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Estimating the number of clusters k while clustering the data is achallenging task. An incorrect cluster assumption indicates that the number ofclusters k gets wrongly estimated. Consequently, the model fitting becomes lessimportant. In this work, we focus on the concept of unimodality and propose aflexible cluster definition called locally unimodal cluster. A locally unimodalcluster extends for as long as unimodality is locally preserved across pairs ofsubclusters of the data. Then, we propose the UniForCE method for locallyunimodal clustering. The method starts with an initial overclustering of thedata and relies on the unimodality graph that connects subclusters formingunimodal pairs. Such pairs are identified using an appropriate statisticaltest. UniForCE identifies maximal locally unimodal clusters by computing aspanning forest in the unimodality graph. Experimental results on both real andsynthetic datasets illustrate that the proposed methodology is particularlyflexible and robust in discovering regular and highly complex cluster shapes.Most importantly, it automatically provides an adequate estimation of thenumber of clusters.

UniForCE: The Unimodality Forest Method for Clustering and Estimation of the Number of Clusters