## 3 Proposed Method
### Search and Evaluation of the Cross-Domain Knowledge  
The patent database contains more than 90% of the world technical information, providing a wealth of resource for the acquisition of cross-domain knowledge [65; 66]. At the same time, the number of patents distributed in different patent classes reflects the technological focus and advantages of firms [67]. More importantly, the patent activity can characterize the knowledge base in most industries that actively pursue R&D and engage in cross-industry research to explore new technologies [68; 69]. Therefore, we use a patent database as a knowledge storage pool to capture cross-domain knowledge for RCG. The details are as follows:  
1. Identifying related patents and firms. In order to accurately search for cross-domain knowledge, it is necessary to establish and combine keywords or technical language to describe the main function of the target subsystem based on the next-generation technology. With the description and constraints of the keywords and technical language, firms with patents related to the next-generation technology are captured in the patent database. We define them as related patents and related firms. It is important to note that these related firms should belong to different industries from the target firm in the retrieval process. For example, if a traditional car firm (target firm) wants to develop an electric vehicle, it had better look for firms related to battery technology development rather than automobile firms. 2. Technological position description. Representation of technological status of a firm is based on the technological space described by patents and International Patent Classification (IPC) codes [70]. According to the IPC codes, patents are divided into eight categories (A, B, C, D, E, F, G, H) in 120 subcategories [71]. Each firm occupies its unique position based on its technological knowledge characterized by its patent classification and patent portfolio. The technological position of a firm can be represented by a vector \(P\) as follows: \[P=(P_{1},P_{2},\ldots P_{k},\ldots,P_{n}),P_{k}\geq 0,\sum_{k=1}^{n}P_{k}=1\] (1)  
Figure 4: Determination of directions of cross-domain knowledge. where \(P\) is the technical position of the firm, \(k\) is the classification number of the patent, \(P_{k}\) is the ratio of the number of patents under classification k to the total patents of the firm, \(n\) is the total number of patent classifications of the firm. 3. Measuring technological distance. According to the minimal complementary distance measure [59], the technological distance between firm \(I\) and firm \(J\) can be decided as follows. \[M\big{(}P_{I},P_{J}\big{)}=1-\sum_{k=1}^{n}min\big{\{}P_{lk},P_{lk}\big{\}}\] (2) where \(M\) is the technological distance between firms \(I\) and firm \(J\), \(P_{I}\) is the technical position of the firm \(I\), \(P_{J}\) is the technical position of the firm \(J\). \(M\)\(\in\) [0,1], and when \(M\) = 0 the technological distance between the two firms is the closest. 4. Appropriate cross-domain knowledge. Technological distance affects both knowledge acquisition and innovation performance, but there are two opposing mechanisms at work, as described in the first paragraph of 2.3 [72]. That is why the relationship between technological distance and innovation performance is an inverted U-shaped curve, as illustrated in Figure 5.  
Obviously, ideal firms that provide appropriate cross-domain knowledge should be those close to the optimal technological distance 0.5 under ideal conditions. In fact the optimal distance is not unique and constant, because the desire for innovation (Novelty Value) and employee learning ability (Absorptive Capacity) of the firms is not absolutely reciprocal. [PERSON] et al. [53] tested the relation between cognitive distance and innovation performance of firms engaged in technology-based alliances and pointed out that the optimal cognitive distance at the mean value of technological capital is 38.4 on a scale between zero and hundred.