Overlapping Clustering Models, and One (class) SVM to Bind Them All
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 [1] and its degree-corrected variants [16], as well as topic models such as LDA [9]. 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.
The paper studies the problem of overlapping clustering in relational data under a model that encompasses some other popular models for community detection and topic modeling. In this model, the samples are represented in a latent space  that represents the clustering memberships in which the coordinates are convex combinations of the corners of a cone. The authors propose a method to find these corners using one-class SVM, which is shown to exactly recover the corners in the population matrix, and vectors that are close to the corners in an empirical matrix. The authors establish consistency results for clustering recovery in network and topic models, and evaluate the performance of the method in synthetic and real data, comparing with other state-of-the-art methods.  The problem of overlapping clustering has received increasing attention and is of great interest in different communities. The authors presented a method that can be used in several contexts. The geometric aspects of overlapping clustering models have been studied previously, but the approach followed by the authors is very original and theoretically justified. The method is simple and efficient. I found the method especially relevant for overlapping clustering in network models, as the current approaches in the literature usually require stronger assumptions or make use of combinatorial algorithms. I am not very familiar with the literature in topic modeling, but the method requires to have anchor words on each topic, which seems to be a strong assumption (see Huang et al. "Anchor-Free Correlated Topic Modeling: Identifiability and Algorithm" NIPS 2016). Additionally, there seems to be other work that study the geometrical aspects of topic models, so it would be worth if the authors make more comments in the literature review or numerical comparisons (see for example Yurochkin and Nguyen "Geometric Dirichlet Means algorithm for topic inference", NIPS 2016).  The paper is in general clearly written, and Section 2 is well explained and motivated. However, I found the conditions and results in Section 3 hard to interpret since the authors do not introduce identifiability constraints on the parameters. Maybe this issue can be clarified if the authors are able to obtain closed-forms of the rates for special cases, and compare with other rates in the literature.  The authors make reference to other models which I think should be formally defined (at least in the appendix) for completeness.  UPDATE: Thanks to the authors for clarifying my questions in the rebuttal letter