  People belong to multiple communities, words belong to multiple topics, and
books cover multiple genres; overlapping clusters are commonplace. Many
existing overlapping clustering methods model each person (or word, or book) as
a non-negative weighted combination of "exemplars" who belong solely to one
community, with some small noise. Geometrically, each person is a point on a
cone whose corners are these exemplars. This basic form encompasses the widely
used Mixed Membership Stochastic Blockmodel of networks (Airoldi et al., 2008)
and its degree-corrected variants (Jin et al., 2017), as well as topic models
such as LDA (Blei et al., 2003). We show that a simple one-class SVM yields
provably consistent parameter inference for all such models, and scales to
large datasets. Experimental results on several simulated and real datasets
show our algorithm (called SVM-cone) is both accurate and scalable.
