Shanghai is most likely to have a partnership in the future are Anqing, Huangshan and Tongling. Consequently, to promote the balanced development of AI in China’s YRD, it is necessary to promote the development of AI synergy and innovation between core cities and edge cities in addition to maintaining the existing cooperative relationships between core cities themselves.

6. Spatio-Temporal Evolution Analysis of the YRD-AIPC Network

At present, a great number of innovation cooperation and exchange relationships have been established among various innovation bodies in China’s YRD. With the development of the AI industry, these innovation bodies have carried out much cooperative research and applied for numerous patents in the AI field. Their patent cooperation relationship can reflect the development status and trend of the AI industry in the YRD. Thus, we take innovation bodies as nodes and build the patent cooperation network to explore the cooperation mechanism and developing trends among innovation subjects in the AI field.

6.1. Construction of the YRD-AIPC Network

In the patent cooperation data, patent applicants represent innovation bodies, including enterprises, universities and research institutes. If two innovation bodies jointly apply for a patent, then there is a cooperative relationship between the two innovation bodies. To illustrate the cooperative relationship between innovation bodies more intuitively, this study utilizes Gephi software to draw the Yangtze River Delta AI patent cooperation (YRD-AIPC) network of innovation bodies from 2012 to 2016 and 2017 to 2021, as shown in Figure 5 and Figure 6. In these two networks, the node represents the innovation body, and the edge indicates the cooperative relationship between two innovation bodies. Meanwhile, the size of a given node is related to the number of nodes connected to itself, that is, the more partners the innovation body cooperates with, the larger the node is. The color of a given node represents the number of cooperative relationships, that is, nodes with the same color indicate that they have the same number of cooperative relationships. The connected edges portray the intensity of cooperation between innovation bodies, and the thicker connected edges indicate more frequent cooperation. Similarly, the YRD-AIPC network is also an undirected and weighted network.

As depicted in Figure 5, the overall scale of the YRD-AIPC network from 2012 to 2016 is smaller, and there are fewer connections between individuals in the network. Only some nodes are located in the core of the network, while the majority of nodes are located at the edges of the network. In addition, the control of information flow in the network is easier to achieve at this stage because only a few innovative entities can realize the effective circulation of information in a short period, and most individuals cannot obtain timely first-hand information. As shown in Figure 6, compared with the previous stage, the scale of the YRD-AIPC network and the number of innovation bodies have increased significantly from 2017 to 2021, and the connections between nodes have become closer. At the same time, the number of key nodes in the network is significantly higher than in the first stage, so the information flow of these key nodes can be transmitted to more nodes at a faster speed, which helps to promote the development of collaborative innovation in the YRD and also highlights that the patent partnership in the AI field has entered into a high-speed development stage.

6.2. Basic Characteristics of the YRD-AIPC Network

Table 5. Main topological properties of the YRD-AIPC network, including the number of nodes (N), number of edges (M), average degree of centrality ($\langle DC\rangle$), average weighted degree of centrality ($\langle WDC\rangle$), network diameter (D), graph density ($\rho$), average clustering coefficient ($\langle C\rangle$) and average path length (L).

Year	N	M	$\langle \mathit{DC}\rangle$	$\langle \mathit{WDC}\rangle$	D	$\mathit{\rho }$	$\langle \mathit{C}\rangle$	L
2012–2016	2163	2096	1.8377	3.5076	12	0.0009	0.1858	1.8769
2017–2021	3970	4432	2.0494	3.7950	12	0.0006	0.1954	2.6086

shows the basic topological characteristics of the YRD-AIPC network. The number of nodes refers to the number of AI innovation bodies, which increased from 2163 to 3970. This means that the scale of AI innovation bodies continues to expand, and the expansion speed is obvious. At the same time, the number of network connections has doubled, which shows that the cooperation opportunities between AI innovation bodies in the YRD have increased significantly and the connections have become closer. The network density is decreased to some extent; in other words, the number of new cooperative relationships between innovation bodies is smaller than the number of new nodes in the network. Thus, there is still a large space for cooperation in the YRD. The increase in the average clustering coefficient shows that the innovation bodies are more closely connected. We also note that the path of establishing cooperative relationships between innovation bodies is extended, which indicates that there are still some potential cooperation opportunities to be explored in the YRD.

