Showing papers on "Graph (abstract data type) published in 2009"

ggplot2: Elegant Graphics for Data Analysis

Abstract: This book describes ggplot2, a new data visualization package for R that uses the insights from Leland Wilkisons Grammar of Graphics to create a powerful and flexible system for creating data graphics. With ggplot2, its easy to: produce handsome, publication-quality plots, with automatic legends created from the plot specification superpose multiple layers (points, lines, maps, tiles, box plots to name a few) from different data sources, with automatically adjusted common scales add customisable smoothers that use the powerful modelling capabilities of R, such as loess, linear models, generalised additive models and robust regression save any ggplot2 plot (or part thereof) for later modification or reuse create custom themes that capture in-house or journal style requirements, and that can easily be applied to multiple plots approach your graph from a visual perspective, thinking about how each component of the data is represented on the final plot. This book will be useful to everyone who has struggled with displaying their data in an informative and attractive way. You will need some basic knowledge of R (i.e. you should be able to get your data into R), but ggplot2 is a mini-language specifically tailored for producing graphics, and youll learn everything you need in the book. After reading this book youll be able to produce graphics customized precisely for your problems,and youll find it easy to get graphics out of your head and on to the screen or page.

Complex brain networks: graph theoretical analysis of structural and functional systems

Abstract: Recent developments in the quantitative analysis of complex networks, based largely on graph theory, have been rapidly translated to studies of brain network organization. The brain's structural and functional systems have features of complex networks--such as small-world topology, highly connected hubs and modularity--both at the whole-brain scale of human neuroimaging and at a cellular scale in non-human animals. In this article, we review studies investigating complex brain networks in diverse experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans) and provide an accessible introduction to the basic principles of graph theory. We also highlight some of the technical challenges and key questions to be addressed by future developments in this rapidly moving field.

The Graph Neural Network Model

Abstract: Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) isin IRm that maps a graph G and one of its nodes n into an m-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.

A Dynamic Survey of Graph Labeling

Abstract: A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

Group lasso with overlap and graph lasso

Abstract: We propose a new penalty function which, when used as regularization for empirical risk minimization procedures, leads to sparse estimators. The support of the sparse vector is typically a union of potentially overlapping groups of co-variates defined a priori, or a set of covariates which tend to be connected to each other when a graph of covariates is given. We study theoretical properties of the estimator, and illustrate its behavior on simulated and breast cancer gene expression data.

Graph clustering based on structural/attribute similarities

Abstract: The goal of graph clustering is to partition vertices in a large graph into different clusters based on various criteria such as vertex connectivity or neighborhood similarity. Graph clustering techniques are very useful for detecting densely connected groups in a large graph. Many existing graph clustering methods mainly focus on the topological structure for clustering, but largely ignore the vertex properties which are often heterogenous. In this paper, we propose a novel graph clustering algorithm, SA-Cluster, based on both structural and attribute similarities through a unified distance measure. Our method partitions a large graph associated with attributes into k clusters so that each cluster contains a densely connected subgraph with homogeneous attribute values. An effective method is proposed to automatically learn the degree of contributions of structural similarity and attribute similarity. Theoretical analysis is provided to show that SA-Cluster is converging. Extensive experimental results demonstrate the effectiveness of SA-Cluster through comparison with the state-of-the-art graph clustering and summarization methods.

An Introduction to the Theory of Graph Spectra

Abstract: This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment assumes only a little knowledge of graph theory and linear algebra. The authors include many developments in the field which arise as a result of rapidly expanding interest in the area. Exercises, spectral data and proofs of required results are also provided. The end-of-chapter notes serve as a practical guide to the extensive bibliography of over 500 items.

