NetLSD

An important component of current research in big data is graph analytics on very large graphs. Of the many problems of interest in this domain, graph pattern matching is both challenging and practically important. The problem is, given a relatively small query graph, finding matching patterns in a large data graph. Algorithms to address this problem are used in large social networks and graph databases. Though fast querying is highly desirable, the scalability of pattern matching algorithms is hindered by the NP-completeness of the subgraph isomorphism problem. This paper presents a conceptually simple, memory-efficient, pruning-based algorithm for the subgraph isomorphism problem that outperforms commonly used algorithms on large graphs. The high performance is due in large part to the effectiveness of the pruning algorithm, which in many cases removes a large percentage of the vertices not found in isomorphic matches. In this paper, the runtime of the algorithm is tested alongside other algorithms on graphs of up to 10 million vertices and 250 million edges.

Protein-protein interaction (PPI) networks carry vital information on the organization of molecular interactions in cellular systems. The identification of functionally relevant modules in PPI networks is one of the most important applications of biological network analysis. Computational analysis is becoming an indispensable tool to understand large-scale biomolecular interaction networks. Several types of computational methods have been developed and employed for the analysis of PPI networks. Of these computational methods, graph comparison and module detection are the two most commonly used strategies. This review summarizes current literature on graph kernel and graph alignment methods for graph comparison strategies, as well as module detection approaches including seed-and-extend, hierarchical clustering, optimization-based, probabilistic, and frequent subgraph methods. Herein, we provide a comprehensive review of the major algorithms employed under each theme, including our recently published frequent subgraph method, for detecting functional modules commonly shared across multiple cancer PPI networks.

We developed a parallel algorithm to improve the cache behavior and overall performance for multiplication of sparse matrices with sparse vectors (SpMSpV), an operation used increasingly in large graph analytics, particularly dynamic graphs in social networks and homeland security applications. The proposed algorithm builds upon the two-phase approach of partitioning the multiplication into a scaling phase and an aggregation phase, to achieve more cache-friendly access patterns individually in each phase [6], [3]. However, to handle dynamic graphs and achieve better load balancing for parallel implementation, we use a combination of private and shared bins, with synchronized access to shared bins to exchange the product terms between the two phases. The new algorithm accumulates product terms in private bins for each thread. The algorithm then performs a bulk transfer between a private bin and a shared bin, when the private bin becomes full. Then results are aggregated from the shared bins. In addition, we employ heuristics to decide the best algorithm for SpMSpV based on the number of nonzeros involved in the operation. When the number of nonzeros is large, it may be better to perform the operation as SpMV (sparse matrix times dense vector) despite the added conversion cost. Also, if the number of nonzeros is low it is advantageous to use a simplified algorithm. We compared our algorithm with existing algorithms for SpMSpV, and our evaluation shows that execution time is reduced by several times when large graphs are considered.

Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner’s guide to kernel-based graph classification.

Many Big Data analytics essentially explore the relationship among interconnected entities, which are naturally represented as graphs. However, due to the irregular data access patterns in the graph computations, it remains a fundamental challenge to deliver highly efficient solutions for large scale graph analytics. Such inefficiency restricts the utilization of many graph algorithms in Big Data scenarios. To address the performance issues in large scale graph analytics, we develop a graph processing system called System G, which explores efficient graph data organization for parallel computing architectures. We discuss various graph data organizations and their impact on data locality during graph traversals, which results in various cache performance behavior on processor side. In addition, we analyze data parallelism from architecture's perspective and experimentally show the efficiency for System G based graph analytics. We present experimental results for commodity multicore clusters and IBM PERCS supercomputers to illustrate the performance of System G for large scale graph analytics.

Graph kernels are of vital importance in the field of graph comparison and classification. However, how to compare and evaluate graph kernels and how to choose an optimal kernel for a practical classification problem remain open problems. In this paper, a comprehensive evaluation framework of graph kernels is proposed for unattributed graph classification. According to the kernel design methods, the whole graph kernel family can be categorized in five different dimensions, and then several representative graph kernels are chosen from these categories to perform the evaluation. With plenty of real-world and synthetic datasets, kernels are compared by many criteria such as classification accuracy, F1 score, runtime cost, scalability and applicability. Finally, quantitative conclusions are discussed based on the analyses of the extensive experimental results. The main contribution of this paper is that a comprehensive evaluation framework of graph kernels is proposed, which is significant for graph-classification applications and the future kernel research.

