Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

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Educational Attainment in the United States: March 1977 and 1976. Current Population Reports, Population Characteristics, Series P-20, No. 314.

America’s Changing Religious Landscape

Graph pattern matching is typically defined in terms of subgraph isomorphism, which makes it an np-complete problem. Moreover, it requires bijective functions, which are often too restrictive to characterize patterns in emerging applications. We propose a class of graph patterns, in which an edge denotes the connectivity in a data graph within a predefined number of hops. In addition, we define matching based on a notion of bounded simulation, an extension of graph simulation. We show that with this revision, graph pattern matching can be performed in cubic-time, by providing such an algorithm. We also develop algorithms for incrementally finding matches when data graphs are updated, with performance guarantees for dag patterns. We experimentally verify that these algorithms scale well, and that the revised notion of graph pattern matching allows us to identify communities commonly found in real-world networks.

Graph Pattern Matching.

With the rapid development of information technologies, various big graphs are prevalent in many real applications (e.g., social media and knowledge bases). An important component of these graphs is the network community. Essentially, a community is a group of vertices which are densely connected internally. Community retrieval can be used in many real applications, such as event organization, friend recommendation, and so on. Consequently, how to efficiently find high-quality communities from big graphs is an important research topic in the era of big data. Recently, a large group of research works, called community search, have been proposed. They aim to provide efficient solutions for searching high-quality communities from large networks in real time. Nevertheless, these works focus on different types of graphs and formulate communities in different manners, and thus, it is desirable to have a comprehensive review of these works. In this survey, we conduct a thorough review of existing community search works. Moreover, we analyze and compare the quality of communities under their models, and the performance of different solutions. Furthermore, we point out new research directions. This survey does not only help researchers to have better understanding of existing community search solutions, but also provides practitioners a better judgment on choosing the proper solutions.

A survey of community search over big graphs

In this paper, we propose an efficient hierarchical index, G*-tree, to optimize spatial queries on road networks. Most existing graph indexes can only support one kind of query, and thus we need to build multiple indexes on a road network to handle various kinds of spatial queries, which is inefficient and unscalable for real-world applications. To address the problem, a recent study proposes G-tree to support multiple types of spatial queries on road networks within one framework. However, the assembly-based method on G-tree is not efficient enough to handle spatial queries when vertices, which are close in a road network, are distant in G-tree. To address the inefficiency problem of G-tree, in this paper, we propose a novel index structure on road networks, namely G*-tree, whose key idea is to build shortcuts between selected leaf nodes. Based on G*-tree, we propose three shortcut-based algorithms to answer distance queries, k-nearest neighbor queries and range queries, respectively, which are more efficient than the existing assembly-based algorithms on G-tree. Moreover, we propose a shortcut selection algorithm to optimize the performance of spatial queries on G*-tree. We conduct extensive experiments to compare our G*-tree and the state-of-the-art indexing methods on various large-scale road networks, where the results demonstrate that our G*-tree has better efficiency and scalability than the competitors to handle spatial queries.

G*-Tree: An Efficient Spatial Index on Road Networks

Truss decomposition is to divide a graph into a hierarchy of subgraphs, or trusses. A subgraph is a k-truss (k 2) if each edge is in at least k --- 2 triangles in the subgraph. Existing algorithms ...

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Accelerating Truss Decomposition on Heterogeneous Processors

Community search problem, which is to find good communities given a set of query nodes in a graph, has attracted increasing research interest recently. Though various measurement models have been proposed to define and solve community search problem. Few of them could define a community concisely and have good quality of query results. They either involve additional constraints for modeling communities, such as size and diameter, or suffer from the free rider effect, i.e., include irrelevant subgraphs. In this paper, we propose a new k-plex based community model for community search. We show that our model not only is simple and clear, but also meets with basic requirements of defining a community search problem. We formulate the maximum k-plex community query (MCKPQ) problem, that is, given a set of query nodes Q, searching for optimal k-plex containing Q. We prove that MCKPQ is NP-hard, and it is hard to approximate in any constant factor. We first give exact solutions. Then, we propose an efficient branch-and-bound (B&B) method and design an effective upper bound function and a pruning strategy. Furthermore, we optimize the basic B&B by fast candidate generation. We also give a fast heuristic solution, which produces high-quality results in practice. The effectiveness of our model of community and the efficiency of our methods are verified by elaborate experiments.

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Query Optimal k-Plex Based Community in Graphs

SimRank is a popular link-based similarity measurement among nodes in a graph. To compute the all-pairs SimRank matrix accurately, iterative methods are usually used. For static graphs, current iterative solutions are not efficient enough, both in time and space, due to unnecessary cost and storage by the nature of iterative updating. For dynamic graphs, all current incremental solutions for updating the Sim-Rank matrix are based on an approximated SimRank definition, and thus have no accuracy guarantee. In this paper, we propose a novel local push based algorithm for computing all-pairs SimRank. We show that our algorithms outperform the state-of-the-art static and dynamic all-pairs SimRank algorithms.

Efficient SimRank Tracking in Dynamic Graphs

Community search in heterogeneous information networks (HINs) has attracted much attention in graph analysis. Given a vertex, the goal is to find a densely-connected sub-graph that contains the ver...

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Yue Wang

Papers

G*-Tree: An Efficient Spatial Index on Road Networks

Accelerating Truss Decomposition on Heterogeneous Processors

Query Optimal k-Plex Based Community in Graphs

Efficient SimRank Tracking in Dynamic Graphs

Effective and efficient relational community detection and search in large dynamic heterogeneous information networks