A Survey of Evolutionary Algorithms for Clustering

Abstract: This paper presents a survey of evolutionary algorithms designed for clustering tasks. It tries to reflect the profile of this area by focusing more on those subjects that have been given more importance in the literature. In this context, most of the paper is devoted to partitional algorithms that look for hard clusterings of data, though overlapping (i.e., soft and fuzzy) approaches are also covered in the paper. The paper is original in what concerns two main aspects. First, it provides an up-to-date overview that is fully devoted to evolutionary algorithms for clustering, is not limited to any particular kind of evolutionary approach, and comprises advanced topics like multiobjective and ensemble-based evolutionary clustering. Second, it provides a taxonomy that highlights some very important aspects in the context of evolutionary data clustering, namely, fixed or variable number of clusters, cluster-oriented or nonoriented operators, context-sensitive or context-insensitive operators, guided or unguided operators, binary, integer, or real encodings, centroid-based, medoid-based, label-based, tree-based, or graph-based representations, among others. A number of references are provided that describe applications of evolutionary algorithms for clustering in different domains, such as image processing, computer security, and bioinformatics. The paper ends by addressing some important issues and open questions that can be subject of future research.

Personalizing PageRank for Word Sense Disambiguation

Abstract: In this paper we propose a new graph-based method that uses the knowledge in a LKB (based on WordNet) in order to perform unsupervised Word Sense Disambiguation. Our algorithm uses the full graph of the LKB efficiently, performing better than previous approaches in English all-words datasets. We also show that the algorithm can be easily ported to other languages with good results, with the only requirement of having a wordnet. In addition, we make an analysis of the performance of the algorithm, showing that it is efficient and that it could be tuned to be faster.

Stabilisation of infinitesimally rigid formations of multi-robot networks

Abstract: This article considers the design of a formation control for multivehicle systems that uses only local information. The control is derived from a potential function based on an undirected infinitesimally rigid graph that specifies the target formation. A potential function is obtained from the graph, from which a gradient control is derived. Under this controller the target formation becomes a manifold of equilibria for the multivehicle system. It is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold. A complete study of the stability of the regular polygon formation is presented and results for directed graphs are presented as well. Finally, the controller is validated experimentally.

Expander flows, geometric embeddings and graph partitioning

Abstract: We give a O(√log n)-approximation algorithm for the sparsest cut, edge expansion, balanced separator, and graph conductance problems. This improves the O(log n)-approximation of Leighton and Rao (1988). We use a well-known semidefinite relaxation with triangle inequality constraints. Central to our analysis is a geometric theorem about projections of point sets in Rd, whose proof makes essential use of a phenomenon called measure concentration.We also describe an interesting and natural “approximate certificate” for a graph's expansion, which involves embedding an n-node expander in it with appropriate dilation and congestion. We call this an expander flow.

Social Network Analysis for Information Flow in Disconnected Delay-Tolerant MANETs

Abstract: Message delivery in sparse mobile ad hoc networks (MANETs) is difficult due to the fact that the network graph is rarely (if ever) connected. A key challenge is to find a route that can provide good delivery performance and low end-to-end delay in a disconnected network graph where nodes may move freely. We cast this challenge as an information flow problem in a social network. This paper presents social network analysis metrics that may be used to support a novel and practical forwarding solution to provide efficient message delivery in disconnected delay-tolerant MANETs. These metrics are based on social analysis of a node's past interactions and consists of three locally evaluated components: a node's "betweenness" centrality (calculated using ego networks) and a node's social 'similarity' to the destination node and a node's tie strength relationship with the destination node. We present simulations using three real trace data sets to demonstrate that by combining these metrics delivery performance may be achieved close to epidemic routing but with significantly reduced overhead. Additionally, we show improved performance when compared to PRoPHET routing.

An artificial bee colony algorithm for the leaf-constrained minimum spanning tree problem

Abstract: Given an undirected, connected, weighted graph, the leaf-constrained minimum spanning tree (LCMST) problem seeks on this graph a spanning tree of minimum weight among all the spanning trees of the graph that have at least @? leaves. In this paper, we have proposed an artificial bee colony (ABC) algorithm for the LCMST problem. The ABC algorithm is a new metaheuristic approach inspired by intelligent foraging behavior of honeybee swarm. We have compared the performance of our ABC approach against the best approaches reported in the literature. Computational results demonstrate the superiority of the new ABC approach over all the other approaches. The new approach obtained better quality solutions in shorter time.

