# Extension of DBSCAN in Online Clustering: An Approach Based on Three-Layer Granular Models
## 1 Introduction  
In today's information age, the most important task is to process huge information and data. Data mining is the basic tool in data analysis, which extracts interesting hidden patterns or features from data sources, and uses them in decision-making or future studies [1, 2]. Among quantities of computational intelligence activities, clustering plays a fundamental and essential role in extensive applications, since the overwhelming majority of data are unlabeled nowadays. Clustering algorithms' major purpose is to group analogous objects into clusters by some intrinsic properties between data points [3], e.g., structural, statistical, distance-based, and density-based similarity, and so on. The resulted clusters are required to have maximum-similarity intra clusters, and a minimum of one inter cluster [4]. Due to these specialties, clustering results are usually utilized as the preprocessed step in further data mining studies, such as classification, prediction, anomaly detection, correlation analysis, etc. [5]. Therefore, to extract effective information in datasets efficiently, it is necessary and important to find a suitable clustering algorithm in data mining analysis. Clustering algorithms have been studied and developed for the last several decades, as well as applied in real engineering applications, e.g., pattern recognition, scientific and social research, economic analysis, industrial engineering, biomedical data analysis, and so on [6, 7]. According to the application preference, available data types, and particular purposes or requirements, clustering algorithms are mainly divided into five categories [8]: hierarchical, partition-based, model-based, grid-based, and density-based models. The hierarchical models try to build tree structures, and to generate a hierarchy of groupsaccording to the criterions of distance, including agglomerative and divisive ways. The well-known hierarchical models are CURE and CHEMELON [9]. The partition-based models tend to find meaningful partitions in the dataset, and then complete clustering according to specific partitions, e.g., PAM and CLARA [10; 11]. The model-based algorithms usually train a model first, based on special mathematical functions on the training dataset, and then complete the clustering, e.g., self-organizing-map (SOM) algorithm [12]. The grid-based models mesh feature space into a finite number of cells, and then cluster data by aggregating similar sub-grids, e.g., CLIQUE [13]. Density-based models group data points according to data's density distribution, and can determine clusters with arbitrary shapes, e.g., typical DBSCAN and OPTICS [14; 15]. However, none of these algorithms can be ranked as the most effective one, since all these models have advantages at specific applications. However, orienting to nonlinearly-inseparable data, e.g., clustering spatial data, most of these algorithms have limitations. To address this problem, an enhanced clustering algorithm is generally required. On the other hand, the computation cost is also a critical issue in clustering, especially in big data analysis. As we know, one disadvantage of traditional clustering algorithms is the high computational complexity [16], which makes them limited in dealing with datasets with a very large size. However, real-world data sources not only have large quantities, but also generate new data continuously as a system operation. Due to the unsupervised character of clustering, some clustering models have to run the whole process once again to determine new data's belonging. In actual engineering applications, it is not practical due to the limitations on RAM and time consumption [17]. An available way is the usage of the model-based methods which can apply the trained model on testing data. In this way, the model-based algorithms can be feasible in online clustering, e.g., utilizing the trained mathematical models to realize new data clustering online [18].