6.3. Evolutionary Analysis of the YRD-AIPC Network

To more clearly illustrate the evolution trend of the AI field in China’s YRD, we build two YRD-AIPC networks with nodes denoting the innovation bodies, which correspond to two different stages, namely from 2012 to 2016 and from 2017 to 2021. The degree of centrality and weighted degree of centrality are connection-based statistics indices, while betweenness centrality and closeness centrality are shortest path-based statistics indices. In the YRD-AIPC network, the degree of centrality can simply and directly indicate the local influence of a node. A higher degree of centrality of a node indicates that it has a greater number of connections to other nodes. The weighted degree of centrality indicates the frequency of cooperation in the network, and the higher the value, the more cooperation the node has in the AI industry. In addition, the nodes with high betweenness centrality are more likely to interact with other nodes in the network and also obtain more cooperation resources. Meanwhile, the nodes with high closeness centrality indicate that individuals are located in the relative core of the cooperation network, with shorter distances and closer ties to the remaining nodes in the network.

Table 6. The top 10 innovation bodies in the AI field of China’s YRD from 2012 to 2016.

Ranking	DC	WDC	BC	CC
1	Zhejiang University	Zhejiang Geely Holding Co., Ltd.	Shanghai Jiao Tong University	Zhejiang University
2	Shanghai Jiao Tong University	Zhejiang Geely Automobile Research Institute Co., Ltd.	Shanghai Aircraft Manufacturing Co., Ltd.	Shanghai Aircraft Design and Research Institute
3	Southeast University	Southeast University	Zhejiang University	Shanghai Jiao Tong University
4	Donghua University	Zhejiang University	Southeast University	State Grid Shanghai Electric Power Company
5	Tongji University	Shanghai Jiao Tong University	East China University of Science and Technology	Southeast University
6	Nanjing University	Donghua University	Donghua University	Jiangsu University
7	East China University of Science and Technology	Magang Holding Co., Ltd.	Nanjing University	Nanjing University of Aeronautics and Astronautics
8	Nantong University	Tongji University	Tongji University	Hefei University of Technology
9	Nanjing Tech University	Commercial Aircraft Corporation of China Ltd	Shanghai Machine Tool Factory	Hohai University
10	Nanjing University of Aeronautics and Astronautics	NR Electric Co., Ltd.	Nanjing University of Aeronautics and Astronautics	Tongji University

and

Table 7. The top 10 innovation bodies in the AI field of China’s YRD from 2017 to 2021.

Ranking	DC	WDC	BC	CC
1	Zhejiang University	Zhejiang University	Shanghai Jiao Tong University	Zhejiang University
2	Shanghai Jiao Tong University	Shanghai Jiao Tong University	Zhejiang University	Shanghai Jiao Tong University
3	Southeast University	Southeast University	Southeast University	Zhejiang Geely Holding Co., Ltd.
4	Nanjing University of Aeronautics and Astronautics	State Grid Shanghai Electric Power Company	Nanjing University of Aeronautics and Astronautics	Southeast University
5	Tongji University	NARI Technology Co., Ltd.	East China University of Science and Technology	Southeast University
6	Zhejiang University of Technology	Zhejiang Nankong Electric Technology Co., Ltd.	State Grid Shanghai Electric Power Company	Hefei University of Technology
7	China University of Mining and Technology	Nanjing University of Aeronautics and Astronautics	Hefei University of Technology	State Grid Shanghai Electric Power Company
8	Donghua University	Huadong Electric Power Experimental & Research Institute Co.,Ltd.	Hohai University	Shanghai University
9	State Grid Shanghai Electric Power Company	China University of Mining and Technology	Jiangsu Provincial Electric Power Corporation	Jiangsu University
10	Nanjing University	Nanjing University	Shanghai University	Nanjing University

present the top 10 innovation bodies from 2012 to 2016 and from 2017 to 2021, respectively.

