Introduction

Radical innovation, as a highly revolutionary and powerful disruptive innovation behavior, is considered to be a major breakthrough in overcoming innovation bottlenecks1. Its groundbreaking and non-imitable nature empowers enterprises to reshape the trajectory of new technologies, which drives enterprise innovation and growth. Therefore, with the increasingly fierce market competition and insufficient innovation in core technologies, determining the ways in which to achieve radical innovation in the technological field to improve performance is not only a key challenge that enterprises must urgently solve, but also one of the focuses of extensive academic discussion. In general, an in-depth discussion of how enterprises can improve radical innovation performance by optimizing the allocation of different internal and external resources is of great practical significance for making up for the limitations of technological innovation in enterprises and promoting an improvement in technological innovation.

With the significant increase in technological complexity and integration in innovation activities, it is becoming more and more difficult for enterprises to achieve effective breakthroughs in the field of innovation with their own resources and capabilities. Consequently, enterprises are facing huge challenges in carrying out radical innovation activities independently. Against this background, one of the business community’s primary focuses is the enhancement of radical innovation performance through collaboration with external innovation entities to leverage advantageous external resources2. Industry–university–research institute collaboration is a collaborative innovation activity between three main entities—enterprises, universities, and research institutes. Depending on the external collaboration entities, this category can be divided into industry–university (IU) collaboration pattern, industry–research institute (IR) collaboration pattern, and industry–university–research institute (IUR) collaboration pattern. Serving as a critical interface linking enterprises with universities and research institutes, industry–university–research institute collaboration demonstrates distinct innovation advantages in foundational research domains. It provides enterprises with access to new knowledge, technologies, and insights, enabling them to break through the constraints of their own resources and capabilities, overcome the path dependence in relation to technological innovation processes, and obtain more groundbreaking radical innovation achievements.

In addition, the differences between enterprises’ internal knowledge element configuration and their external collaboration network position are also highly correlated with their radical innovation performance level. The former serves as a foundation for enterprises to effectively apply and generate knowledge, while the latter offers a viable means for enterprises to acquire external knowledge and technical resources. First of all, in order to achieve radical innovation, enterprises need to have a sound configuration of their own technical knowledge elements3. The Knowledge-based View (KBV) states that an enterprise is a conglomeration of knowledge elements, which play an important role in the diversification and specialization of its innovation activities, serving as the primary factor determining its innovation performance4. Previous studies have shown that patents represent novel knowledge elements, and the relevant patents applied for by enterprises are regarded as the collection of knowledge elements they possess5. Hence, this study explores the structural characteristics of internal knowledge elements and investigates the impact of knowledge diversity and knowledge complexity on enterprises’ innovation performance, based on the patents of enterprises. Moreover, external collaborative networks emerge as a strategic option for enterprises seeking to transcend resource constraints and advance innovation objectives, functioning as a viable mechanism to access heterogeneous knowledge pools. The industry–university–research institute collaborative innovation network spontaneously forms through the interaction of three core stakeholders—industry, universities, and research institutes. This networked structure systematically harnesses synergistic effects, optimizes resource allocation, accelerates knowledge dissemination, and ultimately catalyzes transformative scientific and technological progress6. Currently, an increasing number of enterprises are progressively engaging in the construction of industry–university–research institute collaboration networks, further enhancing their innovation vitality by strengthening collaboration with different types of entities to avoid the pitfalls of rigidity and capacity constraints, so as to occupy a favorable position within the market.

For an in-depth exploration of the impact mechanism and influence degree of the internal knowledge elements and external collaboration networks of Specialized, Refined, Differentiated, and Innovative (SRDI) enterprises adopting heterogeneous collaboration patterns, in order to reveal the multiple pathways towards enhancing enterprises’ radical innovation performance, this study focuses on the following issues: (1) Among enterprises adopting three collaboration patterns of IU, IR, and IUR, which pattern is most conducive for achieving a radical innovation performance? What are the differences in enterprises adopting different collaboration patterns? (2) To enterprises adopting heterogeneous collaboration patterns, what characteristics of knowledge elements and collaboration networks are the key factors affecting their radical innovation performance? How do these factors affect radical innovation performance in a complex nonlinear way? (3) What are the effective pathways for enterprises to improve radical innovation performance? How do key factors influence radical innovation performance? To address these critical inquiries, this study categorizes enterprises into three heterogeneous collaboration patterns—enterprises adopting industry–university collaboration pattern (IU enterprises), enterprises adopting industry–research institute collaboration pattern (IR enterprises), and enterprises adopting industry–university–research institute collaboration pattern (IUR enterprises)—based on the differential configurations of enterprises’ external partners. Machine learning methods such as the CART algorithm and Bayesian network analysis are employed to explore the complex nonlinear relationships between knowledge elements’ structural characteristics, collaboration networks’ structural characteristics, and the radical innovation performance of enterprises adopting heterogeneous collaboration patterns, so as to provide a theoretical basis and decision-making reference for enterprises to enhance radical innovation performance.

The remainders of this paper are organized as follows. In Sect. Literature Review, the impact of knowledge elements or collaboration networks on enterprises’ innovation performance are reviewed. In Sect. Research Design and Variable Measurement, research design, data processing and variable measurement are proposed. The influencing factors and improvement paths of enterprises’ radical innovation performance are obtained based on machine learning methods such as the classification and regression tree (CART) algorithm and Bayesian network analysis method in Sects. Analysis of Influencing Factors on Enterprises’ Radical Innovation Performance and Improvement Pathways of Enterprises’ Radical Innovation Performance. In Sect. Conclusions and Discussions, the related conclusions are presented. In addition, the theoretical contributions, innovations and the existing limitations of this paper are further discussed.

Literature review

Based on the KBV and Social Network Theory (SNT), this study conducts a literature review from three different research perspectives—the impact of knowledge elements on enterprises’ innovation performance, the impact of collaboration networks on enterprises’ innovation performance, and the interactive impact of the two on enterprises’ innovation performance.

Knowledge elements and enterprises’ innovation performance

Enterprises’ innovation is driven by enterprises’ ability to use and reorganize their own existing technologies. Therefore, enterprises’ knowledge elements play an important role in innovation activities and have significant impact on the diversity, specialization, and integration of enterprise innovation activities. In recent years, the impact of knowledge elements on enterprises’ innovation performance has become a growing focus of academic research. For example, Luo et al. believed that different combinations of knowledge elements have an important impact on innovation7. Leng et al. found that generative artificial intelligence may change the mechanism of innovation performance formation by enhancing the diversity and recombination capability of internal knowledge8,9. Among the characteristics of knowledge elements, knowledge diversity and knowledge complexity, as important variables reflecting the distribution of knowledge elements within an enterprise, are considered to be significantly correlated with innovation performance. Pinter et al. emphasized that knowledge elements serve as a primary driver in sustaining heterogeneity among enterprises and industries, and the innovation performance level of an enterprise was positively correlated with its ability to expand its knowledge element10. Lian et al. believed that the knowledge diversity within an enterprise can regulate the influence of the intensity, breadth, and novelty of knowledge flows on exploratory innovation11. Hao et al. found that a higher diversity of knowledge elements had a significant impact on enterprises’ innovation performance12. They discovered that an increase in knowledge diversity led to a more varied structure and level of knowledge within the enterprise. This enhanced diversity was beneficial for fostering breakthrough innovations, which necessitate higher degrees of knowledge richness and heterogeneity. However, Lungeanu et al. argued that the excessive diversification of an enterprise’s knowledge elements could lead to the excessive dispersion of technological resources, which prevents synergistic advantages and inhibits exploratory innovation13. In addition, Eisenman and Paruchuri proposed that knowledge complexity had a complex impact on breakthrough innovation performance from a life cycle perspective based on the KBV14. In general, prior research has confirmed that the knowledge elements within an enterprise significantly influence innovation performance. However, scholars have rarely delved deeply into the specific mechanisms through which each characteristic variable affects radical innovation performance. Furthermore, there is a lack of clarity regarding the degree to which knowledge element characteristics impact radical innovation performance. Therefore, an in-depth analysis of correlations among these variables is critical, forming a key objective of this study.

