2013/06/14 by Thomas Bühler, Bühler, Thomas, Syama Sundar Rangapuram +5 · 3 citations
Business, Management and Accounting · Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Face and Expression Recognition #Facility Location and Emergency Management #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Metaheuristic Optimization Algorithms Research #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1306.3409
openalex publication_date 2013/06/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice. While these relaxations can be solved globally optimally, they are often too loose and thus lead to results far away from the optimum. In this paper we show that every constrained minimization problem of a ratio of non-negative set functions allows a tight relaxation into an unconstrained continuous optimization problem. This result leads to a flexible framework for solving constrained problems in network analysis. While a globally optimal solution for the resulting non-convex problem cannot be guaranteed, we outperform the loose convex or spectral relaxations by a large margin on constrained local clustering problems.