In this paper, we consider the question of determining whether a function f has property P or is e-far from any function with property P. A property testing algorithm is given a sample of the value of f on instances drawn according to some distribution. In some cases, it is also allowed to query f on instances of its choice. We study this question for different properties and establish some connections to problems in learning theory and approximation.In particular, we focus our attention on testing graph properties. Given access to a graph G in the form of being able to query whether an edge exists or not between a pair of vertices, we devise algorithms to test whether the underlying graph has properties such as being bipartite, k-Colorable, or having a p-Clique (clique of density p with respect to the vertex set). Our graph property testing algorithms are probabilistic and make assertions that are correct with high probability, while making a number of queries that is independent of the size of the graph. Moreover, the property testing algorithms can be used to efficiently (i.e., in time linear in the number of vertices) construct partitions of the graph that correspond to the property being tested, if it holds for the input graph.

Property Testing and its connection to Learning and Approximation

1 July 7, 2010, marks the fifth anniversary of the 2005 terrorist attacks on London’s Metro system. In 2005, terrorists launched a coordinated attack against London’s transportation system, with 3 bombs detonating simultaneously at three different Metro stations and a fourth bomb exploding an hour later on a city bus. In all, there were 52 victims in these bombings with an additional 700 injuries resulting. The four terrorists who executed the attacks were killed in the explosions.

National Consortium for the Study of Terrorism and Responses to Terrorism

In this paper we provide a comprehensive introduction to knowledge graphs,
which have recently garnered significant attention from both industry and
academia in scenarios that require exploiting diverse, dynamic, large-scale
collections of data. After some opening remarks, we motivate and contrast
various graph-based data models and query languages that are used for knowledge
graphs. We discuss the roles of schema, identity, and context in knowledge
graphs. We explain how knowledge can be represented and extracted using a
combination of deductive and inductive techniques. We summarise methods for the
creation, enrichment, quality assessment, refinement, and publication of
knowledge graphs. We provide an overview of prominent open knowledge graphs and
enterprise knowledge graphs, their applications, and how they use the
aforementioned techniques. We conclude with high-level future research
directions for knowledge graphs.

Knowledge Graphs

With an ever-increasing amount of options, the task of selecting machine learning tools for big data can be difficult. The available tools have advantages and drawbacks, and many have overlapping uses. The world’s data is growing rapidly, and traditional tools for machine learning are becoming insufficient as we move towards distributed and real-time processing. This paper is intended to aid the researcher or professional who understands machine learning but is inexperienced with big data. In order to evaluate tools, one should have a thorough understanding of what to look for. To that end, this paper provides a list of criteria for making selections along with an analysis of the advantages and drawbacks of each. We do this by starting from the beginning, and looking at what exactly the term “big data” means. From there, we go on to the Hadoop ecosystem for a look at many of the projects that are part of a typical machine learning architecture and an understanding of how everything might fit together. We discuss the advantages and disadvantages of three different processing paradigms along with a comparison of engines that implement them, including MapReduce, Spark, Flink, Storm, and H2O. We then look at machine learning libraries and frameworks including Mahout, MLlib, SAMOA, and evaluate them based on criteria such as scalability, ease of use, and extensibility. There is no single toolkit that truly embodies a one-size-fits-all solution, so this paper aims to help make decisions smoother by providing as much information as possible and quantifying what the tradeoffs will be. Additionally, throughout this paper, we review recent research in the field using these tools and talk about possible future directions for toolkit-based learning.

/pdf/a-survey-of-open-source-tools-for-machine-learning-with-big-3zyg93jtm4.pdf

A survey of open source tools for machine learning with big data in the Hadoop ecosystem

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ACM Transactions on Database Systems

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.

/pdf/graph-pattern-matching-from-intractable-to-polynomial-time-571evrwcqi.pdf

Graph pattern matching: from intractable to polynomial time

Graph Pattern Matching.