Collaboration networks and enterprises’ innovation performance

Existing research focusing on the relationships between external collaboration and enterprises’ innovation performance confirms that collaboration network characteristics impact innovation outcomes. For example, Wang et al. believed that alliance networks have a significant impact on enterprises’ innovation performance by facilitating rapid knowledge acquisition and enhancing innovation capabilities15. Leng et al. pointed out that the characteristics of collaboration networks in complex relational networks may simultaneously affect innovation performance as well as system resilience and adaptability16,17. Wen et al. found that the information asymmetry brought about by structural holes expanded the innovation risk and negatively moderated bimodal innovation performance18. Khanna and Guler also pointed out that the structural holes had a negative effect on enterprise innovation performance19, while Wang et al. argued that structural holes could help enterprises to acquire new technologies, information, and knowledge, thus positively affecting innovation performance20. Zhang et al. pointed out that the collaborative network structure hole has a positive impact on the radical innovation of enterprises21. Cheng et al. concluded that enterprises with a higher degree of centrality typically had extensive access to innovation resources, which could help enterprises to acquire a large amount of external innovation knowledge in the context of reducing the cost of knowledge searches5. Leng et al. discussed how blockchain and federated learning support decentralized collaboration networks, further reinforcing the important role of networks in innovation22,23. Based on the above understanding, the collaboration network characteristics have an obvious influence on enterprises’ innovation performance. However, in reality, due to the enterprises being affected by a combination of factors, the role of collaboration network characteristics on enterprises’ innovation performance is very complex and multifaceted. Consequently, an in-depth study of the complex nonlinear effects of collaboration network characteristics on enterprise innovation performance is one of the main problems that this study hopes to solve.

The interplay of knowledge elements and collaboration networks

Scholars have explored the interactive effects of knowledge elements and collaboration networks on enterprises’ innovation performance. Zhao et al. argued that the increase in knowledge diversity could challenge the existing cognitive pattern of enterprises, which prompted the creation of new network relationships links, reducing the pressure of the enterprise to identify, assimilate, and utilize the external knowledge24. Tsouri pointed out that different structural characteristics and embedded characteristics of the network could lead to the differences observed in the diversity of knowledge elements in the network and the efficiency of knowledge transfer among members, which would affect the enterprise’s innovation performance25. Chen et al. found that the centrality of the enterprises’ collaboration networks had a positive moderating effect on the diversity of knowledge elements and knowledge innovation, with higher level of centrality, a greater diversity of knowledge elements, and a stronger positive effect on knowledge innovation26. Zhao et al. also reached a similar conclusion, whereby when the strength of network relationships was high, high-frequency links between enterprises could shorten the average path of information transfer, promoting the transfer and sharing of knowledge and other innovative resources in the network, while stable collaborative relationships enabled the enterprise to better perceive, assimilate, and apply heterogeneous innovative resources from partners, increasing the internal knowledge diversity of the enterprise, which had a positive effect on innovation performance27. However, Caloghirou et al. argued that, when the knowledge elements held by an enterprise were more diversified and, at the same time, the enterprise’s collaboration network possessed high-density characteristics, the cognitive tendency to consensus binding brought about by frequent exchanges would weaken the possibility of new knowledge combinations brought about by diversified knowledge28. As a result, knowledge element characteristics and collaboration network characteristics exhibit an interactive effect on enterprises’ innovation performance. However, most prior research has overlooked the possible impact of differences between enterprises on the dependent variable and their conclusions lack relevance. Therefore, this study specifically classifies three heterogeneous collaboration patterns according to the differences in enterprises’ collaboration partners, revealing the decision rules and multiple pathways for different types of enterprises to obtain radical innovation performance.

In summary, although existing research has confirmed that there are close relationships between enterprises’ knowledge elements, collaboration networks, and radical innovation performance, most studies focus only on the relationships of either one in relation to radical innovation performance, while fewer have combined internal knowledge elements with external collaboration networks to explore the interactive effects on radical innovation performance. Secondly, the complex nonlinear relationships between knowledge elements, collaboration networks, and enterprises’ radical innovative performance is not clear. Additionally, the influence mechanism and the degree of influence of each variable on enterprises’ radical innovation performance has not been clarified. Based on the above, this study classifies heterogeneous external collaboration into three patterns—IU collaboration pattern, IR collaboration pattern, and IUR collaboration pattern. Selecting four important characteristics based on KBV and SNT, this study analyzes the complex nonlinear relationships between knowledge elements, collaboration networks, and the radical innovation performance of enterprises adopting different collaboration patterns, using the CART algorithm. Furthermore, it deeply examines the complex mechanism of how knowledge element characteristics and collaboration network characteristics affect enterprises’ radical innovation performance by utilizing Bayesian network analysis across three distinct collaboration patterns. This integrated approach provides an in-depth investigation of the complex mechanism of knowledge elements and collaboration networks that jointly affect enterprises’ radical innovation performance.

Research design and variable measurement

This section mainly introduces the research ideas and methods of this study, including the Cloud Model, CART algorithm, and Bayesian network analysis. Then, the data acquisition and processing of this study are explained in detail. Finally, the four variables selected in this study and the specific measurement methods used are introduced.

Research ideas and research methods

In order to explore the key influencing factors and influencing pathways in relation to enhancing the radical innovation performance of IU, IR, and IUR enterprises, this study starts from the interactive perspective of enterprises’ internal knowledge elements and external collaboration networks29, analyzing the characteristic differences in IU, IR, and IUR enterprises, constructing three collaboration networks. Then, the CART algorithm is employed to thoroughly investigate the complex nonlinear relationships between the characteristics of enterprises’ knowledge elements, collaboration networks, and radical innovation performance. Finally, Bayesian network analysis is utilized to further elucidate the multiple pathways and varying degree of influence that the structural characteristics of both knowledge elements and collaboration networks exert on radical innovation performance. This analysis aims to provide a decision-making reference and theoretical foundation for enterprises seeking to enhance their radical innovation performance.

The logic of this study is as follows: Firstly, a network is constructed. Based on the patent data of SRDI enterprises, this study focuses on three main entities in heterogeneous collaboration patterns—industry, universities, and research institutes, respectively—constructing IU, IR, and IUR collaboration networks. Secondly, the variables are selected. Based on the KBV and SNT, and a through a review of existing research, knowledge diversity and knowledge complexity are selected as the variables to measure the structural characteristics of enterprises’ internal knowledge elements, while degree centrality and structural holes are selected as the variables to measure the structural characteristics of enterprises’ external collaboration networks. Then, the key influencing factors are analyzed. The four characteristic variables of knowledge elements and collaboration networks are used as conditional attributes, while enterprises’ radical innovation performance is used as the decision attribute. The CART algorithm30 is used to further identify the key influencing factors and factor combinations that affect the radical innovation performance of IU, IR, and IUR enterprises. Finally, an analysis of multiple influencing pathways is conducted. Bayesian network analysis is used to provide an in-depth exploration of the multiple pathways by which the characteristics of knowledge elements and collaboration networks affect enterprises’ radical innovation performance. In addition, the specific degree of influence between related variables is subjected to an in-depth analysis through an dependence analysis of Bayesian networks. The research framework is shown in Fig. 1.

