# A Clustering Algorithm for Evolving Data Streams Using Temporal Spatial Hyper Cube
## 2 Literature Review  
Among the first online clustering algorithms, an algorithm called clustering online data streams into arbitrary shapes (CODAS) [17], was introduced to enable the generation of arbitrary shaped clusters for real-time data streams. CODAS is a data-driven algorithm that constructs micro-clusters to summarize data points and then scales to multi-dimensional data streams. Yet, in CODAS, the generated clusters are not capable of evolving. After that, CODAS was enhanced and CEDAS was proposed by [14], CEDAS introduces a simple linear aging mechanism to deal with the evolving features of data streams. This is the first technique to perform live clustering fully on evolving data streams. CEDAS is divided into two stages. The first phase involves the creation of micro-clusters or the insertion of data into existing micro-clusters, followed by information correction. The second phase involves intersecting micro-clusters and grouping them into kernel and shell areas. Every macro-cluster in this method contains a graph illustrating intersecting micro-clusters for every micro-cluster. The adjacency relations are stored as a property of the micro-cluster. CEDAS quickly produces high-quality clustering results and is capable of coping with the dynamic features of a data stream and outliers. CEDAS, like other density-based clustering techniques, requires a significant amount of processing time. Concurrently, a novel framework for clustering the evolving data stream called Cauchy was proposed [18]. It is an online technique that can adjust to the classifier in real-time. Additionally, the authors propose a strategy for developing a cyber-attack detection technique. The technique was evaluated using a 1999 KDD intrusion detection database to tackle the costly and time-consuming issues associated with traditional offline methods. The findings indicate that the cost of labeling learning data was reduced. Due to the online nature of this approach, adding definitions for new threats is considerably easier and simpler than with batch learning methods. Nevertheless, as with other density-based clustering methods, the Cauchy technique has a significant disadvantage: it lacks a mechanism for merging clusters, which would reduce the number of clusters formed, and it is inefficient for high-dimensional data. In the same year, an algorithm called xStream was introduced to address the problem of features evolving in data streams [10]. This work addresses a previously unstudied problem by proposing xStream, which is a density-based ensemble anomaly detector with the following three characteristics: (1) it is a constant-space and constant-time (per incoming update) algorithm, (2) it detects anomalies at multiple scales or granularities, and (3) it can handle (3i) high-dimensionality via distance-preserving projections and (3 ii) non-stationarity via O (1)-time model updates as the stream progresses. However, no attempt was made to address the issue of cluster evolving, which affects the overall outlier detection. Furthermore, in [19], the authors presented a technique called Online Clustering for Evolving Data Streams with Anomaly Detection (OnCAD). The suggested technique considers both the temporal and spatial proximity of observations to detect abnormalities in real-time. It detects cluster evolution in noisy streams, incrementally updates the model, and calculates the minimal window length over the evolving data stream without sacrificing speed. Nonetheless, the technique is incapable of dealing with high-dimensional data, as clusters of data typically occur in a subspace of the original input space. Another enhanced version of CODAS is named i-CODAS. It operates based on the concept of maintaining the local radius for each micro-cluster independently [20]. CODAS, like other density-based clustering methods, maintains a global and constant radius for each micro-cluster.