Nuclear norm minimization for the planted clique and biclique problems

• Published in: Mathematical programming Vol. 129; no. 1; pp. 69 - 89
• Main Authors: Ames, Brendan P. W., Vavasis, Stephen A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.09.2011; Springer Nature B.V
• Subjects: Algorithms; Bypasses; Calculus of Variations and Optimal Control; Optimization; Combinatorics; Convex analysis; Data mining; Exact solutions; Full Length Paper; Graphs; Mathematical analysis; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematical programming; Mathematics; Mathematics and Statistics; Mathematics of Computing; Minimization; Norms; Numerical Analysis; Optimization; Studies; Theoretical; 68Q25; 90C25; 65K05

We consider the problems of finding a maximum clique in a graph and finding a maximum-edge biclique in a bipartite graph. Both problems are NP-hard. We write both problems as matrix-rank minimization and then relax them using the nuclear norm. This technique, which may be regarded as a generalizatio...