Dependency Parsing

Abstract: Dependency-based methods for syntactic parsing have become increasingly popular in natural language processing in recent years. This book gives a thorough introduction to the methods that are most widely used today. After an introduction to dependency grammar and dependency parsing, followed by a formal characterization of the dependency parsing problem, the book surveys the three major classes of parsing models that are in current use: transition-based, graph-based, and grammar-based models. It continues with a chapter on evaluation and one on the comparison of different methods, and it closes with a few words on current trends and future prospects of dependency parsing. The book presupposes a knowledge of basic concepts in linguistics and computer science, as well as some knowledge of parsing methods for constituency-based representations. Table of Contents: Introduction / Dependency Parsing / Transition-Based Parsing / Graph-Based Parsing / Grammar-Based Parsing / Evaluation / Comparison / Final Thoughts

Comparing stars: on approximating graph edit distance

Abstract: Graph data have become ubiquitous and manipulating them based on similarity is essential for many applications. Graph edit distance is one of the most widely accepted measures to determine similarities between graphs and has extensive applications in the fields of pattern recognition, computer vision etc. Unfortunately, the problem of graph edit distance computation is NP-Hard in general. Accordingly, in this paper we introduce three novel methods to compute the upper and lower bounds for the edit distance between two graphs in polynomial time. Applying these methods, two algorithms AppFull and AppSub are introduced to perform different kinds of graph search on graph databases. Comprehensive experimental studies are conducted on both real and synthetic datasets to examine various aspects of the methods for bounding graph edit distance. Result shows that these methods achieve good scalability in terms of both the number of graphs and the size of graphs. The effectiveness of these algorithms also confirms the usefulness of using our bounds in filtering and searching of graphs.

An Introduction to the Theory of Graph Spectra: Spectral techniques

Abstract: Preface 1. Introduction 2. Graph operations and modifications 3. Spectrum and structure 4. Characterizations by spectra 5. Structure and one eigenvalue 6. Spectral techniques 7. Laplacians 8. Additional topics 9. Applications Appendix Bibliography Index of symbols Index.

Learning Graph Matching

Abstract: As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the 'labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.

Min-cut based segmentation of point clouds

Abstract: We present a min-cut based method of segmenting objects in point clouds. Given an object location, our method builds a k-nearest neighbors graph, assumes a background prior, adds hard foreground (and optionally background) constraints, and finds the min-cut to compute a foreground-background segmentation. Our method can be run fully automatically, or interactively with a user interface. We test our system on an outdoor urban scan, quantitatively evaluate our algorithm on a test set of about 1000 objects, and compare to several alternative approaches.

Clustering to Find Exemplar Terms for Keyphrase Extraction

Abstract: Keyphrases are widely used as a brief summary of documents. Since manual assignment is time-consuming, various unsupervised ranking methods based on importance scores are proposed for keyphrase extraction. In practice, the keyphrases of a document should not only be statistically important in the document, but also have a good coverage of the document. Based on this observation, we propose an unsupervised method for keyphrase extraction. Firstly, the method finds exemplar terms by leveraging clustering techniques, which guarantees the document to be semantically covered by these exemplar terms. Then the keyphrases are extracted from the document using the exemplar terms. Our method outperforms sate-of-the-art graph-based ranking methods (TextRank) by 9.5% in F1-measure.

