A Density Peaks Clustering Algorithm With Sparse Search and K-d Tree

Abstract

Density peaks clustering has become a nova of clustering algorithm because of its simplicity and practicality. However, there is one main drawback: it is time-consuming due to its high computational complexity. Herein, a density peaks clustering algorithm with sparse search and K-d tree is developed to solve this problem. Firstly, a sparse distance matrix is calculated by using K-d tree to replace the original full rank distance matrix, so as to accelerate the calculation of local density. Secondly, a sparse search strategy is proposed to accelerate the computation of relative-separation with the intersection between the set of k nearest neighbors and the set consisting of the data points with larger local density for any data point. Furthermore, a second-order difference method for decision values is adopted to determine the cluster centers adaptively. Finally, experiments are carried out on datasets with different distribution characteristics, by comparing with other six state-of-the-art clustering algorithms. It is proved that the algorithm can effectively reduce the computational complexity of the original DPC from O(n 2 K) to O(n(n 1−1/K + k)). Especially for larger datasets, the efficiency is elevated more remarkably. Moreover, the clustering accuracy is also improved to a certain extent. Therefore, it can be concluded that the overall performance of the newly proposed algorithm is excellent.INDEX TERMS Density peaks clustering, sparse search strategy, K-d tree, computational complexity, second-order difference method.

Dual-level clustering ensemble algorithm with three consensus strategies

“…Meanwhile, DPC is an advanced density-based clustering algorithm that has been intensively studied in recent years. It is suitable for a wider range of data structures 58 – 60 . Generating base clustering under these two distinct and complementary partitioning methods can better achieve a balance of quality and diversity.…”

Research on Ground Object Echo Simulation of Avian Lidar

“…The collision detection tree is a tree structure based on bounding volumes, designed to optimize the calculation of collision detection. Commonly used tree structures include the Bounding Volume Hierarchy (BVH) tree [23], Binary Space Partitioning (BSP) tree [24], and k-dimensional (k-D) tree [25]. The collision detection tree consists of a root node, intermediate nodes, and leaf nodes.…”

“…The BVH tree [23] or k-D tree [25] is constructed using the AABB [20] or SBV [22] bounding volumes to investigate the efficiency of collision detection for different combinations. The total time required for constructing the collision detection tree and performing collision detection under various combinations varies with the number of triangular surfaces, as depicted in Figure 9.…”

A New Density Peak Clustering Algorithm Based on Cluster Fusion Strategy

“…Xu et al [24] proposed two density screening strategies, grid division (GDPC) and circle division (CDPC), which improved the efficiency of the DPC algorithm. Shan et al [25] proposed a density peak clustering algorithm (SKTDPC) based on sparse search and k-d tree. The algorithm is based on the kd tree theory to find the k nearest neighbors of data points and calculate the sparse distance matrix, realizing the double acceleration of local density and relative distance calculation, reducing the complexity of the algorithm and improving the efficiency of the DPC algorithm.…”

“…Lv et al [27] calculated the difference change between the decision values, and automatically obtained the cluster centers according to the position of the inflection point. Shan et al [25] used the second-order difference method to adaptively determine the cluster centers. The above improved algorithms of DPC avoid the inaccuracy and subjectivity of the artificial selection of clustering centers.…”