## 2 Background and Related Work
Some examples include: CluStream [11], which is based on hierarchy and works partly offline with K-Means and online part for new managers; DenStream [12], based on density, which initially has an offline learning phase for the creation of microclusters and macroclusters at the end of the algorithm execution, and an online learning phase for updating and creating new microclusters; C-DenStream [13], which is an extension of DenStream that includes domain information for clusters and changes in the offline phase, replacing DBSCAN for C-DBSCAN; SDStream [14], based on the radius and density for creating microclusters in the online training phase, also having an offline training phase, which generates the final macroclusters. Figure 1: Four types of patterns of changes over time. There are also HDDSREAM [31] and PreDeConStream [18] that are based on density, which group high-flow data and have online and offline training phases. More recently, OEC [16] performs the data grouping using the correlation; SwarmStream algorithm [3], which is inspired by self-organizing phenomena in complex systems; and Auto-Cloud [17] is based on the concept of Typicality and Eccentricity Data Analysis (TEDA) [32]. Another evolving algorithm is SOStream [15] with entirely online learning and based on self-organizing density (Self-organizing Maps--SOM) for data stream clustering. It also uses the concept of microclusters. The algorithm has seven sub-algorithms, which describe the creation, determination of close neighbors, updating, search for intersection, fusion, and forgetting of the microclusters. However, the cluster-forgetting algorithm is optional. Many recent and interesting proposals address the data stream clustering problem using the microcluster and macrocluster concepts in literature. Among them, we can cite the HCMstream [19], VHEC [33], BEstream [20], ACSC [34], DyClee [21], and DGStream [22]. The HCMstream, Hyper-cylindrical micro-clustering for streaming data [19], proposes to use hyper-cylindrical forms to merge the spherical microclusters. The macroclusters are composed of connected microclusters and have arbitrary shapes. The proposal is interesting, and the results indicate its efficiency in determining arbitrary form clusters. The VHEC, Versatile Hyper-Elliptic Clustering [33], and BEstream, Batch Capturing with Elliptic Function for One-Pass Data Stream Clustering [20], create hyper-elliptic microclusters with arbitrary rotation. Both algorithms determine a new similarity distance measure to the data stream clustering, and the BEstream can be used in high-dimensional space. The ACSC or Ant Colony Stream Clustering algorithm [34] works with windows of the data stream and in two steps. First, the algorithm identifies clusters, and then these clusters are summarized in statistics and stored offline. The DyClee, dynamic clustering for tracking evolving environments [21], is a dynamic clustering algorithm that uses the two-stage distance and density-based clustering approach to determine the macroclusters. First, the distance-based clustering obtains the microclusters, and then the density-based clustering is used to eliminate the outlier clusters (clusters with a small amount of data). The microcluster density is defined low, medium, or high and is used to create the arbitrary shape macroclusters by a density-based approach. Thus, the macroclusters are composed of connected microclusters. Moreover, data samples are associated with a microcluster using the Manhattan distance as the similarity metric. Finally, the DGStream, Density and Grid-based data Stream clustering [22], is an online-offline grid and density-based stream clustering algorithm. In its online phase, it uses a grid-based approach to represent the microcluster. While in its offline phase, DGStream employs the DBSCAN algorithm to determine the macroclusters, similar to the DenStream algorithm. Table 1 summarizes the main features of these algorithms.