As shown in Table 6, the DC and WDC values of Zhejiang University are 81 and 111, respectively, which means that Zhejiang University has established 111 cooperative relationships with 81 different innovation bodies in the YRD. Zhejiang University ranks first in terms of DC and WDC, which means that Zhejiang University has cooperated with many innovation bodies in the YRD and has established multiple cooperative relationships. At the same time, Shanghai Jiao Tong University and Southeast University also have a high influence on the network. In addition, although Zhejiang Geely Holding Co., Ltd. and Zhejiang Geely Automobile Research Institute Co., Ltd. have high WDC values, their DC values are not in the top 10 list. In other words, although they have a high frequency of cooperation, their partners are relatively few, and their influence on the long-term development of AI in the YRD is limited.

From the shortest path-based statistics, Shanghai Jiao Tong University, Zhejiang University, and Southeast University are the top 3 innovation bodies in the comprehensive ranking, and their BC and CC values are relatively high, which shows that they play a key role in the YRD. At the same time, we also found that Shanghai Aircraft Manufacturing Co., Ltd. and Shanghai Aircraft Design and Research Institute have high BC and CC values, respectively, which means that they are also located in key positions and have great achievements in knowledge exchange and resource transfer.

Table 7 gives the four statistical quantities for the YRD-AIPC network from 2017 to 2021. It is obvious that there is a significant difference in the top 10 innovation bodies compared with the first stage. In particular, Zhejiang University, Shanghai Jiao Tong University, and Southeast University are always in the top three in terms of connection-based statistics, while Zhejiang Geely Holding Co., Ltd. and Zhejiang Geely Automobile Research Institute Co., Ltd. have fallen below the top 10 in terms of WDC value. According to the shortest path-based statistics, Zhejiang University, Shanghai Jiao Tong University, and Southeast University still have high BC and CC values, which is consistent with the previous stage. This also indicates that these three universities are stable and always leading in the AI field in the YRD. In addition, Nanjing University of Aeronautics and Astronautics and Hefei University of Technology are also ranked relatively high.

In summary, several high universities are the important bridges of AI industry in the YRD of China, and their cooperation relationship can traverse the whole network in the shortest time. These core innovation bodies can well maintain their proper function of the whole network and are the key factors to promoting the further development of AI in the YRD.

6.4. Cooperation Prediction between Innovation Bodies in YRD

Cooperation prediction is also an important research topic in collaborative networks. Here, we utilize the link prediction method to predict the potential cooperation probability among all innovation bodies in the YRD. The AUC is also used as an evaluation metric for prediction accuracy. For the YRD-AIPC network from 2012 to 2021, the prediction accuracy results are shown in Figure 7.

As depicted in Figure 7, the LP index and the proposed SCL-WTNS algorithm perform well on the YRD-AIPC network because their AUC values are higher than 0.9. The AUC values of the CN, Jaccard, HPI, AA and RA indices are greater than 0.85 but less than 0.9; thus, CN, Jaccard, HPI, AA and RA perform slightly worse than the former two methods. The AUC value of PA index was significantly less than 0.85, and it performs the worst on the YRD-AIPC network. LP and SCL-WTNS utilize two-step and three-step path information; thus, they achieve better performance. Based on the above comparative experiment, we apply the SCL-WTNS algorithm for link prediction in the YRD-AIPC network to identify the potential cooperative relationships in the AI industry of China’s YRD. As a result, the top 10 innovation bodies that are most likely to generate collaborative relationships are given in

Table 8. Top 10 potential cooperative innovation bodies in the AI industry of China’s YRD.

Ranking	Innovation Body 1	Innovation Body 2	Similarity Score
1	Tongji University	Shanghai Jiao Tong University	1.9443
2	NARI Technology Co., Ltd.	Southeast University	1.7124
3	Fudan University	Shanghai Jiao Tong University	1.4751
4	Shanghai University of Technology	Shanghai Jiao Tong University	1.1047
5	NARI Technology Co., Ltd.	NR Electric Co., Ltd.	1.0719
6	Hohai University	Nanjing University of Posts and Telecommunications	1.0319
7	State Grid Jiangsu Electric Power Company	Southeast University	0.9639
8	Information and Communication Branch of State Grid Jiangsu Electric Power Co., Ltd.	Southeast University	0.9596
9	NARI Group Corporation	State Grid Jiangsu Electric Power Company	0.9172
10	NARI Technology Co., Ltd.	NR Engineering Co., Ltd.	0.9052

.

