# 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  
After completing the first step, we successfully constructed a matrix of the co-occurrence between verbs (in fact, the senses of verbs) and various aspectual markers. That is, taking verbs as the index column in the first column, taking each aspectual marker as the header in the first row, and filling each cell in the middle with a specific value, indicating whether they can be collocated (generally, 0 represents that they cannot be collocated, and 1 represents that they can be collocated). Based on this matrix, we completed the construction of the situation type system in three steps. First, combine the words with exactly the same co-occurrence situations. Verbs with exactly the same co-occurrence situations indicate that their syntactic and semantic distributions in terms of aspect are completely the same. Therefore, they can be represented by the same representative word, and their co-occurrence situations can also be combined and represented by the same multi-dimensional vector. The vector here can be simply regarded as a row in the co-occurrence matrix table mentioned above. A column represents one dimension, so the number of columns determines the number of different dimensions. There are six dimensions representing the six aspectual markers, respectively. Then, visualize the co-occurrence matrix to observe the clustering tendency and semantic distance among each representative word. The classification system of lexical aspects has a prototype structure, which is shared by [PERSON] [23], [PERSON] [6], [PERSON] [7] and [PERSON] [10]. Prototype theory believes that members within a certain category are distributed around the most typical one and other ones become increasingly untypical. The similarity between members of that category is called family resemblance, which is represented by the semantic distance between verbs calculated according to their position in the matrix of co-occurrence in this paper. However, there are co-occurrences with six different aspectual markers for a verb, which means that a six-dimensional graph should be depicted. This is not possible for human eyes, and thus, we should reduce the dimensions. Dimensionality reduction is a technique used in data analysis and machine learning. The main idea is to simplify data without losing too much important information. Imagine you have a lot of data that have many features, like a long list of numbers that describe something. These features might be related to each other, or some of them might not be very useful. Dimensionality reduction helps to find a way to represent the data with fewer features but still keep most of the important information. This makes the data easier to understand, analyze, and most importantly, to be projected to lower dimensions, thus making it possible to observe. We choose Principal Component Analysis (PCA) for the task as it is one of the most commonly used methods for dimensionality reduction. It is a statistical method designed to simplify complex datasets by identifying the most significant patterns of variation. It works by transforming a large set of correlated variables into a smaller set of uncorrelated variables called principal components (PCs). These PCs are linear combinations of the original variables, ordered by their ability to explain variance in the data. The first PC captures the direction of maximum variability, the second PC accounts for the next highest variance, and so on. By retaining only the top few PCs, researchers can reduce data dimensionality while preserving critical information. Principal Component Analysis (PCA) was implemented with the following configurations using the scikit-learn library (v1.3.0) in Python:  
* Data preprocessing: Since the co-occurrence matrix consists entirely of dummy variables (i.e., yes/no variables or 0/1 variables), standardization processing is unneessary to avoid distorting their categorical nature. Redundant variables with perfect collinearity were removed.