Distributed-memory clusters are used for in-memory processing of very large graphs with billions of nodes and edges. This requires partitioning the graph among the machines in the cluster. When a graph is partitioned, a node in the graph may be replicated on several machines, and communication is required to keep these replicas synchronized. Good partitioning policies attempt to reduce this synchronization overhead while keeping the computational load balanced across machines. A number of recent studies have looked at ways to control replication of nodes, but these studies are not conclusive because they were performed on small clusters with eight to sixteen machines, did not consider work-efficient data-driven algorithms, or did not optimize communication for the partitioning strategies they studied. This paper presents an experimental study of partitioning strategies for work-efficient graph analytics applications on large KNL and Skylake clusters with up to 256 machines using the Gluon communication runtime which implements partitioning-specific communication optimizations. Evaluation results show that although simple partitioning strategies like Edge-Cuts perform well on a small number of machines, an alternative partitioning strategy called Cartesian Vertex-Cut (CVC) performs better at scale even though paradoxically it has a higher replication factor and performs more communication than Edge-Cut partitioning does. Results from communication micro-benchmarks resolve this paradox by showing that communication overhead depends not only on communication volume but also on the communication pattern among the partitions. These experiments suggest that high-performance graph analytics systems should support multiple partitioning strategies, like Gluon does, as no single graph partitioning strategy is best for all cluster sizes. For such systems, a decision tree for selecting a good partitioning strategy based on characteristics of the computation and the cluster is presented.

We present Ringo, a system for analysis of large graphs. Graphs provide a way to represent and analyze systems of interacting objects (people, proteins, webpages) with edges between the objects denoting interactions (friendships, physical interactions, links). Mining graphs provides valuable insights about individual objects as well as the relationships among them. In building Ringo, we take advantage of the fact that machines with large memory and many cores are widely available and also relatively affordable. This allows us to build an easy-to-use interactive high-performance graph analytics system. Graphs also need to be built from input data, which often resides in the form of relational tables. Thus, Ringo provides rich functionality for manipulating raw input data tables into various kinds of graphs. Furthermore, Ringo also provides over 200 graph analytics functions that can then be applied to constructed graphs. We show that a single big-memory machine provides a very attractive platform for performing analytics on all but the largest graphs as it offers excellent performance and ease of use as compared to alternative approaches. With Ringo, we also demonstrate how to integrate graph analytics with an iterative process of trial-and-error data exploration and rapid experimentation, common in data mining workloads.

This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation, which is constructed using the Dirac operator of Kostant. Their explicit evaluation is obtained by localization on geodesics in the symmetric space, in a formula closely related to the Atiyah-Bott fixed point formulas. Orbital integrals associated with the wave kernel are also computed. Estimates on the hypoelliptic heat kernel play a key role in the proofs, and are obtained by combining analytic, geometric, and probabilistic techniques. Analytic techniques emphasize the wavelike aspects of the hypoelliptic heat kernel, while geometrical considerations are needed to obtain proper control of the hypoelliptic heat kernel, especially in the localization process near the geodesics. Probabilistic techniques are especially relevant, because underlying the hypoelliptic deformation is a deformation of dynamical systems on the symmetric space, which interpolates between Brownian motion and the geodesic flow. The Malliavin calculus is used at critical stages of the proof.Author: Bismut, Jean-Michel Publisher: Princeton University Press Illustration: N Language: ENG Title: Hypoelliptic Laplacian and Orbital Integrals (AM-177) Pages: 00320 (Encrypted EPUB) / 00320 (Encrypted PDF) On Sale: 2011-08-28 SKU-13/ISBN: 9780691151304 Category: Mathematics : Geometry Analytic Category: Mathematics : Mathematical Analysis Category: Mathematics : Matrices

Existing Big Data streams coming from social and other connected sensor networks exhibit intrinsic inter-dependency enabling unique challenges to scalable graph analytics. Data from these graphs is usually collected in different geographically located data servers making it suitable for distributed processing on clouds. While numerous solutions for large scale static graph analysis have been proposed, addressing in real-time the dynamics of social interactions requires novel approaches that leverage incremental stream processing and graph analytics on elastic clouds. We propose a scalable solution based on our stream processing engine, Floe, on top of which we perform real-time data processing and graph updates to enable low latency graph analytics on large evolving social networks. We demonstrate the platform on a large Twitter data set by performing several fast graph and non-graph analytics to extract in real-time the top k influential nodes, with different metrics, during key events such as the US NFL playoffs. This information allows advertisers to maximize their exposure to the public by always targeting the continuously changing set of most influential nodes. Its applicability spans multiple domains including surveillance, counter-terrorism, or disease spread monitoring. The evaluation will be performed on a combination our local cluster of 16 eight-core nodes running Eucalyptus fabric and 100s of virtual machines on the Amazon AWS public cloud. We will showcase the low latency in detecting changes in the graph under variable data streams, and also the efficiency of the platform to utilize resources and to elastically scale to meet demand.

