Lovasz ϑ, SVMs and applications

Finding Dense Subgraphs in Relational Graphs

“…Jethava et al [13] present a parameter-less algorithm based on a multiple kernel learning (MKL) [3,27] formulation for finding an ordering of vertices which maximizes the minimum relative density (across all graphs) of the induced subgraph. Their approach also provides weak graph-dependent bounds on the density of the induced subgraphs [see 14, Lemma 11 and Theorem 12].…”

“…; thus covering a wide range of practical scenarios [17]. This was used for experimental evaluation in [13] and we repeat their experimental setup. snap-as.…”

“…Several data-mining methods have addressed the problem of enumerating dense recurrent subgraphs [see,e.g., 6,12,13,24,26,31,33]. Most existing approaches enumerate all frequent quasicliques depending on parameters such as minimum support threshold and minimum relative density.…”

“…The approach of [24] yields a non-convex cubic programming problem which is solved approximately using multi-stage convex relaxation [34] and used in the analysis of coexpression networks in order to identify small biologically relevant modules. [13] present a method to identify large dense subgraphs based on solving a Multiple Kernel Learning (MKL) problem [3,27] with precomputed kernels.…”

“…In this paper, we formalize the notion of Densest Common Subgraph (i.e., a subset of nodes which maximizes the density of the induced subgraph in each of the graphs in the relational graph set) which was previously discussed in [13]. We present an approximation algorithm (DCS LP) for finding the densest common subgraph in a relational graph set based on an extension of Charikar's LP based approach [7,20] for finding the densest subgraph (DS) in a single graph.…”