Below are quoted from: Cao, Feng, Martin Estert, Weining Qian, and Aoying Zhou. "Density-based clustering over an evolving data stream with noise." In Proceedings of the 2006 SIAM international conference on data mining, pp. 328-339. Society for industrial and applied mathematics, 2006. https://doi.org/10.1137/1.9781611972764.29 

      Clustering is an important task in mining evolving data streams. Beside the limited memory and one-pass constraints, the nature of evolving data streams implies the following requirements for stream clustering: no assumption on the number of clusters, discovery of clusters with arbitrary shape and ability to handle outliers. While a lot of clustering algorithms for data streams have been proposed, they offer no solution to the combination of these requirements. In this paper, we present DenStream, a new approach for discovering clusters in an evolving data stream. The “dense” micro-cluster (named core-micro-cluster) is introduced to summarize the clusters with arbitrary shape, while the potential core-micro-cluster and outlier micro-cluster structures are proposed to maintain and distinguish the potential clusters and outliers. A novel pruning strategy is designed based on these concepts, which guarantees the precision of the weights of the micro-clusters with limited memory. Our performance study over a number of real and synthetic data sets demonstrates the effectiveness and efficiency of our method.

Below are quoted from: Li, Manqi, Arie Croitoru, and Songshan Yue. "GeoDenStream: An improved DenStream clustering method for managing entity data within geographical data streams." Computers & Geosciences 144 (2020): 104563. https://doi.org/10.1016/j.cageo.2020.104563 

      In order to conceptualize the DenStream in the context of entity stream data in geographical space consider a data stream in which each record is comprised of a data “point”, i.e., a geographic location (for example, in the form of geographic coordinates), a timestamp, and a set of related attributes that describe an entity. The DenStream clustering method applies the core-micro-cluster approach to detect arbitrary-shaped clusters (Cao et al., 2006). In this approach, a core-micro-cluster is constructed by points that are sufficiently dense according to a density threshold, and such cluster evolves over time as data points are received. In addition, each core-micro-cluster is assigned a weight that decreases exponentially with time. Based on their weights, core-micro-clusters with higher weights (i.e., potential-clusters) are acquired for building clusters, and core-micro-clusters with lower weights (i.e., outlier-clusters) are removed from the final clustering results.

      There are four phases in the original DenStream clustering method, as shown in Fig. 1: an Initializing phase in which the potential-cluster and outlier-cluster lists are constructed; an Online phase in which newly arrived data points are either merged into a potential-cluster or form a new outlier-cluster; a Pruning phase in which potential- and outlier-clusters with lower weights are removed from the corresponding lists; and finally, an Offline phase in which DBSCAN (Density-Based Spatial Clustering of Applications with Noise) clustering (Ester et al., 1996) is used for generating offline-clusters based on the potential-cluster list. In this process, a set of parameters are used, including initial_points and min_points in the Initializing phase, epsilon, lambda, beta, and mu in the Online phase, tp in the Pruning phase, and offline in the Offline phase. A more detailed description of these parameters is provided in Appendix A.

Fig. 1. Processing flow of DenStream clustering method for geographical data stream.