The distance dependent Chinese restaurant process (ddCRP) provides a flexible framework for clustering data with temporal, spatial, or other structured dependencies. Here we model multiple groups of structured data, such as pixels within frames of a video sequence, or paragraphs within documents from a text corpus. We propose a hierarchical generalization of the ddCRP which clusters data within groups based on distances between data items, and couples clusters across groups via distances based on aggregate properties of these local clusters. Our hddCRP model subsumes previously proposed hierarchical extensions to the ddCRP and allows more flexibility in modeling complex data. This flexibility poses a challenging inference problem, and we derive a MCMC method that makes coordinated changes to data assignments both within and between local clusters. We demonstrate the effectiveness of our hddCRP on video segmentation and discourse modeling tasks, achieving results competitive with state-of-the-art methods.
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