## 3 Research Framework and Methodology
### Patent Technological Subject Acquisition Based on the LDA Model  
In order to extract technological topics from a vast amount of patent text data, the classification of all patents' technological texts is performed by utilizing the LDA topic analysis algorithm. The LDA algorithm is a text topic generation model and an unsupervised machine learning algorithm [56]. It adopts a multilayer probabilistic model with a three-layer structure comprising words, documents, and topics. LDA assumes that words are generated from a mixture of topics, and each topic is generated by a polynomial distribution over a fixed word list. These topics are shared across all documents in the dataset. The generation process of the LDA topic model is depicted in Figure 2.  
Figure 1: Research framework. Figure 2: LDA model. Suppose a collection of patent documents, \(D=\{d_{1},\,d_{2},\,...,\,d_{M}\}\), \(N_{m}\) represents the number of words in the \(m\)th document, \(t\) denotes the number of topics, \(T_{m,n}\) is the \(n\)th topic in the \(m\)th patent document, and \(w_{m,n}\) is the \(n\)th word in the \(m\)th document. Here, \(\varphi_{k}\) is a parameter obeying a Dirichlet distribution with \(\beta\), and \(\theta_{m}\) is a parameter obeying a Dirichlet distribution with \(\alpha\). Given a set of one document, \(w_{m,n}\) are the observed known variables, \(\beta\) and \(\alpha\) are the a priori parameters given based on manual experience, and \(T_{m,n}\), \(\varphi_{k}\) and \(\theta_{m}\) are unknown implicit variables. Two main parameter inference methods, variational Bayesian inference and Gibbs sampling, are used for the subject model [57]. The algorithm of variational Bayesian inference is characterized by its myopic nature, as it approximates the expressions of posterior probabilities for model parameters using a straightforward variational distribution. Through the iterative application of the EM algorithm, it aims to maximize the variational lower bound to estimate the parameters. On the other hand, Gibbs sampling is a stochastic algorithm that relies on samples drawn from a Markov chain. In comparison to variational Bayesian inference, the Gibbs sampling algorithm is considered simpler and more user-friendly. As a result, LDA topic models often favor the adoption of Gibbs sampling. It should be noted that the superiority of the LDA topic representation results is significantly influenced by the number of different topics, which must be predetermined using the LDA algorithm [58]. Currently, various metrics exist to determine the number of topics, including coherence and perplexity. Coherence has high computational complexity and is suitable on large-scale datasets. By contrast, perplexity has a higher recall rate and efficiency, which is more prominent in long texts such as patent technology texts and is a common determination index [59]. Therefore, the perplexity index is introduced to measure the superiority of the subject modeling results, enabling the assessment of the model's predictive ability for uncertain data. The formula for calculating perplexity is as follows:  
\[Perplexity(D)=\exp\left\{-\frac{\sum\limits_{m=1}^{M}\log p(w_{m})}{\sum \limits_{m=1}^{M}N_{m}}\right\} \tag{1}\]  
where \(D\) denotes the test set in the corpus, \(\sum\
olimits_{m=-1}^{M}N_{m}\) denotes the number of words in the entire test dataset, and \(p(w_{m})\) refers to the probability of occurrence of word \(w_{m}\) in the test set. It can be seen that the confusion formula is primarily based on the information entropy, and the entropy obtained from the number of topics is evaluated by calculating the probability of word occurrence across different topics. A lower perplexity indicates a more effective outcome in terms of topic clustering. While LDA can provide a substantial number of technological topics, there are often duplicates among these topics [59]. To address this, manual detection is employed to identify and merge similar topics, followed by the individual marking of technological classifications for each patent.