Showing papers on "Graph (abstract data type) published in 2005"

A Practical Guide To Factorial Validity Using PLS-Graph: Tutorial And Annotated Example

Abstract: This tutorial explains in detail what factorial validity is and how to run its various aspects in PLS. The tutorial is written as a teaching aid for doctoral seminars that may cover PLS and for researchers interested in learning PLS. An annotated example with data is provided as an additional tool to assist the reader in reconstructing the detailed example.

Constructing free-energy approximations and generalized belief propagation algorithms

Abstract: Important inference problems in statistical physics, computer vision, error-correcting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree, but only approximate when the factor graph has cycles. We show that BP fixed points correspond to the stationary points of the Bethe approximation of the free energy for a factor graph. We explain how to obtain region-based free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms. We emphasize the conditions a free energy approximation must satisfy in order to be a "valid" or "maxent-normal" approximation. We describe the relationship between four different methods that can be used to generate valid approximations: the "Bethe method", the "junction graph method", the "cluster variation method", and the "region graph method". Finally, we explain how to tell whether a region-based approximation, and its corresponding GBP algorithm, is likely to be accurate, and describe empirical results showing that GBP can significantly outperform BP.

A new model for learning in graph domains

Abstract: In several applications the information is naturally represented by graphs. Traditional approaches cope with graphical data structures using a preprocessing phase which transforms the graphs into a set of flat vectors. However, in this way, important topological information may be lost and the achieved results may heavily depend on the preprocessing stage. This paper presents a new neural model, called graph neural network (GNN), capable of directly processing graphs. GNNs extends recursive neural networks and can be applied on most of the practically useful kinds of graphs, including directed, undirected, labelled and cyclic graphs. A learning algorithm for GNNs is proposed and some experiments are discussed which assess the properties of the model.

Semi-supervised learning with graphs

Abstract: In traditional machine learning approaches to classification, one uses only a labeled set to train the classifier. Labeled instances however are often difficult, expensive, or time consuming to obtain, as they require the efforts of experienced human annotators. Meanwhile unlabeled data may be relatively easy to collect, but there has been few ways to use them. Semi-supervised learning addresses this problem by using large amount of unlabeled data, together with the labeled data, to build better classifiers. Because semi-supervised learning requires less human effort and gives higher accuracy, it is of great interest both in theory and in practice. We present a series of novel semi-supervised learning approaches arising from a graph representation, where labeled and unlabeled instances are represented as vertices, and edges encode the similarity between instances. They address the following questions: How to use unlabeled data? (label propagation); What is the probabilistic interpretation? (Gaussian fields and harmonic functions); What if we can choose labeled data? (active learning); How to construct good graphs? (hyperparameter learning); How to work with kernel machines like SVM? (graph kernels); How to handle complex data like sequences? (kernel conditional random fields); How to handle scalability and induction? (harmonic mixtures). An extensive literature review is included at the end.

Anytime dynamic A*: an anytime, replanning algorithm

Abstract: We present a graph-based planning and replanning algorithm able to produce bounded suboptimal solutions in an anytime fashion. Our algorithm tunes the quality of its solution based on available search time, at every step reusing previous search efforts. When updated information regarding the underlying graph is received, the algorithm incrementally repairs its previous solution. The result is an approach that combines the benefits of anytime and incremental planners to provide efficient solutions to complex, dynamic search problems. We present theoretical analysis of the algorithm, experimental results on a simulated robot kinematic arm, and two current applications in dynamic path planning for outdoor mobile robots.

Network and psychological effects in urban movement

Abstract: Correlations are regularly found in space syntax studies between graph-based configurational measures of street networks, represented as lines, and observed movement patterns. This suggests that topological and geometric complexity are critically involved in how people navigate urban grids. This has caused difficulties with orthodox urban modelling, since it has always been assumed that insofar as spatial factors play a role in navigation, it will be on the basis of metric distance. In spite of much experimental evidence from cognitive science that geometric and topological factors are involved in navigation, and that metric distance is unlikely to be the best criterion for navigational choices, the matter has not been convincingly resolved since no method has existed for extracting cognitive information from aggregate flows. Within the space syntax literature it has also remained unclear how far the correlations that are found with syntactic variables at the level of aggregate flows are due to cognitive factors operating at the level of individual movers, or they are simply mathematically probable network effects, that is emergent statistical effects from the structure of line networks, independent of the psychology of navigational choices. Here we suggest how both problems can be resolved, by showing three things: first, how cognitive inferences can be made from aggregate urban flow data and distinguished from network effects; second by showing that urban movement, both vehicular and pedestrian, are shaped far more by the geometrical and topological properties of the grid than by its metric properties; and third by demonstrating that the influence of these factors on movement is a cognitive, not network, effect.

