## 3 Methodology
### Iterative Clustering  
This phase divides abstracts into small clusters iteratively according to the semantic similarity through the three steps shown in Figure 2. In Step 1, we use the pretrained GPT-3 similarity embedding model (\"_text-similarity-curie-001_\") through OpenAI's API service to map the abstracts to the embeddings with 4096 semantic features. In Step 2, the high-dimension space of the abstract embeddings is reduced to a reasonable range because HDBSCAN requires the dimension size to be smaller than the number of abstracts, in our case, smaller than 593 (the total number of abstracts in our dataset). This also minimizes the computation complexity, resulting in an increased clustering accuracy. We use a dimension reduction technique, Uniform Manifold Approximation and Projection (UMAP) [50], along with the HDBSCAN algorithm to determine a range of dimensions that lead to a result that contains more than one distinct cluster. The experiments with a number of different sizes show that a dimension size below 500 always produces at least 3 or more clusters.  
In Step 3, HDBSCAN is used to separate the abstracts into small clusters through several iterations as shown in Figure 2. Each iteration produces a number of clusters of different sizes and outliers are treated as one cluster and used in the next iteration because some of them are data points that fall on the cluster borders. The cluster that contains more than 50 abstracts is fed to the next iteration. This process continues until the number of abstracts in every cluster is fewer than 50, a stopping threshold that we chose for good usability when visualizing clustering results and it can be adjusted to 40 or 60. The larger the threshold is, the fewer the number of clusters generated.  
HDBSCAN has a number of parameters for fine-tuning the clustering results. We focus on the _minimal cluster size_ parameter because it plays an important role in selecting the clusters from a number of candidate clusters whilst other parameters are used as supplementary when the _minimal cluster size_ alone cannot make decisions [51]. A larger minimal cluster size results in a fewer number of clusters as small clusters are merged to a large cluster at the cost of a reduced clustering quality. On the other hand, a small minimal cluster size leads to a large number of micro clusters (2 to 4 documents per cluster) and outliers. Therefore, the experiments were conducted by adjusting two parameters: the dimension size of abstract embeddings from 20 to 500 (i.e., 500, 450, 400, 350, 300, 250, 200, 150, 100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 30, 25, 20) and the minimal cluster size from 10 to 50, in increments of 5. In total, there are 225 (\(25\times 9\)) combinations of parameters, and each combination produces a set of clusters, which is then evaluated with their silhouette scores to determine a set of optimal clusters.  
The silhouette score of a cluster (\(C_{i}\)) is calculated using the formula \(\frac{b-a}{\max(a,\,b)}\), where \(a\) is the _intra-cluster similarity_, which measures the mean similarity of an abstract to all the other abstracts within the same cluster; and \(b\) is the _outra-cluster similarity_, which measures the mean similarity of an abstract to all abstracts within the nearest cluster, which has the smallest mean dis-similarity to the cluster \(C_{i}\). The final score is normalized to a decimal value between \(1\) and \(-1\), where a large positive score indicates the abstracts within a cluster are highly similar to each other. Studies by [PERSON] et al. (2013) [52] and [PERSON] et al. (2011) [53] suggested that the silhouette score is one of the best clustering validation indexes.