Fast LDP-MST: An Efficient Density-Peak-Based Clustering Method for Large-Size Datasets

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 $O(N\log N+M^{2})$ time, where $N$ denotes the dataset size and $M$ is an intermediate variable denoting the number of local density peaks. As our experimental results reveal, when processing large-size datasets, the value of $M$ could be very large and consequently those steps of LDP-MST involving $O(M^{2})$ time term would be time-consuming. And in the worst case, the value of $M$ could be very close to that of $N$, which means that the time complexity of LDP-MST could be $O(N^{2})$ in the worst case of $M$. In this study, we use more efficient algorithms to implement those steps of LDP-MST that involve the $O(M^{2})$ time term such that the proposed method, Fast LDP-MST, has $O(N\log N)$ time complexity even if $M\approx N$. 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.