Fig. 1
figure 1

Research framework.

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In previous studies, traditional statistical approaches have been widely used to solve theoretical and practical problems in the field of management and play a significant role in management research. However, in actual management scenarios, some phenomena usually arise from the combined influence of multiple factors, and the relationships among variables are intricate and complex. Traditional empirical methods, on the other hand, focus more on discussing the linear or simple nonlinear relationships among variables. It is rather difficult to clearly explore and present the multi-factor combined effects, complex nonlinear influences and causal dependencies among multiple variables in management science. Introducing machine learning methods such as decision tree algorithm and Bayesian network analysis into the research of management can, to a certain extent, make up for the limitations of traditional statistical approaches in exploring the complex relationships among variables. For instance, the Cloud Model can effectively control outliers and uncertainties through data calibration, providing a high-quality data foundation for subsequent analysis. Decision tree algorithms can identify complex nonlinear relationships among variables and extract interpretable decision rules. The Bayesian network analysis can further reveal the intrinsic dependence among variables, jointly providing more comprehensive and in-depth methodological support for analyzing the complex influence mechanism of enterprises’ radical innovation performance under heterogeneous collaboration models. At present, some scholars have made innovative explorations. For instance, Ebersberger et al.31, Zhou and Li32, Zhang et al.33, Chanda and Goyal34 have introduced machine learning methods such as the Cloud Model, decision tree algorithms, and Bayesian network analysis into the field of management research, providing innovative research paradigm references for exploring complex management issues and playing important roles in promoting the theoretical research of management. Drawing on previous research, this study employs machine learning methods, including the Cloud Model, CART algorithm, and Bayesian network analysis, to thoroughly examine the multi-factor combinations, complex nonlinear relationships, and multi-pathway effects through which knowledge elements and collaboration networks influence enterprises’ radical innovation performance35. Firstly, this study uses the Cloud Model36 to calibrate the raw data and eliminate the influence of outliers in the sample data on the results, laying a data foundation for subsequent complex factor analysis. The Cloud Model precisely describes the mapping relationships between data characteristics and cloud model parameters in the form of a mathematical model, which has the ability to significantly reduce data errors and uncertainties. Then, this study uses the CART algorithm37 to identify the key influencing factors and decision rules for enterprises to obtain radical innovation performance, objectively revealing the multi-factor combination effect of knowledge elements and collaboration network structural characteristics on enterprises’ radical innovation performance, as well as the complex nonlinear relationships between variables. The CART algorithm is an important classification and prediction method that can reflect the mapping relationships between object attributes and object values. The advantages of the CART algorithm lie in its ease of understanding and interpretation, and its ability to capture nonlinear relationships, as well as its wide applicability38. Finally, this study uses Bayesian network analysis to analyze the dependence level among variables, further exploring the multiple pathways for enterprises to enhance their radical innovation performance. A Bayesian network39 is a non-cyclic directed acyclic graph that primarily consists of three basic elements—nodes, directed arcs, and probabilities. Among them, nodes represent the basic variables of the modeled events. Directed arcs represent the causal relationships between nodes, with associated probabilities quantifying the degree of influence from parent nodes to child nodes. The advantage of Bayesian network analysis lies in its ability to simulate the probability of events with causal relationships in reality, which provides a better understanding and prediction of the world40. At the same time, since Bayesian networks can add or delete elements of the original probability model, a good result can be obtained by constructing a Bayesian model based on some influencing factors.

Data sources and processing

This study primarily selects SRDI enterprises as the research object. SRDI enterprises possess significant characteristics of Small and Medium-sized Enterprises (SMEs). They are deeply influenced by the German concept of ‘hidden champions’, which emphasizes the specialization level and technological innovation ability of enterprises41. It is a concrete manifestation of China’s practice and localization of the concept of ‘hidden champions’. SRDI enterprises, as outstanding representatives of China’s SMEs, are characterized by a stronger focus on market segments, the mastery of key core technologies, outstanding innovation capabilities, high market shares, and better quality and efficiency. Exploring how to better promote and uplift the level of radical innovation among SRDI enterprises is not only of great significance for promoting the high-quality development of the Chinese economy, but also has important reference value for the development of SMEs in other countries.

This study obtains 1,257,050 authorized patents of SRDI enterprises between 2013 and 2022 from the China National Intellectual Property Administration database as a research sample, retaining fields such as the original enterprise name, patent applicant, patent type, IPC classification number, and patent application year. First, drawing on the method of Moaniba et al.42, patents with greater than or equal to two applicants are defined as collaborative patents. The number of patent applicants is calculated by identifying the separator in this field. Then, it is determined whether it is a collaborative patent. As such, we obtained 119,511 collaborative patents in this study. Then, the patents that include non-IUR related collaboration entities are removed from the collaborative patents category, thus constructing collaboration networks through the collaborative entities of the patents. All the collaborative entities are matched with the ‘Little Giant’ SRDI enterprises, using a side table to determine the number of collaborative entities of an enterprise. Enterprises that have at least three collaborative entities at the same time are regarded as key enterprises. In addition, in order to classify and construct networks of collaboration entities, this study uses tools such as the R language to identify keywords in patent entities. Keywords for enterprises include terms such as“company”, while scientific research institutes include “research institutes”and “research academy”, and universities include “college”or “university”. After removing the ambiguous keywords, a total of 1933 focal enterprises are selected. After removing the focal enterprises whose partners are all enterprises, it is finally determined that there are 550, 287, and 524 focal enterprises adopting the collaboration patterns of IU, IR, and IUR, respectively.

Variable selection and measurement

This study selects the structural characteristics of two knowledge elements and two collaboration networks as the variables, based on the KBV and SNT. Among them, the knowledge diversity reflects the richness and dispersion of knowledge elements within enterprises, while knowledge complexity represents the dependence degree of the knowledge elements within enterprises. The structural holes in external collaboration networks of enterprises show the opportunity to obtain non-redundant resources, while the degree centrality reflects the position and influence of enterprises in the collaboration network.

  1. (1)

    Variables of knowledge element structural characteristics.

  1. ①

    Knowledge diversity (KD) is a variable that measures the richness and dispersion of an enterprise’s knowledge elements. Drawing on the approach of Ran et al.43, KD is measured based on the number of patents containing technical knowledge elements that the enterprise has applied for and obtained authorization for in the first and subsequent years.

