# Named Entity Recognition Method Based on Multi-Feature Fusion
## 3 Research Design
### Stage 1: NMF Topic Clustering Model  
Non-negative Matrix Factorization (NMF) is a matrix decomposition method based on linear algebra, first proposed by [PERSON] and [PERSON] in 2000 [PERSON] and [PERSON] (2000). NMF is mainly used to extract features from high-dimensional data. Its characteristic is that the elements of the matrix after decomposition are non-negative, which is suitable for fields that need to maintain data non-negativity, such as image analysis, text mining and bioinformatics. The basic idea of NMF is to decompose a non-negative matrix V into two non-negative matrices W and H, that is:  
\[\mathrm{V_{m\times n}}\approx\mathrm{W_{m\times r}}\times\mathrm{H_{r\times n}} \tag{1}\]  
The matrix V is the original data matrix, and its background space is \(\mathrm{R_{+}^{m\times n}}\), which represents a non-negative real matrix of m\(\times\)n, where m represents the number of documents and n represents the number of words; the background space of the matrix W is \(\mathrm{R_{+}^{m\times r}}\), where r represents the number of topics and each column of the matrix W represents the distribution weight of each topic in all documents, which is the topic distribution of the documents; the background space of the matrix H is \(\mathrm{R_{+}^{r\times n}}\), and each row of the matrix H represents the weight distribution of a certain topic to all words. When processing text, NMF transforms the topic identification problem into a constrained optimization problem to solve it. Topic identification is achieved through a matrix decomposition calculation, in which clusters are interpreted as topics and each document is regarded as a cumulative combination of multiple overlapping topics [PERSON] and [PERSON] (2000). The goal of NMF is to achieve optimal decomposition by minimizing the reconstruction error between the original matrix V and its decomposition result:  
\[\mathrm{min}_{W,H}\Big{|}\big{|}V-W\cdot H\big{|}\big{|}_{\mathrm{F}}^{2} \tag{2}\]  
The selection of the number of topics k is crucial in NMF applications. If the value of k is too small, the extracted topics will be too broad and lack details; if the value of k is too large, it may lead to too high similarity between topics or even duplicate topics. Therefore, reasonably determining the number of topics k is an important step to improve the model effect and interpretability [PERSON] and [PERSON] (2000). Researchers will combine indicators such as topic consistency, silhouette coefficient and perplexity to evaluate and optimize the number of topics. This article uses the method in the reference to select two indicators, topic consistency and silhouette coefficient, to finally determine the number of topics [PERSON] and [PERSON] (2000).  
The advantage of NMF lies in its non-negativity constraint, which makes the decomposition results more interpretable, especially suitable for the deconstruction of non-negative data in reality. Due to its excellent dimensionality reduction and data interpretation capabilities, NMF has been widely used in various data processing tasks, such as text topic extraction, signal separation and gene expression analysis. In this study, we use NMF for topic clustering of online comments in order to extract the potential structure and features in online comments.