Given a user-specified minimum degree threshold γ, a γ-quasi-clique is a subgraph where each vertex connects to at least γ fraction of the other vertices. Quasi-clique is a natural definition for dense structures, so finding large and hence statistically significant quasi-cliques is useful in applications such as community detection in social networks and discovering significant biomolecule structures and pathways. However, mining maximal quasi-cliques is notoriously expensive, and even a recent algorithm for mining large maximal quasi-cliques is flawed and can lead to a lot of repeated searches. This paper proposes a parallel solution for mining maximal quasi-cliques that is able to fully utilize CPU cores. Our solution utilizes divide and conquer to decompose the workloads into independent tasks for parallel mining, and we addressed the problem of (i) drastic load imbalance among different tasks and (ii) difficulty in predicting the task running time and the time growth with task subgraph size, by (a) using a timeout-based task decomposition strategy, and by (b) utilizing a priority task queue to schedule long-running tasks earlier for mining and decomposition to avoid stragglers. Unlike our conference version in PVLDB 2020 where the solution was built on a distributed graph mining framework called G-thinker, this paper targets a single-machine multi-core environment which is more accessible to an average end user. A general framework called T-thinker is developed to facilitate the programming of parallel programs for algorithms that adopt divide and conquer, including but not limited to our quasi-clique mining algorithm. Additionally, we consider the problem of directly mining large quasi-cliques from dense parts of a graph, where we identify the repeated search issue of a recent method and address it using a carefully designed concurrent trie data structure. Extensive experiments verify that our parallel solution scales well with the number of CPU cores, achieving 26.68× runtime speedup when mining a graph with 3.77M vertices and 16.5M edges with 32 mining threads. Additionally, mining large quasi-cliques from dense parts can provide an additional speedup of up to 89.46×.
more »
« less
A Local Algorithm for Structure-Preserving Graph Cut
Nowadays, large-scale graph data is being generated in a variety of real-world applications, from social networks to co-authorship networks, from protein-protein interaction networks to road traffic networks. Many existing works on graph mining focus on the vertices and edges, with the first-order Markov chain as the underlying model. They fail to explore the high-order network structures, which are of key importance in many high impact domains. For example, in bank customer personally identifiable information (PII) networks, the star structures often correspond to a set of synthetic identities; in financial transaction networks, the loop structures may indicate the existence of money laundering. In this paper, we focus on mining user-specified high-order network structures and aim to find a structure-rich subgraph which does not break many such structures by separating the subgraph from the rest.
A key challenge associated with finding a structure-rich subgraph is the prohibitive computational cost. To address this problem, inspired by the family of local graph clustering algorithms for efficiently identifying a low-conductance cut without exploring the entire graph, we propose to generalize the key idea to model high-order network structures. In particular, we start with a generic definition of high-order conductance, and define the high-order diffusion core, which is based on a high-order random walk induced by user-specified high-order network structure. Then we propose a novel High-Order Structure-Preserving LOcal Cut (HOSPLOC) algorithm, which runs in polylogarithmic time with respect to the number of edges in the graph. It starts with a seed vertex and iteratively explores its neighborhood until a subgraph with a small high-order conductance is found. Furthermore, we analyze its performance in terms of both effectiveness and efficiency. The experimental results on both synthetic graphs and real graphs demonstrate the effectiveness and efficiency of our proposed HOSPLOC algorithm.
