基于局部化水平集概率的模式聚类的袋装$k$ -距离
Bagged $k$-Distance for Mode-Based Clustering Using the Probability of Localized Level Sets
摘要：
在本文中，我们提出了一个集成学习算法命名为\textit{bagged $k$-distance for mode-based clustering}（\textit{BDMBC}）通过提出一个新的测量称为\textit{probability of localized level sets}（\textit{PLLS}），这使我们能够找到所有的集群为不同的密度与一个全局阈值。在理论方面，我们表明，与适当选择的最近邻数$k_D$在袋装$k$ -距离，子样本大小$s$，装袋轮$B$，和最近邻数$k_L$的本地化水平集，BDMBC可以实现最佳的模式估计的收敛速度。事实证明，在相对小的$B$的情况下，子样本大小$s$可以远小于每个装袋轮的训练数据$n$的数量，并且可以同时减少最近邻居$k_D$的数量。此外，我们建立的水平集估计的PLLS的Hausdorff距离方面的最佳收敛结果，这表明，BDMBC可以找到本地化的水平集的不同密度，从而享有局部自适应性。在实际应用方面，通过数值实验验证了BDMBC算法在模式估计和水平集估计中的有效性，证明了算法的准确性和有效性.
英文摘要：
In this paper, we propose an ensemble learning algorithm named \textit{bagged $k$-distance for mode-based clustering} (\textit{BDMBC}) by putting forward a new measurement called the \textit{probability of localized level sets} (\textit{PLLS}), which enables us to find all clusters for varying densities with a global threshold. On the theoretical side, we show that with a properly chosen number of nearest neighbors $k_D$ in the bagged $k$-distance, the sub-sample size $s$, the bagging rounds $B$, and the number of nearest neighbors $k_L$ for the localized level sets, BDMBC can achieve optimal convergence rates for mode estimation. It turns out that with a relatively small $B$, the sub-sample size $s$ can be much smaller than the number of training data $n$ at each bagging round, and the number of nearest neighbors $k_D$ can be reduced simultaneously. Moreover, we establish optimal convergence results for the level set estimation of the PLLS in terms of Hausdorff distance, which reveals that BDMBC can find localized level sets for varying densities and thus enjoys local adaptivity. On the practical side, we conduct numerical experiments to empirically verify the effectiveness of BDMBC for mode estimation and level set estimation, which demonstrates the promising accuracy and efficiency of our proposed algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
