Compositional Clustering: Applications to Multi-Label Object Recognition and Speaker Identification

We consider a novel clustering task in which clusters can have compositional relationships, e.g., one cluster contains images of rectangles, one contains images of circles, and a third (compositional) cluster contains images with both objects. In contrast to hierarchical clustering in which a parent cluster represents the intersection of properties of the child clusters, our problem is about finding compositional clusters that represent the union of the properties of the constituent clusters. This task is motivated by recently developed few-shot learning and embedding models can distinguish the label sets, not just the individual labels, assigned to the examples. We propose three new algorithms -- Compositional Affinity Propagation (CAP), Compositional k-means (CKM), and Greedy Compositional Reassignment (GCR) -- that can partition examples into coherent groups and infer the compositional structure among them. We show promising results, compared to popular algorithms such as Gaussian mixtures, Fuzzy c-means, and Agglomerative Clustering, on the OmniGlot and LibriSpeech datasets. Our work has applications to open-world multi-label object recognition and speaker identification & diarization with simultaneous speech from multiple speakers.