Coherent closed quasi-clique discovery from large dense graph databases

Abstract

Frequent coherent subgraphs can provide valuable knowledge about the underlying internal structure of a graph database, and mining frequently occurring coherent subgraphs from large dense graph databases has been witnessed several applications and received considerable attention in the graph mining community recently. In this paper, we study how to efficiently mine the complete set of coherent closed quasi-cliques from large dense graph databases, which is an especially challenging task due to the downward-closure property no longer holds. By fully exploring some properties of quasicliques, we propose several novel optimization techniques, which can prune the unpromising and redundant sub-search spaces effectively. Meanwhile, we devise an efficient closure checking scheme to facilitate the discovery of only closed quasi-cliques. We also develop a coherent closed quasi-clique mining algorithm, Cocain 1 . Thorough performance study shows that Cocain is very efficient and scalable for large dense graph databases.

Multi-way set enumeration in weight tensors

“…There exist several competitive approaches that deal with sets of unweighted networks. We compared our DCE approach with Cocain (COC) (Zeng et al 2006) and Codense (COD) (Hu et al 2005). Cocain is an enumerative method that detects frequent quasi-cliques.…”

“…Relational data mining approaches (Ji et al 2006) are equivalent to DCE with density threshold 100%, so we did not consider them separately in our biological evaluation. The COC code was obtained from the original authors (Zeng et al 2006), and COD was downloaded from http://zhoulab.usc.edu/CODENSE/. The minimum network frequency and the minimum number of genes per cluster were set in all approaches to 3 and 6, respectively; there were 4745 frequent edges involving 411 nodes.…”

“…One fundamental approach is clique discovery, i.e., the enumeration of fully connected subgraphs from an unweighted input graph (e.g., see Spirin and Mirny 2003). As real-world datasets are usually incomplete, various methods relax this criterion by tolerating missing edges to a certain extent (Haraguchi and Okubo 2006;Palla et al 2005;Farkas et al 2007;Uno 2007;Zeng et al 2006) or by explicitly considering edge weights (Georgii et al 2009a;Ulitsky and Shamir 2009). Beside these enumerative approaches to cluster detection, there exist a number of methods that employ local search techniques starting from a set of seed clusters (Everett et al 2006;Bader and Hogue 2003).…”

“…While many approaches focus on the detection of frequently occurring subgraphs in large databases of small graphs (Yan and Han 2002), methods for larger networks often use density criteria combined with additional constraints (Hu et al 2005;Jiang and Pei 2009;Robardet 2009;Zeng et al 2006).…”

“…Clearly, a balanced cluster is also a dense cluster with respect to θ , but not vice versa. For the specific case of a binary-valued symmetric input matrix, i.e., a graph, the balance criterion is equivalent to the concept of quasi-cliques (Zeng et al 2006): a γ -quasi-clique is defined as a set of nodes U such that each of them has edges to at least γ (|U | − 1) other nodes in U . As our implementation stores the degree of each instance with respect to the current cluster, it is straightforward to integrate a filtering step that checks the balance criterion.…”