The similarity score between Tongji University and Shanghai Jiao Tong University is the greatest, which means that the two universities are most likely to generate cooperation in the AI field. NARI Technology Co., Ltd. and Southeast University rank the second, and they are most likely to cooperate in the future. Fudan University and Shanghai Jiao Tong University rank third; both of them are well-known universities located in Shanghai, and the possibility of future cooperation between these two universities is very large. Among the universities, Shanghai Jiao Tong University (SJTU) and Southeast University (SEU) appear three times in the top 10 list, which indicates that SJTU and SEU will play a crucial role in future collaborative cooperation in AI technology. It is worthwhile to note that NARI Technology Co., Ltd. appears three times. This shows that the enterprise has an important position in the future cooperation of AI patent technology. As shown in Table 8, university-university cooperation is four times, while the enterprise-enterprise and university-enterprise cooperation are both three times, which indicates that the future AI patent cooperation among innovation bodies in the YRD have been moving towards greater balance.

7. Conclusions and Suggestions

This paper selects the patent cooperation data in the AI field of China’s YRD from 2012 to 2021. We first construct the YRD-AICI network with urban agglomerations as nodes and investigate the interprovincial, intra-city and inter-city collaborative innovation relationship from the perspective of complex networks. Then, we construct the YRD-AIPC network with innovation bodies as nodes, and the topological properties and spatio-temporal evolution are investigated for the two developing stages. Moreover, the pioneering innovation bodies of the AI industry in China’s YRD are identified by some classic centrality measures. At the same time, compared with several classical link prediction algorithms, our proposed algorithm, SCL-WTNS, achieves the best performance in predicting the potential partners between future cities and innovative bodies. Based on the above analysis, the following conclusions and suggestions are drawn in this paper.

(1) There are significant differences in the spatial distribution of urban agglomerations in the YRD-AICI network. Shanghai, Jiangsu and Zhejiang provinces in the east have strong strengths and high collaborative innovation capabilities in the AI field. Among them, the three core cities, namely Shanghai, Nanjing and Hangzhou, occupy important hub positions and are connected to most cities in the YRD, highlighting the “rich-rich” phenomenon of the network. In contrast, the development of Anhui Province in the west of the YRD is relatively slow, with more peripheral cities, and its collaborative innovation capacity needs to be improved.

(2) The evolution characteristics of the innovation bodies in the two time phases of the YRD-AIPC network are remarkable. From 2012 to 2016, the development in the AI field of YRD was still in the embryonic stage, and there was less cooperation among various innovation bodies. The number of patent cooperation among innovation bodies has increased significantly from 2017 to 2021. Universities dominate, while corporations and research institutes have a relatively low status of collaboration.

(3) From the link prediction results, it can be concluded that the collaborative partnership in the YRD may develop from the core cities to the surrounding central cities in the future, which also indicates the obvious trend of regional integration in the YRD, and the development gap between cities in the AI field is expected to be reduced. In addition, the collaborative and cooperative relationship between innovation bodies may still be dominated by universities, and the development of enterprises and scientific research institutions in the AI field still needs to be further strengthened.

(4) The cooperative relationship in the AI field of the YRD is related to the geographical location of the innovation bodies. Innovation bodies are more inclined to cooperate within cities or provinces, while the frequency of cooperation across provinces is relatively low. To promote the long-term and stable development of AI technology in the YRD, we should encourage innovation bodies to communicate across regions and look for more partners to promote wider collaboration in the entire region and achieve mutual benefit.

(5) The core cities in the AI industry of the YRD should play a leading and radiating role. The core cities, such as Shanghai, Nanjing, and Hangzhou, can drive the development of central cities, such as Wuxi, Changzhou, Suzhou, Hefei, and Ningbo, and then jointly lead the development of other peripheral cities. Then, the YRD will strive to form an AI collaborative city collaboration network dominated by core cities, driven by central cities, and developed by peripheral cities. The coordinated development of AI across regions will be promoted through complementary advantages.

(6) Innovation bodies should consider the complementarity of their positions and capabilities when selecting future partners. For innovation bodies just starting in the AI field, they should make full use of the university resources in the city where they are located to promote exchanges through cooperation and then enhance their development. In addition, innovation bodies with higher rankings should continue to maintain active cooperative relations and strive to expand cooperation with other innovation bodies, which can focus on enterprises and research institutions.