18.S096: Community dection and the Stochastic Block Model
نویسنده
چکیده
Community detection in a network is a central problem in data science. A few lectures ago we discussed clustering and gave a performance guarantee for spectral clustering (based on Cheeger’s Inequality) that was guaranteed to hold for any graph. While these guarantees are remarkable, they are worst-case guarantees and hence pessimistic in nature. In what follows we analyze the performance of a convex relaxation based algorithm on typical instances of the community detection problem (where typical is defined through some natural distribution of the input). We focus on the problem of minimum graph bisection. The objective is to partition a graph in two equal-sized disjoint sets (S, Sc) while minimizing cut(S) (note that in the previous lecture, for the Max-Cut problem, we were maximizing it instead!).
منابع مشابه
Consistency of community detection in networks under degree-corrected stochastic block models
Community detection is a fundamental problem in network analysis, with applications in many diverse areas. The stochastic block model is a common tool for model-based community detection, and asymptotic tools for checking consistency of community detection under the block model have been recently developed. However, the block model is limited by its assumption that all nodes within a community ...
متن کاملA Chance Constrained Integer Programming Model for Open Pit Long-Term Production Planning
The mine production planning defines a sequence of block extraction to obtain the highest NPV under a number of constraints. Mathematical programming has become a widespread approach to optimize production planning, for open pit mines since the 1960s. However, the previous and existing models are found to be limited in their ability to explicitly incorporate the ore grade uncertainty into the p...
متن کاملStochastic Block Models with Multiple Continuous Attributes
The stochastic block model (SBM) is a probabilistic model for community structure in networks. Typically, only the adjacency matrix is used to perform SBM parameter inference. In this paper, we consider circumstances in which nodes have an associated vector of continuous attributes that are also used to learn the node-to-community assignments and corresponding SBM parameters. While this assumpt...
متن کامل