# A Clustering Algorithm for Evolving Data Streams Using Temporal Spatial Hyper Cube
## 3 Methodology
### Developed Algorithms
#### 3.4.4 BOCEDS Micro-Cluster Update
#### 4.2.2 Computational Cost

Visualizing Figure 9, it is found that computational cost is also correlated with memory usage. Hence, CEDAS is the worst in terms of the computational cost followed by MuDi-Stream while all BOCEDS, BOCEDS Inc, and TSHC are the least in terms of the

\[ADR=\frac{CAS}{Total\ Anomaly\ Samples} \tag{9}\]1 Memory Usage Comparison using KDDCup’99, Landsat, Spiral, DNA, and Traffic Datasets. \[ADR=\frac{CAS}{Total\ Anomaly\ Samples} \tag{9}\]2 Normalized Mutual Information Comparison Using KDDCup’99, Landsat, Spiral, and DNA Datasets. computational cost. This is also clearer when we visualize the bar chart that is provided in \[ADR=\frac{CAS}{Total\ Anomaly\ Samples} \tag{9}\]3 We interpret this with light memory consumption which requires low effort for data processing and low computational cost. Theoretically, clustering algorithms are required to have a fixed and small memory usage as well as low computational cost for the entire process of the clustering data stream. Memory usage is calculated based on the number of Micro-clusters generated by an algorithm. The more the algorithm requires to generate Micro-cluster till it reaches its final clusters the more memory usage it requires. In evaluating the memory usage of a clustering algorithm, the developed algorithm uses the core mini-clusters that are stored for calculating the results of clustering as a measure of memory usage. Similarly, the computational cost is calculated based on the time the algorithm requires to perform the mathematical calculation of the distance to the Core-cluster. Thus, the more the algorithm perform mathematical calculation the more computational cost it requires. In evaluating the computational cost of a clustering algorithm, the developed algorithm uses the number of calling the distance function as an indicator for computational complexity. ## 5 Finding and Summary

The results and analysis of the developed BOCEDS TSHC algorithm have been discussed in detail based on two real (KDD Cup'99 and LandSat) and three synthetics (DNA, Spiral, and Traffic) datasets. Both real and syntactic datasets are used for the evaluation of the developed algorithm. The real and synthetic datasets are selected from the most used dataset in the literature. They vary in size, cluster count, and density. In addition, simulated traffic data is generated using MATLAB R2021a to is generated to simulate the evolving behavior in the data for an urban environment scenario. On the other hand, four well-known quality evaluation metrics including (anomaly detection ratio, rand index, adjusted rand index, and normalized mutual information) are selected to demonstrate the superiority of the developed algorithm. Additionally, two efficiency evaluation metrics namely (memory usage and computational cost) are used to illustrate the efficiency of the developed algorithm. The quality evaluation of the developed algorithm to generate clusters in evolving data streams has been evaluated using both real and syntactic datasets. The result demonstrates the superiority of the developed BOCEDS TSHC algorithm in handling evolving data streams using the recursive and dynamic update for adaptive quantization of arrived data when they are projected to the clustering space. Similarly, regarding the efficiency

\[ADR=\frac{CAS}{Total\ Anomaly\ Samples} \tag{9}\]4 Computational Cost Comparison using KDDCup’99, Landsat, Spiral, DNA, and Traffic Datasets. evaluation, the results illustrate the developed BOCEDS TSHC algorithm's superiority in both memory usage and computational cost, where the developed algorithm is found to be using less memory and computational cost. As a result, more applicability to real-world data stream scenarios. In short, the developed BOCEDS TSHC algorithm clearly shows the best performance in terms of quality and efficiency evaluation. BOCEDS TSHC is an effective and efficient clustering algorithm in clustering evolving data streams.