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In this paper, we present a novel semi-supervised clustering approach based on Markov process. It deals with data which include abundant local constraints. We apply the designed model to a topological region extraction problem, where topological segmentation is constructed based on sparse human inputs (potentially provided by human experts). The model considers human indications as seeds for topological regions, i.e. the partially labeled data. It results in a regional topological segmentation of connected free space.