We consider a new kind of clustering problem in which clusters need not be independent of each other, but rather can have compositional relationships with other clusters (e.g., an image set consists of rectangles, circles, as well as combinations of rectangles and circles). This task is motivated by recent work in few-shot learning on compositional embedding models that structure the embedding space to distinguish the label sets, not just the individual labels, assigned to the examples. To tackle this clustering problem, we propose a new algorithm called Compositional Affinity Propagation (CAP). In contrast to standard Affinity Propagation as well as other algorithms for multi-view and hierarchical clustering, CAP can deduce compositionality among clusters automatically. We show promising results, compared to several existing clustering algorithms, on the MultiMNIST, OmniGlot, and LibriSpeech datasets. Our work has applications to multi-object image recognition and speaker diarization with simultaneous speech from multiple speakers.
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