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Data clustering is widely recognized as a fundamental technique of paramount importance in pattern recognition and data mining. It is extensively used in many fields of the sciences, business and engineering, covering a broad spectrum of applications. Despite the large number of clustering methods, only a few of them take advantage of optimum connectivity among samples for more effective clustering. In this work, we aim to fill this gap by introducing a novel graph-based data clustering framework, called Iterative Optimum-Path Forest (IOPF), that exploits optimum connectivity for the design of improved clustering methods. The IOPF framework consists of four fundamental components: (i) sampling of a seed set S, (ii) partition of the graph induced from the dataset samples by an Optimum-Path Forest (OPF) rooted at S, (iii) recomputation of S based on the previous graph partition, and, after multiple iterations of the last two steps, (iv) selection of the forest with the lowest total cost across all iterations. IOPF can be regarded as a generalization of the Iterative Spanning Forest (ISF) framework for superpixel segmentation from the image domain to the feature space. Herein, we present four IOPF-based clustering solutions to illustrate distinct choices of its constituent components. These are thereafter employed to address three different problems, namely, unsupervised object segmentation, road network analysis and clustering of synthetic two-dimensional datasets, in order to assess their effectiveness under various graph topologies, and to ascertain their efficacy and robustness when compared to competitive baselines.

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