## 2 Preliminaries
### Problem Definition
Unlike the binary relevance (BR) method [26], hierarchical multi-label classification decomposes the classification problem with \(n\) labels into an \(n-m\) multi-class classifiers problem where \(n=|C_{T|}\) is the total number of labels including the root node of the label tree and \(m=\)\(|L|\) is the total number of label leaf nodes. According to Definition 2, HTMC-PGT aims to have text with a unique leaf node label. Therefore, from the perspective of leaf node sets alone, HTMC-PGT can be considered a single-label classification, also called the \"flat classification approach\" [27]. However, owing to the imbalanced distribution of label semantics, single-label classification methods often fail to achieve satisfactory classification results. At the same time, it is also impossible to model the problem as a holistic solution that integrates hierarchical label trees and document semantics, as proposed in [24; 28; 29]. Therefore, it is necessary to start from the root node of the label tree and construct a multi-class classifier to gradually reduce the target leaf node label set until the final target label is obtained (Figure 3). **Definition 3 (HTMC-PGT Problem). **_Let \(X\) be the feature vector of a given poverty governance text. Each classifier in the classifier tree shares \(X\) as the input parameter._  
\[\hat{y}_{j}=C_{j}(x)=argmin\;H_{j}(x,y)\quad for\;index\;j=1,\ldots,\left|n-m\right| \tag{2}\]  
In Equation (2), \(\hat{y}_{j}\) is the classification result of feature vector \(x\) in the multi-class classifier \(C_{j}(\cdot)\). \(H_{j}\) is the cost function of the classifier \(C_{j}(\cdot)\). By transforming the classification problem into a minimum cost function problem using \(H_{j}(\cdot)\), the optimal classification result can be obtained. Based on the classification results of the previous classifier, the next classifier can be determined and used to continue classifying text feature vector x. Given a poverty governance text set D and the corresponding hierarchical label tree structure \(\mathcal{T}=(C_{T},\prec)\), first, text set \(\mathcal{D}\) is divided into multiple text sets \(\mathcal{D}_{i}\) based on the classifier set, whereas \(C_{T}\) is divided into several corresponding label sets \(C_{T|}\). The goal of  
Figure 3: Multi-class classifier tree. HTMC-PGT is to learn the parameter \(\Theta_{i}\) of the classifier model \(\Omega_{i}\) based on the text set \(\mathcal{D}_{i}\) and corresponding multiple labels \(C_{Ti}\), and ultimately predict the label sequence of a document using the model in the hierarchical classifier tree. To improve the performance of classifiers with a small sample number \(|\mathcal{D}_{i}|\), this study adopts the method of transfer learning between classifiers, that is, the model parameter \(\Theta_{i}\) of the parent node in set \(S\) is taken as the initial value of the model parameter of the child node, and the training effect of the child node is improved through incremental calculations:  
\[\Omega_{i}(\mathcal{D}_{i},\Theta_{i},\Theta_{ip})\longrightarrow C_{Ti} \tag{3}\]  
where \(\Theta_{ip}\) is the parameter set of the parent node of this classifier in the classifier tree and \(i=1,\cdots,|R\bigcup S|\). The HTMC-PGT problem requires solving Equations (2) and (3) and forming a classifier tree \(\mathrm{Y}=(\Theta,\prec)\), which can be used to classify any PGT:  
\[\Omega(D,Y)\longrightarrow C_{S} \tag{4}\]