Fast LDP-MST: An Efficient Density-Peak-Based Clustering Method for Large-Size Datasets
Teng Qiu, Yongjie Li
Abstract
Recently, a new density-peak-based clustering method, called clustering with local density peaks-based minimum spanning tree (LDP-MST), was proposed, which has several attractive merits, e.g., being able to detect arbitrarily shaped clusters and not very sensitive to noise and parameters. Nevertheless, we also found the limitation of LDP-MST in efficiency. Specifically, LDP-MST has <inline-formula><tex-math notation="LaTeX">$O(N\log N+M^{2})$</tex-math></inline-formula> time, where <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> denotes the dataset size and <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula> is an intermediate variable denoting the number of local density peaks. As our experimental results reveal, when processing large-size datasets, the value of <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula> could be very large and consequently those steps of LDP-MST involving <inline-formula><tex-math notation="LaTeX">$O(M^{2})$</tex-math></inline-formula> time term would be time-consuming. And in the worst case, the value of <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula> could be very close to that of <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> , which means that the time complexity of LDP-MST could be <inline-formula><tex-math notation="LaTeX">$O(N^{2})$</tex-math></inline-formula> in the worst case of <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula> . In this study, we use more efficient algorithms to implement those steps of LDP-MST that involve the <inline-formula><tex-math notation="LaTeX">$O(M^{2})$</tex-math></inline-formula> time term such that the proposed method, Fast LDP-MST, has <inline-formula><tex-math notation="LaTeX">$O(N\log N)$</tex-math></inline-formula> time complexity even if <inline-formula><tex-math notation="LaTeX">$M\approx N$</tex-math></inline-formula> . Our experiments demonstrate that Fast LDP-MST is overall more efficient than LDP-MST on large-size datasets, without sacrificing the merits of LDP-MST in effectiveness, robustness, and user-friendliness.