  2. ②

    Knowledge complexity (KC) is a variable that measures the degree of interdependence between knowledge elements in an enterprise. If the degree of interdependence between two knowledge elements is high, these knowledge elements are included in the same patent at the same time, namely, one patent has multiple technical classification numbers. This study draws on the practices of Yayavaram and Chen44, as follows:

First, the recombination potential of each knowledge element in the enterprise is calculated, using the following equation:

$${\text{E}}_{{\left( {{\text{t}} - 2,{\text{t}} - 1} \right),{\text{k}}}} = \frac{{{\text{C}}_{{\left( {{\text{t}} - 2,{\text{t}} - 1} \right),{\text{k}}}} }}{{{\text{P}}_{{\left( {{\text{t}} - 2,{\text{t}} - 1} \right),{\text{k}}}} }}$$
(1)

Then, the KC of an enterprise is calculated, as follows:

$${\text{KC}}_{{{\text{i}},\left( {{\text{t}} - 2,{\text{t}} - 1} \right)}} = \sum {\text{g}}_{{{\text{i}},\left( {{\text{t}} - 2,{\text{t}} - 1} \right),{\text{k}}}} \times {\text{E}}_{{\left( {{\text{t}} - 2,{\text{t}} - 1} \right),{\text{k}}}}$$
(2)

Among them, the potential for knowledge element restructuring (\({\text{E}}_{{\left( {{\text{t}} - 2,{\text{t}} - 1} \right),{\text{k}}}}\)) represents the ratio of the total number of other types of knowledge elements, where knowledge element \({\text{k}}\) commonly appears in years \({\text{t}} - 2\) and \({\text{t}} -\) 1, to the total number of patents that contain knowledge elements. The weight is the ratio of the number of times that knowledge elements appear in the patents of the focal enterprise in years -2 and -1 to the sum of the number of times that all knowledge elements appear. A larger value of KC indicates a higher degree of interdependence between knowledge elements in an enterprise.

  1. (2)

    Variables of collaboration network structural characteristics.

  1. ①

    Degree centrality (DC) is the most commonly used variable to measure the influence of nodes in a network. The higher the DC, the more complex the collaborative relationships of the node and the easier it is to obtain high-quality resources. This study refers to the research of Guan et al.45, using the number of other nodes directly connected to a node as the calculation method for DC, which is measured using the following formula:

$${\text{DC}} = \mathop \sum \limits_{{\text{j}}} {\text{x}}_{{{\text{ij}}}}$$
(3)

where \({\text{ x}}_{{{\text{ij}}}}\) represents the number of direct links between nodes i and j.

  1. ②

    Structural holes (SHs) are a key element for nodes to obtain and control non-redundant resources in the network. They are key to ensuring a favorable position for nodes in collaboration. The higher the SH level, the stronger the capacity for acquiring non-redundant information, and the greater the possibility of achieving an increased innovation performance. Building on the research of Li et al.46, this study employs the following formulas for measurement:

$${\text{C}}_{{\text{i}}} = \mathop \sum \limits_{{\text{j}}} \left( {{\text{p}}_{{{\text{ij}}}} + \mathop \sum \limits_{{{\text{q}},{\text{q}} \ne {\text{i}},{\text{q}} \ne {\text{j}}}} {\text{p}}_{{{\text{iq}}}} {\text{p}}_{{{\text{qj}}}} } \right)^{2}$$
(4)
$${\text{SH}}_{{\text{i}}} = 2 - {\text{C}}_{{\text{i}}}$$
(5)

where \({\text{p}}_{{{\text{ij}}}}\) indicates the direct relationship input between node i and node j, \({\text{p}}_{{{\text{iq}}}}\) is the strength ratio of the relationship between node i and node q, and \({\text{p}}_{{{\text{qj}}}}\) is the strength ratio of the relationship between node q and node j.

Radical Innovative Performance (RIP): This study draws on the approach used by Zhang et al.47, which regards collaborative patents as a concentrated manifestation of an enterprise’s innovation. The radical innovative performance of an enterprise is measured by taking the natural logarithm of the number of collaborative patents plus one.

Due to the potential impact of collinearity among variables on the multi-factor acquisition of enterprises’ radical innovation performance, to eliminate possible interference, this study conducts a correlation analysis of the structural characteristics of the knowledge element and collaboration network variables using the obtained variable data through SPSS software. The results show that the highest Pearson correlation coefficient among the four variables of KD, KC, DC, and SHs is only 0.36, indicating the absence of high correlation. To further verify whether there is multicollinearity among the variables, a variance inflation factor (VIF) test is conducted on each variable. The results show that the highest VIF value is only 1.535. Referring to the research of Mikalef and Krogstie48, it is indicated that there is no obvious multicollinearity problem between the variables. Therefore, this study conducts an in-depth analysis of the influence relationships between the above four variables and radical innovation performance.

Analysis of influencing factors on enterprises’ radical innovation performance

This section first analyzes the characteristic differences in IU, IR, and IUR enterprises. Then, the CART algorithm is used to explore the key influencing factors and factor combinations that affect the radical innovation performance of SRDI enterprises. Taking DC, SHs, KD, and KC as the condition attributes, and taking the discretized focal enterprises’ radical innovation performance as the decision attributes, this section provides an in-depth analysis of the differential impacts of different characteristic combinations on the radical innovation performance of IU, IR, and IUR enterprises.

Characteristic analysis of IU, IR, and IUR enterprises

According to the differences in focal enterprise external collaboration partners, this study classifies enterprises into three different types, namely IU enterprises, IR enterprises, and IUR enterprises. Table 1 shows the different characteristics of IU, IR, and IUR enterprises, in which the characteristic values of the average values of different enterprise groups are depicted. As shown in Table 1, there are 550 IU enterprises, 524 IUR enterprises, and 286 IR enterprises, which indicates that SRDI enterprises demonstrate a stronger preference for IU and IUR collaboration patterns over IR collaboration pattern. Through an in-depth analysis of Table 1, it can be found that the average radical innovation performance of IU, IR, and IUR enterprises is obviously different, and the probability distribution of obtaining a high radical innovation performance is significantly different among the three collaboration patterns.

Table 1 Characteristics of IU, IR, and IUR enterprises.
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IU enterprises primarily collaborate with universities, resulting in relatively homogeneous collaboration networks, which is similar to the observed characteristics of IR collaboration networks. However, the significant difference is that IU enterprises show a higher level of KD and KC, and their average radical innovation performance is a little higher than that of IU enterprises. However, these enterprises face the challenge of low SH level. Although these enterprises possess rich and complex knowledge elements, their low SH level leads to limited information access, reduced collaboration opportunities, and an inefficient information utilization rate. Therefore, such IU enterprises are more likely to achieve a low radical innovation performance.

IR enterprises mainly take research institutes as collaboration partners, and these partners are relatively homogeneous. These enterprises exhibit low levels of KD and KC, manifesting limited cross-domain knowledge accumulation, homogeneous knowledge elements, and an insufficient depth and breadth of expertise. This constrains enterprises’ capacity to acquire novel knowledge and technologies from multiple perspectives. Furthermore, these enterprises’ low SH level indices weaken access to non-redundant information, consequently increasing the probability of achieving a lower radical innovation performance.

IUR enterprises collaborate with both universities and research institutes, and their collaboration partners are the most diversified. These enterprises exhibit higher levels of KD and KC, indicating extensive and profound knowledge reservoirs that provide abundant innovative materials and inspiration sources. Concurrently, the high KC level helps enterprises to achieve cross-domain technology integration, which is conducive to enhancing radical innovation performance. Moreover, compared to IU and IR enterprises, IUR enterprises have a higher SH level, enabling effective access to non-redundant information. The high DC further reflects that IUR enterprises occupy relatively central network positions, allowing privileged access to diversified non-redundant information resources. This configuration generates stronger innovation momentum, thereby increasing the probability of obtaining a high radical innovation performance.

