# DELER: Distributed Clustering with Local Direction Centrality and Density Measure
## 3 The DEALER Algorithm
### Data Partitioning
#### 3.3.2 Data Partition Adjustment
This synergistic reuse of computational byproducts eliminates redundant operations, significantly reducing algorithmic complexity. (2) Efficiency Optimization: For distributed computing environments, we propose a z-index-enhanced distributed directional centrality clustering algorithm featuring three key innovations: (i) Spatial data organization: \(z\)-value ordering optimizes data locality by colocating proximate data points on the same compute nodes with prefetched reference data, minimizing KNN query communication overhead; (ii) Index structure: A novel z-curve-based spatial index constrains KNN searches to linear intervals containing query points, achieving order-of-magnitude search efficiency gains; (iii) Two-phase processing: The \"local-clustering-first, global-merging-later\" framework reduces overall time complexity from \(O(n^{2})\) to \(O(n\log n)\). The combined improvements simultaneously enhance both processing capability and clustering accuracy compared to the baseline CDC algorithm, demonstrating superior performance in handling large-scale datasets while maintaining precise cluster separation. According to the experimental analysis presented below, the algorithm demonstrates strong performance in terms of effectiveness and clustering efficiency. However, the proposed algorithm is not exclusive to CDC, nor is it universally applicable to all clustering methods. Instead, it is particularly suitable for algorithms that rely on neighborhood information for point evaluation, such as certain density-based approaches, where the measurement of points inherently involves their local neighborhoods. In high-dimensional clustering, the performance of the \(z\)-value index is suboptimal. According to the literature [17, 18], it is theoretically impossible for a single curve to traverse every point in a given multidimensional discrete space without crossing itself without favoring any particular direction and while completely preserving locality. The topological discontinuities and spatial preservation issues across multidimensional spaces lead to locality loss. Consequently, when dealing with high-dimensional data, the \(z\)-value index exhibits poor local order-preserving properties, resulting in increased abrupt changes. Clustering for high-dimensional data remains a key focus for future research. ## 5 Experiment Analysis

This chapter presents the experimental evaluation of the algorithm proposed in this paper. It compares the algorithm with current mainstream approaches, focusing primarily on the accuracy of the results and the computational time. ### Experimental Setup

The experimental setup section outlines the configuration of the environment required for the experiments and the preparation of datasets. This includes details about the hardware and software environment, dataset preparation, and parameter settings. #### 5.1.1 Experimental Environment and Datasets

The cluster consists of five servers, each equipped with 24 GB of memory and dual Intel Xeon E5-2420 six-core processors. The servers operate on the Red Hat Enterprise Linux system. Development is conducted using the Eclipse IDE, with Java as the primary programming language. The experimental datasets selected for this study include both synthetic and real-world datasets: DS1, DS2, Flame, Spiral, Levine, Samusik, UrbanGB, CoverType, Household, Stock, and Sofia. Dataset DS1 consists of 10 spherical clusters, while DS2 contains 6 non-convex clusters with significant density differences. The Flame dataset consists of two clusters, and the Spiral dataset comprises three linear clusters. The Levine dataset, which records human bone marrow cell features, can be obtained from the FlowRepository platform and contains 14 clusters. The Samusik dataset, which records mouse bone marrow cell data, is also available on FlowRepository and includes 24 clusters. The UrbanGB dataset contains geographical coordinates of 469 cities, with 360,177 latitude and longitude points for each city's districts, counties, towns, and villages.