DeepAI AI Chat
Log In Sign Up

Community detection using fast low-cardinality semidefinite programming

by   Po-Wei Wang, et al.
Carnegie Mellon University

Modularity maximization has been a fundamental tool for understanding the community structure of a network, but the underlying optimization problem is nonconvex and NP-hard to solve. State-of-the-art algorithms like the Louvain or Leiden methods focus on different heuristics to help escape local optima, but they still depend on a greedy step that moves node assignment locally and is prone to getting trapped. In this paper, we propose a new class of low-cardinality algorithm that generalizes the local update to maximize a semidefinite relaxation derived from max-k-cut. This proposed algorithm is scalable, empirically achieves the global semidefinite optimality for small cases, and outperforms the state-of-the-art algorithms in real-world datasets with little additional time cost. From the algorithmic perspective, it also opens a new avenue for scaling-up semidefinite programming when the solutions are sparse instead of low-rank.


page 1

page 2

page 3

page 4


Scalable Semidefinite Relaxation for Maximum A Posterior Estimation

Maximum a posteriori (MAP) inference over discrete Markov random fields ...

The Mixing method: coordinate descent for low-rank semidefinite programming

In this paper, we propose a coordinate descent approach to low-rank stru...

Robust Learning from Noisy Side-information by Semidefinite Programming

Robustness recently becomes one of the major concerns among machine lear...

Low-rank semidefinite programming for the MAX2SAT problem

This paper proposes a new algorithm for solving MAX2SAT problems based o...

An Enhanced SDR based Global Algorithm for Nonconvex Complex Quadratic Programs with Signal Processing Applications

In this paper, we consider a class of nonconvex complex quadratic progra...

Accelerated first-order methods for a class of semidefinite programs

This paper introduces a new storage-optimal first-order method (FOM), Ce...