Decision rule analysis of IU enterprises

As shown in Fig. 2, for IU enterprises, KD, KC, DC, and SHs all have a great impact on radical innovation performance, and different variable combinations have different impacts. Specifically, the distinct value combinations of the characteristic variables associated with IU enterprises can facilitate varying levels of radical innovation performance. When the KD level is high, enterprises are more likely to report a high probability of obtaining a high level of radical innovation performance. When the KD level is low, this kind of enterprise has a high probability of obtaining a low level of radical innovation performance. When the KD is maintained within a certain range, the higher the level of SHs, the higher the probability of the enterprise obtaining a high-level radical innovation performance. When the level of SHs is low, the level of DC and KC is also low, and such enterprises have a high probability of obtaining a high-level radical innovation performance.

Fig. 2
figure 2

Decision rules for IU enterprises.

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KD plays a pivotal role in improving IU enterprises’ radical innovation performance. This is primarily because KD can provide a diverse array of resources, assist enterprises in familiarizing themselves with various technological domains, and facilitate the exploration of solutions and ideas for an array of challenges. Furthermore, it encourages enterprises to pursue multiple avenues for investigating new technology fields and establishes essential conditions for the creation of new knowledge within these organizations, promoting them to break through the existing thinking model, generate novel ideas and solutions to problems, and improve their radical innovation performance. At the same time, the higher the level of the enterprise’s SHs, the more the enterprise occupies the positions of the third-party node, which is conducive to obtaining non-redundant information and knowledge, as well as having advantages in obtaining resources, controlling information, exerting influence, etc. Therefore, when KD is not high, improving the level of SHs is conducive to the improvement of enterprises’ radical innovation performance. When enterprises’ SH level is low, the knowledge flow between their internal knowledge and external knowledge has not yet been established. At this stage, the process of searching for and matching knowledge becomes redundant, resulting in a low-efficiency knowledge search and high associated costs. In such contexts, the lower DC level can reduce the resource consumption caused by enterprise collaboration. Similarly, the lower KC can minimize the compatibility costs among knowledge elements, and enterprises can fully leverage their existing resources to carry out innovation activities.

Based on this, to enhance radical innovation performance, IU enterprises should give priority to the richness of internal knowledge elements to improve KD. Secondly, enterprises should occupy more positions of third-party nodes, which help them obtain more non-redundant information and improve their SH level. Enterprises with a low level of SHs can reduce their resource consumption and promote their innovation activities by reducing the number of collaboration partners or the degree of interdependence among knowledge fields in order to enhance their radical innovation performance.

Decision rule analysis of IR enterprises

As shown in Fig. 3, both KD and SHs have a great impact on IR enterprises’ radical innovation performance. When the KD level is high, these enterprises have a high probability of obtaining high level of radical innovation performance. When the KD level is low, these enterprises are more likely to obtain low radical innovation performance. When IR enterprises’ KD level is medium, higher SH level leads them to obtain high level of radical innovation performance. When enterprises’ SH and KD levels are both low, IR enterprises have a high probability of obtaining low radical innovation performance.

Fig. 3
figure 3

Decision rules for IR enterprises.

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The diversified knowledge brought about by the high level of KD helps enterprises to better understand, acquire, and apply novel knowledge, thus improving the absorption capacity of enterprises, accelerating knowledge accumulation and reducing learning costs. Secondly, increasing the KD can effectively reduce average R&D costs. The widespread application of diversified technologies in the development of various products not only promotes cost-sharing, but also decreases the investment required for creating new products. Therefore, the level of KD plays a key role in improving the radical innovation performance. Furthermore, enterprises with higher SH level exhibit enhanced resource control capabilities, which subsequently increases the probability of competitive advantage generation. By increasing the access to enterprise resources, the continuous accumulation of resources can be achieved, the information and resources can be effectively matched and integrated, the market identification speed can be improved, and the advantages of SHs can be used to expand the growth space of enterprises in order to promote the improvement of enterprises’ radical innovation performance.

In summary, IR enterprises should enhance their KD level by giving priority to broadening the scope of their technical resources. They should also be familiar with diverse technical domains and search for innovative solutions and ideas to various challenges, as well as trying more pathways to explore new technical domains, providing the necessary conditions for creating new knowledge elements. Furthermore, by strengthening the ability to identify and integrate external information and increasing the degree of information sharing, the collaboration networks can be optimized. Consequently, this help to occupy more SH positions within collaboration networks, leveraging the positive influence of the SH level.

Decision rule analysis of IUR enterprises

As shown in Fig. 4, the KD of IUR enterprises plays a leading role in their radical innovation performance. Enterprises with high KD level are highly likely to achieve high radical innovation performance. When the KD level is low, such enterprises have a high probability of obtaining a low level of radical innovation performance. The reason for this may be that the improvement in KD can bring about a wide range of resources, help to change the existing knowledge structure of the enterprises, promote the breakthrough of the existing thinking model, and lay the foundation for the enterprise to try more paths to explore new technology fields in order to enhance the level of radical innovation. On the contrary, when the KD level is low, the flexibility of enterprises in exploring innovation fields is poor, and they cannot quickly search and accurately identify valuable technical knowledge, which is not conducive to an improvement in the success rate of innovation. When KD is maintained within a certain range, SHs, KC, and DC affect the radical innovation performance of these enterprises. When the SH level is low and the KC level is high, the IUR collaboration enterprise has a high probability of obtaining a low level of radical innovation performance. However, when the SH level is high and the DC level is low, the IUR enterprise has a high probability of obtaining a high level of radical innovation performance. This may be because when the internal knowledge elements of enterprise is maintained at a certain level but is not high, the enterprises that do not occupy a favorable position in the SHs are less likely to have non-redundant and heterogeneous connections, and thus cannot access the differentiated information fields and achieve screening and integration in a timely manner. In this case, blindly improving the complex interdependence between knowledge elements within the enterprise restricts the radical innovation process and reduces its flexibility. In addition, the external collaboration networks tend to be complex, thereby increasing the operational burden and screening costs for enterprises. This also hinders effective internal and external information exchange and resource sharing, ultimately constraining the radical innovation process of these enterprises.

Fig. 4
figure 4

Decision rules for IUR enterprises.

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Therefore, IUR enterprises should concentrate on enriching and optimizing the diversity and dispersion of their own knowledge elements, paying attention to broadening the scope of knowledge accumulation and reducing the learning cost in the innovation process through the construction and reorganization of the knowledge and resources already mastered, so as to provide necessary conditions for enterprises to improve their radical innovation performance. In addition, IUR enterprises with a low level of knowledge richness should first pay attention to improving their dominant position in the network and occupying favorable positions in innovation collaboration in order to improve the efficiency of resource transformation in the network. If the enterprises do not control the important information channels in the network, they should minimize the interconnection of knowledge elements internally in order to reduce the adaptation costs associated with knowledge elements during the innovation process. Simultaneously, the external collaboration strategy should be appropriately adjusted to mitigate the risk of information overload stemming from excessive collaborative relationships and to lower the cost of screening a large volume of innovative resources.