Urban-Area and Building Detection Using SIFT Keypoints and Graph Theory

Abstract: Very high resolution satellite images provide valuable information to researchers. Among these, urban-area boundaries and building locations play crucial roles. For a human expert, manually extracting this valuable information is tedious. One possible solution to extract this information is using automated techniques. Unfortunately, the solution is not straightforward if standard image processing and pattern recognition techniques are used. Therefore, to detect the urban area and buildings in satellite images, we propose the use of scale invariant feature transform (SIFT) and graph theoretical tools. SIFT keypoints are powerful in detecting objects under various imaging conditions. However, SIFT is not sufficient for detecting urban areas and buildings alone. Therefore, we formalize the problem in terms of graph theory. In forming the graph, we represent each keypoint as a vertex of the graph. The unary and binary relationships between these vertices (such as spatial distance and intensity values) lead to the edges of the graph. Based on this formalism, we extract the urban area using a novel multiple subgraph matching method. Then, we extract separate buildings in the urban area using a novel graph cut method. We form a diverse and representative test set using panchromatic 1-m-resolution Ikonos imagery. By extensive testings, we report very promising results on automatically detecting urban areas and buildings.

Event Detection and Tracking in Social Streams

Abstract: Events and stories can be characterized by a set of de- scriptive, collocated keywords. Intuitively, documents describing the same event will contain similar sets of keywords, and the graph of keywords for a document collection will contain clusters individual events. In this paper we build a network of keywords based on their co-occurrence in documents. We propose and develop a new event detection algorithm which creates a keyword graph and uses community detection methods analo- gous to those used for social network analysis to dis- cover and describe events. Constellations of keywords describing an event may be used to find related articles. We also use the proposed algorithm to analyze events and track stories in social streams.

Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets

Abstract: The main focus of this book is the exploration of the geometric and dynamic properties of a far reaching generalization of a conformal iterated function system - a Graph Directed Markov System. These systems are very robust in that they apply to many settings that do not fit into the scheme of conformal iterated systems. The basic theory is laid out here and the authors have touched on many natural questions arising in its context. However, they also emphasise the many issues and current research topics which can be found in original papers. For example the detailed analysis of the structure of harmonic measures of limit sets, the examination of the doubling property of conformal measures, the extensive study of generalized polynomial like mapping or multifractal analysis of geometrically finite Kleinian groups. This book leads readers onto frontier research in the field, making it ideal for both established researchers and graduate students.

Graph-based mining of multiple object usage patterns

Abstract: The interplay of multiple objects in object-oriented programming often follows specific protocols, for example certain orders of method calls and/or control structure constraints among them that are parts of the intended object usages. Unfortunately, the information is not always documented. That creates long learning curve, and importantly, leads to subtle problems due to the misuse of objects. In this paper, we propose GrouMiner, a novel graph-based approach for mining the usage patterns of one or multiple objects. GrouMiner approach includes a graph-based representation for multiple object usages, a pattern mining algorithm, and an anomaly detection technique that are efficient, accurate, and resilient to software changes. Our experiments on several real-world programs show that our prototype is able to find useful usage patterns with multiple objects and control structures, and to translate them into user-friendly code skeletons to assist developers in programming. It could also detect the usage anomalies that caused yet undiscovered defects and code smells in those programs.

Quantum Computing with Continuous-Variable Clusters

Abstract: Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.

Supervised pattern classification based on optimum-path forest

Abstract: We present a supervised classification method which represents each class by one or more optimum-path trees rooted at some key samples, called prototypes. The training samples are nodes of a complete graph, whose arcs are weighted by the distances between the feature vectors of their nodes. Prototypes are identified in all classes and the minimization of a connectivity function by dynamic programming assigns to each training sample a minimum-cost path from its most strongly connected prototype. This competition among prototypes partitions the graph into an optimum-path forest rooted at them. The class of the samples in an optimum-path tree is assumed to be the same of its root. A test sample is classified similarly, by identifying which tree would contain it, if the sample were part of the training set. By choice of the graph model and connectivity function, one can devise other optimum-path forest classifiers. We present one of them, which is fast, simple, multiclass, parameter independent, does not make any assumption about the shapes of the classes, and can handle some degree of overlapping between classes. We also propose a general algorithm to learn from errors on an evaluation set without increasing the training set, and show the advantages of our method with respect to SVM, ANN-MLP, and k-NN classifiers in several experiments with datasets of various types. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 120–131, 2009. A preliminary version of the paper was presented at the 12th International Workshop on Combinatorial Image Analysis (Papa et al.,2008a).