Actions sketch: a novel action representation

Abstract: In this paper, we propose to model an action based on both the shape and the motion of the performing object. When the object performs an action in 3D, the points on the outer boundary of the object are projected as 2D (x, y) contour in the image plane. A sequence of such 2D contours with respect to time generates a spatiotemporal volume (STV) in (x, y, t), which can be treated as 3D object in the (x, y, t) space. We analyze STV by using the differential geometric surface properties to identify action descriptors capturing both spatial and temporal properties. A set of action descriptors is called an action sketch. The first step in our approach is to generate STV by solving the point correspondence problem between consecutive frames. The correspondences are determined using a two-step graph theoretical approach. After the STV is generated, actions descriptors are computed by analyzing the differential geometric properties of STV. Finally, using these descriptors, we perform action recognition, which is also formulated as graph theoretical problem. Several experimental results are presented to demonstrate our approach.

Learning from labeled and unlabeled data on a directed graph

Abstract: We propose a general framework for learning from labeled and unlabeled data on a directed graph in which the structure of the graph including the directionality of the edges is considered. The time complexity of the algorithm derived from this framework is nearly linear due to recently developed numerical techniques. In the absence of labeled instances, this framework can be utilized as a spectral clustering method for directed graphs, which generalizes the spectral clustering approach for undirected graphs. We have applied our framework to real-world web classification problems and obtained encouraging results.

Hierarchical SLAM: real-time accurate mapping of large environments

Abstract: In this paper, we present a hierarchical mapping method that allows us to obtain accurate metric maps of large environments in real time. The lower (or local) map level is composed of a set of local maps that are guaranteed to be statistically independent. The upper (or global) level is an adjacency graph whose arcs are labeled with the relative location between local maps. An estimation of these relative locations is maintained at this level in a relative stochastic map. We propose a close to optimal loop closing method that, while maintaining independence at the local level, imposes consistency at the global level at a computational cost that is linear with the size of the loop. Experimental results demonstrate the efficiency and precision of the proposed method by mapping the Ada Byron building at our campus. We also analyze, using simulations, the precision and convergence of our method for larger loops.

Theory of semidefinite programming for sensor network localization

Abstract: We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interior-point algorithm theories to prove that the SDP localizes any network or graph that has unique sensor positions to fit given distance measures. Therefore, we show, for the first time, that these networks can be localized in polynomial time. We also give a simple and efficient criterion for checking whether a given instance of the localization problem has a unique realization in R2 using graph rigidity theory. Finally, we introduce a notion called strong localizability and show that the SDP model will identify all strongly localizable subnetworks in the input network.

Video summarization and scene detection by graph modeling

Abstract: We propose a unified approach for video summarization based on the analysis of video structures and video highlights. Two major components in our approach are scene modeling and highlight detection. Scene modeling is achieved by normalized cut algorithm and temporal graph analysis, while highlight detection is accomplished by motion attention modeling. In our proposed approach, a video is represented as a complete undirected graph and the normalized cut algorithm is carried out to globally and optimally partition the graph into video clusters. The resulting clusters form a directed temporal graph and a shortest path algorithm is proposed to efficiently detect video scenes. The attention values are then computed and attached to the scenes, clusters, shots, and subshots in a temporal graph. As a result, the temporal graph can inherently describe the evolution and perceptual importance of a video. In our application, video summaries that emphasize both content balance and perceptual quality can be generated directly from a temporal graph that embeds both the structure and attention information.

Multi-view stereo via volumetric graph-cuts

Abstract: This paper presents a novel formulation for the multi-view scene reconstruction problem. While this formulation benefits from a volumetric scene representation, it is amenable to a computationally tractable global optimisation using Graph-cuts. The algorithm proposed uses the visual hull of the scene to infer occlusions and as a constraint on the topology of the scene. A photo consistency-based surface cost functional is defined and discretised with a weighted graph. The optimal surface under this discretised functional is obtained as the minimum cut solution of the weighted graph. Our method provides a viewpoint independent surface regularisation, approximate handling of occlusions and a tractable optimisation scheme. Promising experimental results on real scenes as well as a quantitative evaluation on a synthetic scene are presented.