Improvement pathways of enterprises’ radical innovation performance

Based on the analysis of CART decision rules, this section identifies and examines the critical factors and their interactions that influence the radical innovation performance of IU, IR, and IUR enterprises. To comprehensively investigate the multiple pathways through which the structural characteristics of knowledge elements and collaboration networks impact radical innovation performance, as well as to accurately quantify the influence degree between variables, Bayesian network analysis is employed. Through the development of a Bayesian network model, the multiple influencing pathways of the radical innovation performance of IU, IR, and IUR enterprises are systematically elucidated. By conducting an in-depth dependence analysis, the specific interactions between variables are thoroughly examined, leading to a deduction of the characteristic variables that comprehensively uncover their complex underlying mechanisms.

Development of Bayesian network model for IU, IR, and IUR enterprises

Initially, this study selects three representative decision rules that, respectively, represent IU, IR, and IUR enterprises, based on the support degree and confidence degree. Subsequently, Bayesian network analysis is conducted. The selected decision rules are presented in Table 2.

Table 2 Representative decision rules of radical innovation performance.
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The construction process of a basic Bayesian network model is described as follows. Initially, data from relevant enterprises and associated variables are selected based on three representative decision rules. Subsequently, the relevant node variables within the Bayesian network undergo discretization. Common discretization methods include equal-width, equal-frequency, and one-dimensional attribute clustering. In this study, to ensure that the classification results of enterprises’ radical innovation performance align with real-world management scenarios, the median of the focal enterprises’ radical innovation performance was used as the standard. Data with enterprises’ radical innovation performance above the median were assigned a value of 1, while data below the median were assigned a value of 0, corresponding respectively to high and low radical innovation performance. This process finalized the grading of enterprises’ radical innovation performance. By employing this method, we effectively avoided the interference of extreme values and ensured that the sample sizes of the high-performance and low-performance groups were roughly balanced, which enhanced the robustness and comparability of the classification results, aligning with the conventional logic of binary performance evaluation in management practice. Following this, Bayesian network structure training was performed on the relevant variables using the hill-climbing algorithm, obtaining an optimally fitted Bayesian network topology. Given that Netica, which is a Bayesian network analysis software, offers ease of operation, superior visualization capabilities, and the rapid presentation of prior and conditional probabilities for each node, it has been chosen for parameter learning to establish the sequential dependence relationships between variables. Ultimately, the basic Bayesian network models relating to the radical innovation performance of IU, IR, and IUR enterprises can be obtained, as illustrated in Figs. 5a, b and c.

Fig. 5
figure 5

Learning results of Bayesian network topological structure parameters for (a) IU enterprises; (b) IR enterprises; and (c) IUR enterprises.

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As illustrated in Fig. 5a, b and c, there are two pathways for IU enterprises to achieve radical innovation performance—”SHs → RIP” and “KD → RIP.” Both SHs and KD have a direct influence on radical innovation performance. Similarly, as with IR enterprises, these two pathways also hold true, whereby the variables of SHs and KD directly impact radical innovation performance. IUR enterprises can enhance their radical innovation performance through five distinct mechanisms. Among these, KD, SHs, and KC exert direct effects on radical innovation performance. Specifically, the relationships can be articulated as follows: “KD → RIP”, “SHs → RIP”, and “KC → RIP”. Moreover, KD and KC indirectly impact enterprises’ radical innovation performance via SHs, that is, “KD → SHs → RIP” and “KC → SHs → RIP”.

To determine the state characteristics under which variables in different types of enterprise groups are most conducive to enhancing radical innovation performance, as well as to understand the impact of each characteristic variable on radical innovation performance, this study utilizes Netica software for variable inference analysis. This analysis is conducted based on the prior probabilities of node variables within a Bayesian network, with the goal of deriving the posterior probabilities of the corresponding variables. To measure the degree of mutual influence between Bayesian network nodes, the dependence level between Bayesian network variables is defined as follows:

$$\phi = \frac{{\chi_{s}^{1} - \chi_{s}^{0} }}{{\chi_{f}^{1} - \chi_{f}^{0} }} \times 100\%$$
(6)

In the Bayesian network, \(\chi_{s}\) denotes the neutron node, where \(\chi_{s}^{1}\) and \(\chi_{s}^{0}\) represent the probabilities of the child node before and after the change, respectively. \(\chi_{f}\) signifies the parent node within the Bayesian network, with \(\chi_{f}^{1}\) and \(\chi_{f}^{0}\) indicating the probabilities of the parent node before and after the change, respectively.

Bayesian analysis of IU enterprises

By adjusting the probability of the parent node and applying the dependence analysis (Formula (6)) to the variables within the Bayesian network, the results presented in Table 3 were ultimately obtained. According to the analysis depicted in Fig. 6, when the probability of a high SH level status reaches 100%, the probability of a high enterprise radical innovation performance increases from 84.2% to 89.7%. The dependence between the SH level and radical innovation performance is found to be 16.5%. Since the KD level for enterprises that adhere to this rule is already at a high level, Bayesian inference cannot be conducted on these cases.

Fig. 6
figure 6

The variable inference of IU enterprises. The forward inference results of a high level of SHs within a Bayesian network.

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Based on the above analysis, IU enterprises that occupy SH positions can acquire diverse knowledge elements and technologies from their collaboration partners. This strategic positioning grants these enterprises an informational control advantage, thereby providing robust support for their innovation activities, facilitating an enhanced radical innovation performance. Furthermore, enterprises positioned in structural holes within IU collaboration networks can promptly receive differentiated information, enabling effective screening and integration. By filtering out redundant information flows, management can focus more effectively on innovation activities. In summary, SHs have a positive impact on the radical innovation performance of IU enterprises. Therefore, while maintaining a high level of KD, these enterprises should proactively seek to occupy SH positions within the network and enhance their capabilities in managing redundant information to further enhance radical innovation performance.

Bayesian analysis of IR enterprises

The results presented in Table 3 are derived through the probability adjustment and dependence analysis of the parent node. A detailed examination of Fig. 7a, b reveals that within IR enterprises, when the probability of a high KD level reaches 100%, the probability of achieving a high radical innovation performance increases from 70.5% to 70.6%. However, the dependence between these variables remains relatively low, at 0.4%. Conversely, when the probability of a high SH level reaches 100%, the probability of achieving a high radical innovation performance decreases from 70.5% to 68.2%, indicating a negative dependence level of -9.5% between the SH level and radical innovation performance.

Fig. 7
figure 7

The variable inference of IR enterprises. (a) The forward inference results of a high level of SHs within a Bayesian network. (b) The forward inference results of a high KD level within a Bayesian network.

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It is evident that most IR enterprises possess a relatively high KD level. Consequently, as the KD level increases, the potential combinations of knowledge elements increase, thereby raising the complexity of innovation activities. Simultaneously, it also requires enterprises to spend more resources and efforts on comprehending and absorbing existing knowledge, which escalates the costs associated with identifying, integrating, and utilizing these knowledge elements. In this situation, enhancing the KD level has little effect on enhancing radical innovation performance. The acquisition of more heterogeneous information and knowledge increase the cognitive costs of enterprises. Moreover, not all the heterogeneous information and knowledge obtained by enterprises are valuable. Their screening of a large number of resources may bring about the risk of information overload, which is not conducive to enhancing radical innovation performance. Therefore, in this situation, improving the SH level of IR enterprises has a negative impact on their radical innovation performance. IR enterprises should first make full use of the existing resources to carry out innovation activities, improve the capabilities to integrate and filter knowledge elements, and rationally plan and allocate enterprises’ resources, rather than blindly occupying too many SH positions.

