## 2 Preliminary
### OPTICS Clustering Algorithm  
In the past few decades, the research of clustering algorithms has undergone significant development. Early, K-means [11] clustering algorithms provided a simple and intuitive framework, but their applicability is limited by the data shape and cluster structure. Then, the hierarchical clustering algorithm introduces a hierarchical structure, which provides convenience for understanding the relationship between clusters at different levels. Next, [PERSON] et al. [17] proposed the DBSCAN algorithm, which focuses on density, making clustering more robust for data with an arbitrary shape and density distribution. In recent years, K-means clustering, the Gaussian mixture model (GMM), and mixtures of multivariate clustering algorithms have been applied to the field of chemistry, which has promoted the application of unsupervised learning in other disciplines [18]. With the development of technology, [PERSON] et al. [19] proposed a density clustering method based on improved inverse formula density estimation. The new method has a good effect when dealing with low dimensional data. In addition, [PERSON] [20] proposed a clustering method based on morphological operations that worked well on 2D and 3D data. The OPTICS clustering algorithm creates an augmented ordering of the database representing its density-based clustering structure. Let the object set be \(O=\{o_{1},\ o_{2},\ldots,o_{m}\}\). Some important definitions associated with the OPTICS clustering algorithm are defined as follows:  
1. \(\epsilon-Domain\): For \(o_{j}\in O\), its \(\epsilon-Domain\) is a subset of \(O\) containing objects whose distance from \(o_{j}\) is not greater than \(\epsilon\). That is, \(N_{\epsilon}(o_{j})=\{\ o_{i}\in O\mid\text{distance}(o_{i},o_{j})\leq\epsilon\}\). The number of objects in \(N_{\epsilon}(o_{j})\) is noted as \(\mid N_{\epsilon}(o_{j})\mid\). Usually, \(eps\) is used to represent the clustering radius \(\epsilon\);
2. Core object: for any \(o_{j}\in O\), \(o_{j}\) is a core object if \(\mid N_{\epsilon}(o_{j})\mid\geq min\_samples\), where \(min\_samples\) is an integer constant;
3. Core distance: the minimum radius that makes an object \(o\) a core object is called the core distance of \(o\);
4. Reachability distance: the reachability distance of an object \(p\) with respect to a core object \(o\) denoted as \(rd(p,o)\) is the maximum value between the actual distance of \(o\) to \(p\) and the core distance of \(o\). Let the clustering radius be infinite, i.e., \(eps=inf\). OPTICS generates the reachability plot as follows:  
1. The core object queue \(Cq\), ordered queue \(Oq\), result queue \(Rq\), and reachability distance queue \(Rdq\) are initialized to empty;
2. All core objects in \(O\) are chosen based on \(min\_samples\) and \(eps\), and then added to \(Cq\);
3. If there is an element in \(Cq\) that has not been processed, jump to 4, and otherwise 8. 4. An unprocessed object \(o\) is randomly taken out from \(Cq\) and placed in \(Rq\). Then, it is marked as processed. Further, each object \(p\) satisfying \(rd(p,o)\leq eps\) is selected from \(Cq\) and added to \(Oq\) in an ascending order of the reachability distance with respect to \(o\);
5. If \(Oq\) is not empty, jump to 6, and otherwise 3;
6. The reachability distance of the first object \(p_{1}\) in \(Oq\), with respect to the last object in \(Rq\), is stored in \(Rdq\). Then, \(p_{1}\) is removed from both \(Oq\) and \(Cq\), and added into \(Rq\);
7. Each object whose reachability distance with respect to the last object \(r\) in \(Rq\) is not greater than \(eps\) is selected from \(Cq\). Then, these objects are sorted in ascending order of the reachability distance with respect to \(r\) and replace the objects in \(Oq\). Finally, jump to 5;
8. The reachability plot is plotted based on \(Rq\) and \(Rdq\). The OPTICS clustering algorithm [12] is considered more effective than K-means [11] and other clustering algorithms when dealing with high-level data because it can identify changes in density.