## 3 Methods
### Co-Word Relation Feature Extraction Based on GCN  
First, we used _TF-IDF_ to identify the words with high occurrence frequency as industry characteristic keywords. Then, we constructed a co-word relation graph where enterprise names are nodes and keywords are edges. Finally, we applied GCN to aggregate neighbor information and extracted features from the co-word relation graph. (1) Keyword extraction  
_TF-IDF_ is a text feature selection method based on statistics and is used to evaluate the importance of words [33]. _TF_ stands for word frequency, which refers to the frequency of a word appearing in an article, while _IDF_ is the inverse text frequency index, which represents the frequency of a keyword appearing in the corpus. If a word appears frequently in an article and rarely appears in other articles, it is considered to have good discriminative ability and can be used as a feature of the article to represent it. Enterprise names generally include industry or business characteristics, so enterprises in related industries may have the same business characteristic words; for example, the textile industry generally has names that contain \"textile\", \"knitting\", and other keywords, which can be used to create a co-word graph. Through the statistical analysis of enterprise names, it was found that they also contain information such as the location and nature of the enterprise (such as limited liability companies or limited companies). Traditional statistical methods can only count high-frequency words representing the industry based on the frequency of word occurrence, making it difficult to mine high-frequency words that can distinguish them from other industries. Therefore, this section introduces the _TF-IDF_ algorithm to mine high-frequency words that can represent industry characteristics. The calculation steps for high-frequency words based on industry characteristics using the _TF-IDF_ algorithm are as follows:  
1. Assuming industry category C, the formula for calculating the _TF_ value of word frequency for this industry category is shown in Equation (2):  
Figure 1: BERT-GCN model technical flow chart. \[TF_{i}=\frac{t_{i}}{M} \tag{2}\]  
where \(t_{i}\) represents the number of times word \(i\) appears in industry category C, and \(M\) is the total number of words obtained by segmenting the names of companies in that industry category. * The corresponding _IDF_ value can be obtained by dividing the total number of industry categories by the number of industry categories containing word \(i\), and then taking the logarithm. The calculation formula for _IDF_ is shown in Equation (3): \[IDF_{i}=lg\frac{N}{n+1}\] (3) where \(N\) is the total number of industry categories; \(n\) is the number of industry categories that contain the word \(i\) (If all industry categories do not contain the word \(i\), the denominator is 1). * The formula for calculating the _TF-IDF_ value of word \(i\) is shown in Equation (4): \[TF\text{-}IDF_{i}=TF_{i}\times IDF\] (4) After calculating the _TF-IDF_ values of each word, keywords that represent industry characteristics can be selected based on a threshold. * Co-word features extraction When a keyword co-appears in two enterprise names, it is assumed that there is a co-word relation between the two enterprises. Based on this, we constructed a co-word relation graph and used a GCN to extract co-word features. A GCN is a type of deep learning model specifically designed for processing graph data and includes nodes, edges, and features. The GCN can extract features from the graph and generate corresponding representation vectors, mainly used for processing data with generalized topological graph structures. The GCN starts with a node and performs convolution operations on the feature information of adjacent nodes, propagating the node information to the surrounding area, so that each node can not only utilize its own features, but also the features of its neighboring nodes.