Bayesian analysis of IUR enterprises

Based on the results shown in Table 3 and Fig. 8a, b, and c, within the context of IUR enterprises, when the probability of high KD level reaches 100%, the probability of a high radical innovation performance decreases from 28.2% to 23.8%. A dependence analysis between characteristic variables and enterprises’ radical innovation performance reveals that the dependence between KD and radical innovation performance is − 6.0%. Furthermore, when the probability of high KC level is increased to 100%, the probability of a high radical innovation performance decrease from 28.2% to 23.8%, with a dependence of − 11.3%. This indicates that the impact of KC on radical innovation performance is more significant than that of KD. Both factors influence the child nodes by affecting the SH level of intermediate nodes. However, the dependence between the SHs and the radical innovation performance of IUR enterprise is zero, indicating that this variable has a negligible direct effect on radical innovation performance.

Fig. 8
figure 8

The variable inference of IUR enterprises. (a) The forward inference results of a high KD level within a Bayesian network. (b) The forward inference results of a high level of SHs within a Bayesian network. (c) The forward inference results of a high KC level within a Bayesian network.

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In summary, due to the excessively high KD level of IUR enterprises, the efficiency of knowledge integration diminishes while the coordination costs increase, thereby affecting the radical innovation performance level. As the KC level increases, the interconnections between various knowledge elements utilized in R&D become more intricate. Changing the knowledge elements within one domain may involve changes across multiple domains, increasing the integration cost of these knowledge elements. The unpredictable outcomes of embedding new knowledge increase the uncertainty of innovation activities and increase the R&D risks for enterprises. IUR enterprises generally exhibit a high SH level, occupying advantageous positions within the network and possessing abundant resources. Compared to IU and IR enterprises, IUR enterprises have access to a broader and more diverse range of resources. Therefore, IUR enterprises should focus more on the innovation and integration of existing resources rather than continually seeking new knowledge elements and resources externally.

Result analysis

Through the dependence analysis among IU, IR, and IUR enterprises, the influence of variables on radical innovation performance is summarized in Table 3. A higher level of dependence indicates a stronger impact of the variable on radical innovation performance, whereas a lower level signifies minimal impact. For IU enterprises, the change of high-level state of SHs has a significant positive impact on enterprises’ radical innovation performance. The dependence between SHs and radical innovation performance is as high as 16.5%, which is at the high dependence level. This implies that for IU enterprises, occupying SH positions enables them to access diverse knowledge sources, control technical information, screen and integrate differentiated information, and focus managerial attention on innovation, thereby enhancing radical innovation performance. Therefore, IU enterprises should proactively seek to occupy SH positions within the network and improve their capacity to manage redundant information. For IR enterprises, the impacts of SHs and KD on radical innovation performance present different characteristics. The dependence between SHs and radical innovation performance is − 9.5%, reflecting a relatively significant negative dependency. This means that for IR enterprises, an increase in the SH level actually results in a marked decline in radical innovation performance. The change of high-level state of KD has a relatively weak impact on the radical innovation performance, with the dependence of only 0.4%, which is at the low dependence level. This indicates that the impact of KD on radical innovation performance of IR enterprises is relatively limited. For IR enterprises, the high KD level increases the complexity and cost of innovation, with limited positive effects on radical innovation performance. Although a high SH level provides heterogeneous information, it also increases cognitive costs and the risk of information overload, negatively impacting radical innovation performance. Consequently, this group of enterprises should prioritize the utilization of existing resources, enhance knowledge integration and filtering capabilities, and allocate resources rationally to avoid blindly occupying too many SHs. For IUR enterprises, the analysis results show that KD and KC have a negative impact on radical innovation performance. The improvement of their high-level state lead to a reduction in the possibility of high radical innovation performance. Among them, the dependence between KD and radical innovation performance is − 6.0%, which is a relatively moderate level of negative dependence. The dependence between KC and radical innovation performance is -11.3%, which is a relatively high level of negative dependence. Within the IUR enterprises, the dependence between SHs and radical innovation performance is 0%, indicating that there is no dependence relationship between the two. For IUR enterprises, the high KD and KC levels can reduce integration efficiency, increase coordination and adaptation costs, and heighten the uncertainty of innovation activities and R&D risks. Given that these enterprises typically hold advantageous positions in the network and possess rich and diversified resources, they should focus more on innovating and integrating existing resources rather than continuously acquiring new knowledge elements.

Table 3 Dependence analysis between characteristic variables and the radical innovation performance of IU, IR, and IUR enterprises.
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Conclusions and discussions

Conclusions

This study takes SRDI enterprises as the research object, and constructs IU collaboration networks, IR collaboration networks, and IUR collaboration networks according to different types of external collaboration partners. Secondly, based on the SNT and KBV, DC and SHs are selected as the structural characteristics of external collaboration networks, while KD and KC are selected as the structural characteristics of internal knowledge elements. Furthermore, the CART algorithm is used to dig deeper into enhancing the pathways relating to the radical innovation performance of IU, IR, and IUR enterprises. Finally, Bayesian network analysis is used to analyze the complex mechanism through which the structural characteristics of knowledge elements and collaboration networks affect enterprises’ radical innovation performance. The main conclusions of this study are as follows.

IUR enterprises have a higher probability of obtaining a high radical innovation performance than IU or IR enterprises, and the average level of IUR enterprises’ radical innovation performance is also higher than that of IU or IR enterprises. Specifically, IUR enterprises demonstrate superior capabilities in resource integration. They simultaneously and effectively leverage the research resources of universities, the expertise of research institutes, and the market insights and practical capabilities of enterprises. The close collaboration among these three parties generates stronger synergistic effects, enhancing radical innovation performance. Consequently, IUR enterprises are more likely to achieve a higher innovation performance than IU or IR enterprises, which collaborate with only one type of partner. This limitation results in less diverse knowledge elements, thereby hindering the enhancement of radical innovation performance.

There are large differences in the factors influencing the radical innovation performance of enterprises adopting heterogeneous collaboration patterns. For IR enterprises, the higher level of KD and SHs has a greater effect on the enhancement of radical innovation performance. For IU and IUR enterprises, KD plays a dominant role in radical innovation performance, while KC, DC, and SHs play moderating roles. KD serves as the pivotal factor influencing radical innovation performance, while enhancing the richness and dispersion of knowledge elements is key to improving the radical innovation performance of enterprises adopting heterogeneous collaboration patterns. In contrast, although collaboration networks can help enterprises enhance external non-redundant and heterogeneous links to collect resources and support for innovation activities, the acquisition of diversified non-duplicative knowledge and technologies to construct new concepts, discover new methods, and create new opportunities is the key to directly promoting radical innovation performance. Therefore, enterprises should prioritize internal knowledge accumulation and integration, while not neglecting the construction of external collaboration networks.

The influence of characteristic variables on radical innovation performance varies significantly among enterprises adopting heterogeneous collaboration patterns, and the management strategies and measures that enterprises should adopt are different. While maintaining a high level of KD, IR enterprises should take the initiative to occupy SH positions in collaboration networks and improve the ability to process non-redundant information. Meanwhile, IU enterprises should make full use of the existing resources, enhance their capability to integrate and filter knowledge, and avoid occupying too many SHs in the collaboration networks. IUR enterprises generally have higher SH level and occupy favorable positions in the collaboration networks. The resources they own are more diverse than those in IU and IR enterprises. Therefore, they should focus on making full use of their existing knowledge elements rather than continuously acquiring them externally. In summary, enterprises adopting heterogeneous collaboration patterns should identify their own strengths, weaknesses, and positioning, as well as optimizing their resource allocation to enhance their radical innovation performance.

