A density peaks clustering algorithm with sparse search and K-d tree

TL;DR

This paper introduces an improved density peaks clustering algorithm that uses sparse search and K-d trees to significantly reduce computational complexity and enhance clustering efficiency and accuracy, especially on large datasets.

Contribution

The paper proposes a novel density peaks clustering method utilizing sparse search and K-d trees to accelerate computation and improve clustering performance.

Findings

Reduces computational complexity from O(n^2K) to O(n(n^{1-1/K}+k))

Enhances clustering efficiency on large datasets

Improves clustering accuracy compared to existing algorithms

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 $O(n^2K)$ 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.