more »
« less
- NSF-PAR ID:
- 10062449
- Date Published:
- Journal Name:
- KDD
- Page Range / eLocation ID:
- 655 to 664
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Networks or graphs provide a natural and generic way for modeling rich structured data. Recent research on graph analysis has been focused on representation learning, of which the goal is to encode the network structures into distributed embedding vectors, so as to enable various downstream applications through off-the-shelf machine learning. However, existing methods mostly focus on node-level embedding, which is insufficient for subgraph analysis. Moreover, their leverage of network structures through path sampling or neighborhood preserving is implicit and coarse. Network motifs allow graph analysis in a finer granularity, but existing methods based on motif matching are limited to enumerated simple motifs and do not leverage node labels and supervision. In this paper, we develop NEST, a novel hierarchical network embedding method combining motif filtering and convolutional neural networks. Motif-based filtering enables NEST to capture exact small structures within networks, and convolution over the filtered embedding allows it to fully explore complex substructures and their combinations. NEST can be trivially applied to any domain and provide insight into particular network functional blocks. Extensive experiments on protein function prediction, drug toxicity prediction and social network community identification have demonstrated its effectiveness and efficiency.more » « less
-
null (Ed.)Given a user-specified minimum degree threshold γ, a γ-quasi-clique is a subgraph g = (Vg, Eg) where each vertex ν ∈ Vg connects to at least γ fraction of the other vertices (i.e., ⌈γ · (|Vg|- 1)⌉ vertices) in g. Quasi-clique is one of the most natural definitions for dense structures useful in finding communities in social networks and discovering significant biomolecule structures and pathways. However, mining maximal quasi-cliques is notoriously expensive. In this paper, we design parallel algorithms for mining maximal quasi-cliques on G-thinker, a distributed graph mining framework that decomposes mining into compute-intensive tasks to fully utilize CPU cores. We found that directly using G-thinker results in the straggler problem due to (i) the drastic load imbalance among different tasks and (ii) the difficulty of predicting the task running time. We address these challenges by redesigning G-thinker's execution engine to prioritize long-running tasks for execution, and by utilizing a novel timeout strategy to effectively decompose long-running tasks to improve load balancing. While this system redesign applies to many other expensive dense subgraph mining problems, this paper verifies the idea by adapting the state-of-the-art quasi-clique algorithm, Quick, to our redesigned G-thinker. Extensive experiments verify that our new solution scales well with the number of CPU cores, achieving 201× runtime speedup when mining a graph with 3.77M vertices and 16.5M edges in a 16-node cluster.more » « less
-
Attributed subgraph matching is a powerful tool for explorative mining of large attributed networks. In many applications (e.g., network science of teams, intelligence analysis, finance informatics), the user might not know what exactly s/he is looking for, and thus require the user to constantly revise the initial query graph based on what s/he finds from the current matching results. A major bottleneck in such an interactive matching scenario is the efficiency, as simply rerunning the matching algorithm on the revised query graph is computationally prohibitive. In this paper, we propose a family of effective and efficient algorithms (FIRST) to support interactive attributed subgraph matching. There are two key ideas behind the proposed methods. The first is to recast the attributed subgraph matching problem as a cross-network node similarity problem, whose major computation lies in solving a Sylvester equation for the query graph and the underlying data graph. The second key idea is to explore the smoothness between the initial and revised queries, which allows us to solve the new/updated Sylvester equation incrementally, without re-solving it from scratch. Experimental results show that our method can achieve (1) up to 16x speed-up when applying on networks with 6M$+$ nodes; (2) preserving more than 90% accuracy compared with existing methods; and (3) scales linearly with respect to the size of the data graph.more » « less
-
Abstract Background Given a collection of coexpression networks over a set of genes, identifying subnetworks that appear frequently is an important research problem known as mining frequent subgraphs. Maximal frequent subgraphs are a representative set of frequent subgraphs; A frequent subgraph is maximal if it does not have a super-graph that is frequent. In the bioinformatics discipline, methodologies for mining frequent and/or maximal frequent subgraphs can be used to discover interesting network motifs that elucidate complex interactions among genes, reflected through the edges of the frequent subnetworks. Further study of frequent coexpression subnetworks enhances the discovery of biological modules and biological signatures for gene expression and disease classification. Results We propose a reverse search algorithm, called RASMA, for mining frequent and maximal frequent subgraphs in a given collection of graphs. A key innovation in RASMA is a connected subgraph enumerator that uses a reverse-search strategy to enumerate connected subgraphs of an undirected graph. Using this enumeration strategy, RASMA obtains all maximal frequent subgraphs very efficiently. To overcome the computationally prohibitive task of enumerating all frequent subgraphs while mining for the maximal frequent subgraphs, RASMA employs several pruning strategies that substantially improve its overall runtime performance. Experimental results show that on large gene coexpression networks, the proposed algorithm efficiently mines biologically relevant maximal frequent subgraphs. Conclusion Extracting recurrent gene coexpression subnetworks from multiple gene expression experiments enables the discovery of functional modules and subnetwork biomarkers. We have proposed a reverse search algorithm for mining maximal frequent subnetworks. Enrichment analysis of the extracted maximal frequent subnetworks reveals that subnetworks that are frequent are highly enriched with known biological ontologies.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3097983.3098015