Extracting key terms from noisy and multitheme documents

Abstract: We present a novel method for key term extraction from text documents. In our method, document is modeled as a graph of semantic relationships between terms of that document. We exploit the following remarkable feature of the graph: the terms related to the main topics of the document tend to bunch up into densely interconnected subgraphs or communities, while non-important terms fall into weakly interconnected communities, or even become isolated vertices. We apply graph community detection techniques to partition the graph into thematically cohesive groups of terms. We introduce a criterion function to select groups that contain key terms discarding groups with unimportant terms. To weight terms and determine semantic relatedness between them we exploit information extracted from Wikipedia.Using such an approach gives us the following two advantages. First, it allows effectively processing multi-theme documents. Second, it is good at filtering out noise information in the document, such as, for example, navigational bars or headers in web pages.Evaluations of the method show that it outperforms existing methods producing key terms with higher precision and recall. Additional experiments on web pages prove that our method appears to be substantially more effective on noisy and multi-theme documents than existing methods.

The refined process structure tree

Abstract: We consider a workflow graph as a model for the control flow of a business process and study the problem of workflow graph parsing, i.e., finding the structure of a workflow graph. More precisely, we want to find a decomposition of a workflow graph into a hierarchy of sub-workflows that are subgraphs with a single entry and a single exit of control. Such a decomposition is the crucial step, for example, to translate a process modeled in a graph-based language such as BPMN into a process modeled in a block-based language such as BPEL. For this and other applications, it is desirable that the decomposition be unique, modular and as fine as possible, where modular means that a local change of the workflow graph can only cause a local change of the decomposition. In this paper, we provide a decomposition that is unique, modular and finer than in previous work. We call it the refined process structure tree. It is based on and extends similar work for sequential programs by Tarjan and Valdes [ACM POPL '80, 1980, pp. 95-105]. We give two independent characterizations of the refined process structure tree which we prove to be equivalent: (1) a simple descriptive characterization that justifies our particular choice of the decomposition and (2) a constructive characterization that allows us to compute the decomposition in linear time. The latter is based on the tree of triconnected components (elsewhere also known as the SPQR tree) of a biconnected graph.

Public transport networks: empirical analysis and modeling

Abstract: Public transport networks of fourteen cities of so far unexplored network size are analyzed in standardized graph representations: the simple graph of the network map, the bipartite graph of routes and stations, and both one mode projections of the latter. Special attention is paid to the inter-relations and spatial embedding of transport routes. This systematic approach reveals rich behavior beyond that of the ubiquitous scale-free complex network. We find strong evidence for structures in PTNs that are counter-intuitive and need to be explained, among these a pronounced diversity in the expression of typical network characteristics within the present sample of cities, a surprising geometrical behavior with respect to the two-dimensional geographical embedding and an unexpected attraction between transport routes. A simple model based on these observations reproduces many of the identified PTN properties by growing networks of attractive self-avoiding walks.

A new graph-based method for pairwise global network alignment

Abstract: In addition to component-based comparative approaches, network alignments provide the means to study conserved network topology such as common pathways and more complex network motifs. Yet, unlike in classical sequence alignment, the comparison of networks becomes computationally more challenging, as most meaningful assumptions instantly lead to NP-hard problems. Most previous algorithmic work on network alignments is heuristic in nature. We introduce the graph-based maximum structural matching formulation for pairwise global network alignment. We relate the formulation to previous work and prove NP-hardness of the problem. Based on the new formulation we build upon recent results in computational structural biology and present a novel Lagrangian relaxation approach that, in combination with a branch-and-bound method, computes provably optimal network alignments. The Lagrangian algorithm alone is a powerful heuristic method, which produces solutions that are often near-optimal and – unlike those computed by pure heuristics – come with a quality guarantee. Computational experiments on the alignment of protein-protein interaction networks and on the classification of metabolic subnetworks demonstrate that the new method is reasonably fast and has advantages over pure heuristics. Our software tool is freely available as part of the LI SA library.