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have graph limits in the sense of Lov\'{a}sz and Szegedy with identifiable limits. This allows simple determination of other features such as the number of triangles. The argument proceeds by studying a natural exponential model having the degree sequence as a sufficient statistic. The maximum likelihood estimate (MLE) of the parameters is shown to be unique and consistent with high probability. Thus $n$ parameters can be consistently estimated based on a sample of size one. A fast, provably convergent, algorithm for the MLE is derived. These ingredients combine to prove the graph limit theorem. Along the way, a continuous version of the Erd\H{o}s--Gallai characterization of degree sequences is derived.

Graph analytics elicits insights from large graphs to inform critical decisions for business, safety and security. Several large-scale graph processing frameworks feature efficient runtime systems; however, they often provide programming models that are low-level and subtly different from each other. Therefore, end users can find implementation and specially optimization of graph analytics error-prone and time-consuming. This paper regards the abstract interface of the graph processing frameworks as the instruction set for graph analytics, and presents Grafs, a high-level declarative specification language for graph analytics and a synthesizer that automatically generates efficient code for five high-performance graph processing frameworks. It features novel semantics-preserving fusion transformations that optimize the specifications and reduce them to three primitives: reduction over paths, mapping over vertices and reduction over vertices. Reductions over paths are commonly calculated based on push or pull models that iteratively apply kernel functions at the vertices. This paper presents conditions, parametric in terms of the kernel functions, for the correctness and termination of the iterative models, and uses these conditions as specifications to automatically synthesize the kernel functions. Experimental results show that the generated code matches or outperforms handwritten code, and that fusion accelerates execution.

An empirical study on budget-aware online kernel algorithms for streams of graphs

We have entered the age of big data. Massive datasets are now common in science, government and enterprises. Yet, making sense of these data remains a fundamental challenge. Where do we start our analysis? Where to go next? How to visualize our findings? We answers these questions by bridging Data Mining and Human- Computer Interaction (HCI) to create tools for making sense of graphs with billions of nodes and edges, focusing on: (1) Attention Routing: we introduce this idea, based on anomaly detection, that automatically draws people’s attention to interesting areas of the graph to start their analyses. We present three examples: Polonium unearths malware from 37 billion machine-file relationships; NetProbe fingers bad guys who commit auction fraud. (2) Mixed-Initiative Sensemaking: we present two examples that combine machine inference and visualization to help users locate next areas of interest: Apolo guides users to explore large graphs by learning from few examples of user interest; Graphite finds interesting subgraphs, based on only fuzzy descriptions drawn graphically. (3) Scaling Up: we show how to enable interactive analytics of large graphs by leveraging Hadoop, staging of operations, and approximate computation. This thesis contributes to data mining, HCI, and importantly their intersection, including: interactive systems and algorithms that scale; theories that unify graph mining approaches; and paradigms that overcome fundamental challenges in visual analytics. Our work is making impact to academia and society: Polonium protects 120 million people worldwide from malware; NetProbe made headlines on CNN, WSJ and USA Today; Pegasus won an opensource software award; Apolo helps DARPA detect insider threats and prevent exfiltration. We hope our Big Data Mantra “Machine for Attention Routing, Human for Interaction” will inspire more innovations at the crossroad of data mining and HCI.

Subgraph enumeration is a fundamental problem in graph analytics, which aims to find all instances of a given query graph on a large data graph. In this paper, we propose a system called HUGE to efficiently process subgraph enumeration at scale in the distributed context. HUGE features 1) an optimiser to compute an advanced execution plan without the constraints of existing works; 2) a hybrid communication layer that supports both pushing and pulling communication; 3) a novel two-stage execution mode with a lock-free and zero-copy cache design; 4) a BFS/DFS-adaptive scheduler to bound memory consumption; and 5) two-layer intra- and inter-machine load balancing. HUGE is generic such that all existing distributed subgraph enumeration algorithms can be plugged in to enjoy automatic speed up and bounded-memory execution.