# DELER: Distributed Clustering with Local Direction Centrality and Density Measure
## 3 The DEALER Algorithm
### Data Partitioning
#### 3.3.2 Data Partition Adjustment
This method effectively mitigates weak connectivity issues to some extent. Based on the experimental evaluation of the different clustering methods, the accuracy of the clustering results was calculated as follows: On the synthetic dataset DS1, the CDC clustering method achieved an accuracy of 0.7007, while the DEALER method achieved an accuracy of 0.9980, representing an improvement of approximately 42.5%. On the real-world Flame dataset, the CDC clustering method resulted in an accuracy of 0.6375, while the DEALER method achieved an accuracy of 0.9917, representing an improvement of approximately 35.7%. These results demonstrate that the local cluster expansion algorithm outperforms the boundary-point-enclosing center-point algorithm, especially when dealing with complex datasets. ### Efficiency Analysis

In response to the data processing demands of the big data era, distributed clustering algorithms have emerged. This section conducts distributed experiments on the DEALER algorithm to evaluate its efficiency. The dataset used in the experiment has a larger scale. Since no CDC algorithm implementation was found for a distributed environment, comparisons are made between the CDC algorithm, the single-machine version of the DEALER algorithm, and one of the most advanced distributed density-based clustering algorithms, the FDDP algorithm [15]. The experiment is designed with two primary objectives. First, it compares the efficiency of the CDC algorithm, the FDDP algorithm, and the DEALER algorithm in both single-machine and distributed settings. Second, it evaluates the speedup and scalability of the DEALER algorithm. Figure 23 presents a comparison of the execution time (in seconds) for the CDC algorithm, the FDDP algorithm, and the DEALER algorithm in both single-machine and distributed environments on the given dataset. As shown in Figure 23, the DEALER algorithm demonstrates a higher computational speed compared to the CDC algorithm. Moreover, the distributed implementation of the DEALER algorithm performs well, achieving a slightly better computational speed than the FDDP algorithm. Figures 24 and 25 present the speedup and scalability performance of the distributed direction centrality clustering algorithm enhanced with \(z\)-value indexing. The former shows the proportion of speed improvement in algorithm runtime as the number of distributed system nodes increases, while the latter tests the algorithm's performance with datasets

Figure 22: Scatter plot of clustering results of the dataset Flame in the DEALER clustering mode. of increasing size, selected randomly in multiples. The experimental results demonstrate that the \(z\)-value-indexing-enhanced distributed-direction centrality-clustering algorithm performs well in terms of both speed and scalability, achieving the expected outcomes of the experiment. ### Z-Value Filtering Effectiveness

The improvement in the speed of the clustering algorithm is achieved by optimizing the process of finding \(k\)-nearest neighbors using the proposed Z-CF algorithm. This optimization reduces the computational cost of calculating distances between points in the data space, lowering the time complexity from \(O\big{(}n^{2}\big{)}\) to \(O(n\log n)\). The efficiency of the Z-CF algorithm is evaluated through experiments. In this experiment, seven datasets (ordered by size from smallest to largest: Flame, Spiral, DS2, DS1, Levine, UrbanGB, and Samusik) are used for testing. The objective is to compare the unoptimized k-nearest neighbor search algorithm (KNN-search) with

Figure 23: Runtime of the distributed direction centrality clustering algorithm enhanced by \(z\)-value index and existing algorithms. Figure 24: Distributed algorithm speed ratio. Figure 25: Distributed algorithm scalability. ## 6 Conclusions

In this paper, we propose DEALER, an efficient and effective distributed clustering algorithm.