It is common to find graphs with millions of nodes and billions of edges in, e.g., social networks. Queries on such graphs are often prohibitively expensive. These motivate us to propose query preserving graph compression, to compress graphs relative to a class Λ of queries of users' choice. We compute a small Gr from a graph G such that (a) for any query Q E Λ Q, Q(G) = Q'(Gr), where Q' E Λ can be efficiently computed from Q; and (b) any algorithm for computing Q(G) can be directly applied to evaluating Q' on Gras is. That is, while we cannot lower the complexity of evaluating graph queries, we reduce data graphs while preserving the answers to all the queries in Λ. To verify the effectiveness of this approach, (1) we develop compression strategies for two classes of queries: reachability and graph pattern queries via (bounded) simulation. We show that graphs can be efficiently compressed via a reachability equivalence relation and graph bisimulation, respectively, while reserving query answers. (2) We provide techniques for aintaining compressed graph Gr in response to changes ΔG to the original graph G. We show that the incremental maintenance problems are unbounded for the two lasses of queries, i.e., their costs are not a function of the size of ΔG and changes in Gr. Nevertheless, we develop incremental algorithms that depend only on ΔG and Gr, independent ofG, i.e., we do not have to decompress Gr to propagate the changes. (3) Using real-life data, we experimentally verify that our compression techniques could reduce graphs in average by 95% for reachability and 57% for graph pattern matching, and that our incremental maintenance algorithms are efficient.

/pdf/query-preserving-graph-compression-4ibo0q25dd.pdf

Query preserving graph compression

It is increasingly common to find graphs in which edges bear different types, indicating a variety of relationships. For such graphs we propose a class of reachability queries and a class of graph patterns, in which an edge is specified with a regular expression of a certain form, expressing the connectivity in a data graph via edges of various types. In addition, we define graph pattern matching based on a revised notion of graph simulation. On graphs in emerging applications such as social networks, we show that these queries are capable of finding more sensible information than their traditional counterparts. Better still, their increased expressive power does not come with extra complexity. Indeed, (1) we investigate their containment and minimization problems, and show that these fundamental problems are in quadratic time for reachability queries and are in cubic time for pattern queries. (2) We develop an algorithm for answering reachability queries, in quadratic time as for their traditional counterpart. (3) We provide two cubic-time algorithms for evaluating graph pattern queries based on extended graph simulation, as opposed to the NP-completeness of graph pattern matching via subgraph isomorphism. (4) The effectiveness, efficiency and scalability of these algorithms are experimentally verified using real-life data and synthetic data.

/pdf/adding-regular-expressions-to-graph-reachability-and-pattern-2nssz49po9.pdf

Adding regular expressions to graph reachability and pattern queries

It is increasingly common to find real-life data represented as networks of labeled, heterogeneous entities. To query these networks, one often needs to identify the matches of a given query graph in a (typically large) network modeled as a target graph. Due to noise and the lack of fixed schema in the target graph, the query graph can substantially differ from its matches in the target graph in both structure and node labels, thus bringing challenges to the graph querying tasks. In this paper, we propose NeMa (Network Match), a neighborhood-based subgraph matching technique for querying real-life networks. (1) To measure the quality of the match, we propose a novel subgraph matching cost metric that aggregates the costs of matching individual nodes, and unifies both structure and node label similarities. (2) Based on the metric, we formulate the minimum cost subgraph matching problem. Given a query graph and a target graph, the problem is to identify the (top-k) matches of the query graph with minimum costs in the target graph. We show that the problem is NP-hard, and also hard to approximate. (3) We propose a heuristic algorithm for solving the problem based on an inference model. In addition, we propose optimization techniques to improve the efficiency of our method. (4) We empirically verify that NeMa is both effective and efficient compared to the keyword search and various state-of-the-art graph querying techniques.

/pdf/nema-fast-graph-search-with-label-similarity-4q4gkx0t1q.pdf

Yinghui Wu

Papers

Graph pattern matching: from intractable to polynomial time

Graph Pattern Matching.

Query preserving graph compression

Adding regular expressions to graph reachability and pattern queries

NeMa: fast graph search with label similarity