Estimating the number of clusters k while clustering the data is a challenging task. An incorrect cluster assumption indicates that the number of clusters k gets wrongly estimated. Consequently, the model fitting becomes less important. In this work, we focus on the concept of unimodality and propose a flexible cluster definition called locally unimodal cluster. A locally unimodal cluster extends for as long as unimodality is locally preserved across pairs of subclusters of the data. Then, we propose the UniForCE method for locally unimodal clustering. The method starts with an initial overclustering of the data and relies on the unimodality graph that connects subclusters forming unimodal pairs. Such pairs are identified using an appropriate statistical test. UniForCE identifies maximal locally unimodal clusters by computing a spanning forest in the unimodality graph. Experimental results on both real and synthetic datasets illustrate that the proposed methodology is particularly flexible and robust in discovering regular and highly complex cluster shapes. Most importantly, it automatically provides an adequate estimation of the number of clusters.

翻译：同时进行数据聚类与估计聚类数k是一项具有挑战性的任务。不正确的聚类假设会导致聚类数k被错误估计，进而使模型拟合的重要性降低。本文聚焦于单峰性概念，提出一种灵活的聚类定义——局部单峰簇。局部单峰簇在数据子簇对间保持局部单峰性时持续扩展。基于此，我们提出UniForCE方法用于局部单峰聚类。该方法首先对数据进行初始过聚类，随后构建连接形成单峰对的子簇的单峰性图，其中单峰对通过适当的统计检验进行识别。UniForCE通过计算单峰性图中的生成森林来识别最大局部单峰簇。在真实与合成数据集上的实验结果表明，该方法在发现规则与高度复杂簇形状方面具有突出的灵活性与鲁棒性。更重要的是，该方法能够自动提供对聚类数k的充分估计。