Modal clustering has a clear population goal, where density estimation plays a critical role. In this paper, we study how to provide better density estimation so as to serve the objective of modal clustering. In particular, we use semiparametric mixtures for density estimation, aided with a novel mode-flattening technique. The use of semiparametric mixtures helps to produce better density estimates, especially in the multivariate situation, and the mode-flattening technique is intended to identify and smooth out spurious and minor modes. With mode flattening, the number of clusters can be sequentially reduced until there is only one mode left. In addition, we adopt the likelihood function in a coherent manner to measure the relative importance of a mode and let the current least important mode disappear in each step. For both simulated and real-world data sets, the proposed method performs very well, as compared with some well-known clustering methods in the literature, and can successfully solve some fairly difficult clustering problems.

模态聚类具有明确的总体目标，其中密度估计起着关键作用。在本文中，我们研究如何提供更好的密度估计，以达到模态聚类的目的。特别是，我们将半参数混合用于密度估计，并借助一种新颖的模式平坦化技术。半参数混合的使用有助于产生更好的密度估计，尤其是在多变量情况下，并且模式平坦化技术旨在识别和消除虚假模式和次要模式。通过模式展平，可以依次减少簇的数量，直到仅剩一种模式为止。此外，我们以相干方式采用似然函数来衡量模式的相对重要性，并让当前最不重要的模式在每个步骤中消失。