In the following, we use X P to denote that the random variable X follows the law P . See Figure 1a for an illustration of such a graph generated by the Stochastic Block Model. Interestingly, Newman [31] has shown that the modularity objective is the maximum likelihood of a variant of the SBM on two communities, with prescribed degree distribution. However, it leaves the natural question open of whether the Louvain heuristic on the SBM with two communities indeed converges to this solution (the hidden partition). Proving the convergence shows that Louvain's local decisions can indeed be powerful enough to reach the global optimum.

A classic problem in machine learning and data analysis is to partition the vertices of a network in such a way that vertices in the same set are densely connected and vertices in different sets are loosely connected. In practice, the most popular approaches rely on local search algorithms; not only for the ease of implementation and the efficiency, but also because of the accuracy of these methods on many real world graphs. For example, the Louvain algorithm - a local search based algorithm - has quickly become the method of choice for clustering in social networks.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

In many applications, the data is of rich structure that can be represented by a hypergraph, where the data items are represented by vertices and the associations among items are represented by hyperedges. Equivalently, we are given an input bipartite graph with two types of vertices: items, and associations (which we refer to as topics). We consider the problem of partitioning the set of items into a given number of components such that the maximum number of topics covered by a component is minimized. This is a clustering problem with various applications, e.g.

We present the Mind the Gap Model (MGM), an approach for interpretable feature extraction and selection. By placing interpretability criteria directly into the model, we allow for the model to both optimize parameters related to interpretabil-ity and to directly report a global set of distinguishable dimensions to assist with further data exploration and hypothesis generation.

In this paper, we study one challenging issue in multi-view data clustering.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/