# Representing Aspectual Meaning in Sentence: Computational Modeling Based on Chinese
## 2 Materials and Methods
### The Construction of Situation Type System and Its Dataset
#### 2.1.3 Semantic Distance Visualization and Hierarchical Clustering
* n_components: The number of principal components was dynamically determined by retaining \(\geq\)80% cumulative explained variance (code: n_components = 0.80). Given the low original dimensionality (six features), this threshold balances dimensionality reduction and information preservation. * svd_solver: The exact solver (svd_solver = 'full') was selected to ensure the numerical stability for low-dimensional data. Then, the dimensionality-reduced data are plotted in two or three dimensions using matplotlib in Python to visualize the spatial distribution and clustering tendencies of words, preparing for subsequent hierarchical clustering. Hierarchical clustering is a robust unsupervised learning technique that constructs a hierarchy of clusters by either merging (agglomerative) or splitting (divisive) data points based on their similarity. This method is particularly advantageous for datasets with inherent hierarchical structures, as it provides a comprehensive dendrogram that visually represents the relationships between clusters. For our analysis, we applied hierarchical clustering to a dataset comprising over 1000 entries, each characterized by six dimensions. The choice of hierarchical clustering was driven by its ability to handle multi-dimensional data effectively while preserving the natural grouping tendencies of the data. Unlike partitioning methods such as k-means, hierarchical clustering does not require predefining the number of clusters, making it more flexible and interpretable. Additionally, the dendrogram offers valuable insights into the clustering process, enabling us to determine the optimal number of clusters based on the data's intrinsic properties. This approach is particularly suitable for exploratory analysis as it facilitates a deeper understanding of the data's structure and relationships. Hierarchical clustering was performed using the scikit-learn library (v1.3.0) in Python. n_clusters and linkage parameters are set according to the Cophenetic Correlation Coefficient (CPCC). The Cophenetic Correlation Coefficient (CPCC) is preferred for hierarchical clustering on our dataset (binary co-occurrence matrices, six dimensions and 1000-2000 observations) because it quantifies how well the dendrogram preserves the original pairwise distances. CPCC calculates the Pearson correlation between the original distance matrix (\(D\)) and the cophenetic distance matrix (\(C\)), reflecting the fidelity of hierarchical structure reconstruction. For sparse binary data, silhouette coefficients are less reliable due to assumptions of dense, continuous clusters, while CPCC directly evaluates hierarchical relationships without requiring predefined clusters. Additionally, CPCC avoids the \(O(n^{2})\) computational burden of silhouette scores, making it efficient for moderate-sized datasets. This ensures robust validation of term association hierarchies inherent in co-occurrence matrices. The Cophenetic Correlation Coefficient (CPCC) is defined as follows:  
\[\text{CPCC}=\frac{\sum\limits_{i<j}(d_{ij}-\bar{D})(c_{ij}-\bar{C})}{\sqrt{ \sum\limits_{i<j}(d_{ij}-\bar{D})^{2}\sum\limits_{i<j}(c_{ij}-\bar{C})^{2}}}\]  
where  
* \(d_{ij}\): Pairwise distance between observations \(i\) and \(j\) in the original space
* \(c_{ij}\): Cophenetic distance (dendrogram height where \(i\) and \(j\) merge)
* \(\bar{D},\bar{C}\): Mean of all \(d_{ij}\) and \(c_{ij}\) values, respectively