VoG: Summarizing and Understanding Large Graphs

How can we succinctly describe a million-node graph with a few simple sentences? How can we measure the "importance" of a set of discovered subgraphs in a large graph? These are exactly the problems we focus on. Our main ideas are to construct a "vocabulary" of subgraph-types that often occur in real graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the most succinct description of a graph in terms of this vocabulary. We measure success in a well-founded way by means of the Minimum Description Length (MDL) principle: a subgraph is included in the summary if it decreases the total description length of the graph. Our contributions are three-fold: (a) formulation: we provide a principled encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop \method, an efficient method to minimize the description cost, and (c) applicability: we report experimental results on multi-million-edge real graphs, including Flickr and the Notre Dame web graph.Comment: SIAM International Conference on Data Mining (SDM) 201

{VoG}: {Summarizing} and Understanding Large Graphs

How can we succinctly describe a million-node graph with a few simple sentences? How can we measure the "importance" of a set of discovered subgraphs in a large graph? These are exactly the problems we focus on. Our main ideas are to construct a "vocabulary" of subgraph-types that often occur in real graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the most succinct description of a graph in terms of this vocabulary. We measure success in a well-founded way by means of the Minimum Description Length (MDL) principle: a subgraph is included in the summary if it decreases the total description length of the graph. Our contributions are three-fold: (a) formulation: we provide a principled encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop \method, an efficient method to minimize the description cost, and (c) applicability: we report experimental results on multi-million-edge real graphs, including Flickr and the Notre Dame web graph

Flow-based Influence Graph Visual Summarization

Visually mining a large influence graph is appealing yet challenging. People are amazed by pictures of newscasting graph on Twitter, engaged by hidden citation networks in academics, nevertheless often troubled by the unpleasant readability of the underlying visualization. Existing summarization methods enhance the graph visualization with blocked views, but have adverse effect on the latent influence structure. How can we visually summarize a large graph to maximize influence flows? In particular, how can we illustrate the impact of an individual node through the summarization? Can we maintain the appealing graph metaphor while preserving both the overall influence pattern and fine readability? To answer these questions, we first formally define the influence graph summarization problem. Second, we propose an end-to-end framework to solve the new problem. Our method can not only highlight the flow-based influence patterns in the visual summarization, but also inherently support rich graph attributes. Last, we present a theoretic analysis and report our experiment results. Both evidences demonstrate that our framework can effectively approximate the proposed influence graph summarization objective while outperforming previous methods in a typical scenario of visually mining academic citation networks.Comment: to appear in IEEE International Conference on Data Mining (ICDM), Shen Zhen, China, December 201

A Graph Theoretic Approach for Object Shape Representation in Compositional Hierarchies Using a Hybrid Generative-Descriptive Model

A graph theoretic approach is proposed for object shape representation in a hierarchical compositional architecture called Compositional Hierarchy of Parts (CHOP). In the proposed approach, vocabulary learning is performed using a hybrid generative-descriptive model. First, statistical relationships between parts are learned using a Minimum Conditional Entropy Clustering algorithm. Then, selection of descriptive parts is defined as a frequent subgraph discovery problem, and solved using a Minimum Description Length (MDL) principle. Finally, part compositions are constructed by compressing the internal data representation with discovered substructures. Shape representation and computational complexity properties of the proposed approach and algorithms are examined using six benchmark two-dimensional shape image datasets. Experiments show that CHOP can employ part shareability and indexing mechanisms for fast inference of part compositions using learned shape vocabularies. Additionally, CHOP provides better shape retrieval performance than the state-of-the-art shape retrieval methods.Comment: Paper : 17 pages. 13th European Conference on Computer Vision (ECCV 2014), Zurich, Switzerland, September 6-12, 2014, Proceedings, Part III, pp 566-581. Supplementary material can be downloaded from http://link.springer.com/content/esm/chp:10.1007/978-3-319-10578-9_37/file/MediaObjects/978-3-319-10578-9_37_MOESM1_ESM.pd