## 3 Research Process
### Research Methodology
#### 3.3.2 Similarity Calculation Based on Weighted Vectors  
Although there are certain semantic deviations between academic papers and patent research in the representation of scientific concepts and the system of technical terms, the basic concepts and context within specific fields remain unchanged. Contextual semantic modeling can effectively compensate for the differences in expression between papers and patents. Word2 vec [35; 36] is a deep learning algorithm launched by Google in 2013. It learns the semantic information of words from a large amount of text data in an unsupervised manner and transforms words into real-valued vectors through training, which can capture the semantic connections between words without clear labels. Word2 vec provides two language training models, CBOW and Skip-gram. The CBOW model can use context words to predict the central word, while the Skip-gram model can predict context words based on the central word. In this part, we aim to conduct a similarity calculation of the central words (i.e., topic words) based on weighted vectors, which is similar in principle to the Skip-gram model. Therefore, this paper selects Skip-gram in Word2 vec to generate keyword vectors.  
This paper first takes the preprocessed global stage dataset of science and technology as word vectors to train the data. Then, Python (python 3.8.0) language is used to train word vectors and construct a word vector model based on them. Secondly, we use the trained word vector model to represent the scientific and technological topic words obtained from clustering in a vectorized form, generating corresponding word vectors for each topic word. Subsequently, we take the probability of the topic words extracted by LDA as weights, multiply them with the corresponding word vectors of the Word2 vec model, and then perform a weighted sum to obtain the vectorized representation of scientific topics and technological topics. The specific calculation process is shown in Equation (1).  
\[W_{z}=P(w_{1}|z)\times w_{i_{1}}+P(w_{2}|z)\times w_{i_{2}}+\cdots+P(w_{k}|z) \times w_{i_{k}} \tag{1}\]  
In Equation (1), \(W_{z}\) represents the vectorized representation of topics, \(z\) denotes a topic, \(i_{k}\) represents a topic word, and \(W_{k_{i}}\) indicates the corresponding word vector of the topic word. \(P(w_{k}|z)\) is the weight value of the word vector and the probability value of the topic \(w_{k}\).  
This paper calculates the similarity of science-technology topics through cosine similarity. Specifically, the first scientific topic is calculated for cosine similarity with all patent topics. Then, the second scientific topic is calculated in the same way as all patent topics successively, and so on, until all scientific topics have been included in the calculation with all patent topics. The calculation formula is shown as follows.  
\[Similar(W_{z1},W_{z2})=\text{Cosine}(W_{z1},W_{z2}) \tag{2}\]  
Equation (2) measures the similarity between two vectors by calculating the cosine of the angle between them. The cosine value of the angle between two vectors ranges from 0 to 1. When the cosine value approaches 1, it means that the two vectors are highly similar. Conversely, when the cosine value is far from 1, it indicates that there are significant differences between the two vectors [37].