Theoretical contributions and managerial implications

The main contributions of this study are as follows. (1) Based on the KBV and SNT, this study explores, from a comprehensive perspective, how the internal knowledge elements and external collaboration networks interactively affect enterprises’ radical innovation performance. By incorporating internal and external factors into the same research framework and exploring their interactions, more credible research conclusions can be obtained, which provide new insights and perspectives for related research. (2) The CART algorithm is used to explore the interactive effects of the structural characteristics of knowledge elements and collaborative networks on the radical innovation performance of IU, IR, and IUR enterprises, which makes up for the limitations of traditional empirical research in presenting the complex nonlinear relationships between variables. (3) Bayesian network analysis is used to reveal the multiple pathways relating to enhancing the radical innovation performance of IU, IR, and IUR enterprises, which enriches and complements research on the complex influencing mechanisms of enhancing enterprises’ radical innovation performance. It also provides theoretical references for enterprises to formulate and optimize resource allocation plans that are suitable for their individual development.

The managerial implications of this study for the enterprises and government departments involved in the heterogeneous collaboration patterns are as follows.

For enterprises adopting heterogeneous collaboration patterns, they should focus on enhancing the synergy and mutual promotion of internal and external R&D forces, especially those relating to the accumulation of the richness of their own R&D knowledge elements. On the one hand, enterprises should adopt a more open and diversified attitude, actively communicating closely with universities and research institutes. For instance, enterprises can establish regularized “University-Enterprise Joint Laboratories” or launch “Visiting Researcher Programs”, and introduce external intellectual resources through institutionalized manner to achieve complementary R&D of key technologies and sharing of research achievements. On the aspect of knowledge management, the more knowledge elements enterprises have at their disposal and the more technological areas they cover, the more leeway and flexibility they have in choosing areas of innovation, and the more successful they are in doing so. However, this advantage also presents the management of the enterprises with complex challenges, such as the difficulty of knowledge integration, the complication of the decision-making process, and the rising cost of communication. Therefore, enterprises can establish an inter-departmental knowledge bases and technology map systems within their organizations to structurally archive and link the diverse knowledge introduced, thereby enhancing the retrieval efficiency and combination potential of technical elements. In addition, enterprises should attach importance to enhancing the comprehensive capabilities of their technology departments, promoting the sharing and reuse of knowledge and technology within enterprises to the greatest extent, further improving the integration efficiency of innovation resources, and ultimately significantly enhancing the enterprises’ radical innovation performance.

For some enterprises that only collaborate with universities or research institutes, they should broaden the scope of collaboration targets and actively collaborate with multiple partners to enrich the heterogeneity and KD level of their own knowledge. On the one hand, enterprises can set clear “heterogeneous collaboration indicators” every year, such as conducting substantive R&D projects with at least two types of new institutions, to promote the continuous updating of knowledge structures through institutional requirements. On the other hand, the research ideas and perspectives of universities and research institutes are different from those of enterprises, so actively carrying out heterogeneous external collaboration can promote the cross-fertilization of different research dimensions, facilitate the transformation and application of scientific and technological achievements, and ultimately help enterprises to acquire new management ideas and further enhance their radical innovation performance. Additionally, enterprises can regularly hold interdisciplinary innovation camps, inviting university researchers and enterprise R&D teams to participate together. By implementing the effective reward mechanisms, they can stimulate breakthrough thinking and set up internal innovation incubation funds to support early-stage ideas with cross-disciplinary characteristics, thereby promoting the improvement of radical innovation performance.

In addition, for relevant government departments, they should actively promote the industry–university–research institute collaborative innovation mechanism, establish a “regional industry–university–research institute integrated digital platform” or innovation alliance, constantly expand the in-depth collaboration and integration among enterprises, universities and research institutes, integrate the technical needs of enterprises, scientific and technological achievements of universities and expert resources, provide one-stop services of online matching, collaboration signing and project management, and reduce the cost of collaboration initiation and coordination. Government departments can provide guarantees in terms of policy guidance, financial support, and resource allocation to form a good situation of complementary advantages and collaborative innovation among heterogeneous collaboration partners. On this basis, the government can also set up special funds for industry–university–research institute collaboration projects, establishing evaluation and incentive mechanisms for the transformation of scientific research results, as well as other measures to guide universities and research institutes to break through the traditional closed R&D model, focus more on market demands to carry out application-oriented innovation, and continuously stimulate the vitality of universities and research institutes in participating in the industrial innovation and development.

Innovations and limitations

The main innovations of this study are as follows. Firstly, focusing on the three main partners in heterogeneous external collaboration—enterprises, universities, and research institutes—and dividing them into three collaboration patterns of IU, IR, and IUR, this study uses the CART algorithm to analyze the multi-factorial combination of influences on the radical innovation performance of enterprises adopting three heterogeneous collaboration patterns, as well as the complex nonlinear relationships between the variables, in order to make the conclusions of this study have a high reference value, which makes up for the limitations of traditional regression analysis that ignore the internal and external heterogeneity of enterprises and lack specificity. Secondly, from the perspective of the interaction between the internal knowledge elements and the external collaboration networks, Bayesian network analysis reveals the key factors and pathways influencing how enterprises enhance radical innovation performance. This involves communicating, collaborating, and acquiring information from external partners, while internally absorbing, transforming, and updating knowledge, leveraging the complementary roles of both. To a certain extent, the findings of this study promote the integration of the SNT and KBV, as well as laying the foundation for further investigation into the influence mechanism between variables.

This study also has several limitations that provide excellent opportunities for future research. First of all, this study focuses primarily on the static analysis rather than dynamic analysis. This research approach fails to fully consider the impacts of the dynamic temporal evolution of knowledge elements and collaboration networks in the process of industry-university-research institute collaboration on enterprises’ radical innovation. Future research can introduce AI-driven dynamic network analysis methods, incorporate time series factors into the research scope based on real-time data to conduct dynamic analysis, ultimately achieving more precise and rigorous research conclusions. Secondly, in order to focus on analyzing the core mechanism of industry-university-research institute collaboration, this study only retained the collaborative patents between enterprises and universities and research institutes during the patent data processing. However, the exclusion of non-IUR collaborative patents may, to a certain extent, introduce selection bias, ultimately affecting the generalizability of conclusions. Furthermore, only patents data are used to measure the enterprises’ knowledge elements, collaboration networks, and radical innovation performance. However, patents represent only one form of radical innovation performance and reflect merely explicit knowledge rather than tacit knowledge, and enterprises’ collaborative outcomes actually encompass multi-dimensional output forms, such as academic papers and copyright registrations. Therefore, future research could adopt more comprehensive data and incorporate more abundant data sources to measure relevant variables, so as to further enhance the robustness and generalizability of the research conclusions. In addition, there are many internal and external influencing factors that affect enterprises’ radical innovation performance, such as R&D investment intensity, market environment dynamics, government policies, etc. Future research perspectives could be further broadened and more dimensions of variables should be adopted to analyze the effective pathways for enterprises to more comprehensively achieve high-level radical innovation performance.