Synthesis of interface specifications for Java classes

Abstract: While a typical software component has a clearly specified (static) interface in terms of the methods and the input/output types they support, information about the correct sequencing of method calls the client must invoke is usually undocumented. In this paper, we propose a novel solution for automatically extracting such temporal specifications for Java classes. Given a Java class, and a safety property such as "the exception E should not be raised", the corresponding (dynamic) interface is the most general way of invoking the methods in the class so that the safety property is not violated. Our synthesis method first constructs a symbolic representation of the finite state-transition system obtained from the class using predicate abstraction. Constructing the interface then corresponds to solving a partial-information two-player game on this symbolic graph. We present a sound approach to solve this computationally-hard problem approximately using algorithms for learning finite automata and symbolic model checking for branching-time logics. We describe an implementation of the proposed techniques in the tool JIST--- Java Interface Synthesis Tool---and demonstrate that the tool can construct interfaces accurately and efficiently for sample Java2SDK library classes.

Worst and best-case coverage in sensor networks

Abstract: Wireless ad hoc sensor networks have recently emerged as a premier research topic. They have great long-term economic potential, ability to transform our lives, and pose many new system-building challenges. Sensor networks also pose a number of new conceptual and optimization problems. Here, we address one of the fundamental problems, namely, coverage. Sensor coverage, in general, answers the questions about the quality of service (surveillance) that can be provided by a particular sensor network. We briefly discuss the definition of the coverage problem from several points of view and formally define the worst and best-case coverage in a sensor network. By combining computational geometry and graph theoretic techniques, specifically the Voronoi diagram and graph search algorithms, we establish the main highlight of the paper - an optimal polynomial time worst and average case algorithm for coverage calculation for homogeneous isotropic sensors. We also present several experimental results and analyze potential applications, such as using best and worst-case coverage information as heuristics to deploy sensors to improve coverage.

Analysis and Visualization of Network Data using JUNG

Abstract: The JUNG (Java Universal Network/Graph) Framework is a free, open-source software library that provides a common and extendible language for the manipulation, analysis, and visualization of data that can be represented as a graph or network. It is written in the Java programming language, allowing JUNG-based applications to make use of the extensive built-in capabilities of the Java Application Programming Interface (API), as well as those of other existing third-party Java libraries. We describe the design, and some details of the implementation, of the JUNG architecture, and provide illustrative examples of its use.

Clio grows up: from research prototype to industrial tool

Abstract: Clio, the IBM Research system for expressing declarative schema mappings, has progressed in the past few years from a research prototype into a technology that is behind some of IBM's mapping technology. Clio provides a declarative way of specifying schema mappings between either XML or relational schemas. Mappings are compiled into an abstract query graph representation that captures the transformation semantics of the mappings. The query graph can then be serialized into different query languages, depending on the kind of schemas and systems involved in the mapping. Clio currently produces XQuery, XSLT, SQL, and SQL/XML queries. In this paper, we revisit the architecture and algorithms behind Clio. We then discuss some implementation issues, optimizations needed for scalability, and general lessons learned in the road towards creating an industrial-strength tool.

Synchronization in networks of nonlinear dynamical systems coupled via a directed graph

Abstract: We study synchronization in an array of coupled identical nonlinear dynamical systems where the coupling topology is expressed as a directed graph and give synchronization criteria related to properties of a generalized Laplacian matrix of the directed graph. In particular, we extend recent results by showing that the array synchronizes for sufficiently large cooperative coupling if the underlying graph contains a spanning directed tree. This is an intuitive yet nontrivial result that can be paraphrased as follows: if there exists a dynamical system which influences directly or indirectly all other systems, then synchronization is possible for strong enough coupling. The converse is also true in general.

What Color Is Your Jacobian? Graph Coloring for Computing Derivatives

Abstract: Graph coloring has been employed since the 1980s to efficiently compute sparse Jacobian and Hessian matrices using either finite differences or automatic differentiation. Several coloring problems occur in this context, depending on whether the matrix is a Jacobian or a Hessian, and on the specifics of the computational techniques employed. We consider eight variant vertex coloring problems here. This article begins with a gentle introduction to the problem of computing a sparse Jacobian, followed by an overview of the historical development of the research area. Then we present a unifying framework for the graph models of the variant matrix estimation problems. The framework is based upon the viewpoint that a partition of a matrix into structurally orthogonal groups of columns corresponds to distance-2 coloring an appropriate graph representation. The unified framework helps integrate earlier work and leads to fresh insights; enables the design of more efficient algorithms for many problems; leads to new algorithms for others; and eases the task of building graph models for new problems. We report computational results on two of the coloring problems to support our claims. Most of the methods for these problems treat a column or a row of a matrix as an atomic entity, and partition the columns or rows (or both). A brief review of methods that do not fit these criteria is provided. We also discuss results in discrete mathematics and theoretical computer science that intersect with the topics considered here.

GLIDER: gradient landmark-based distributed routing for sensor networks

Abstract: We present gradient landmark-based distributed routing (GLIDER), a novel naming/addressing scheme and associated routing algorithm, for a network of wireless communicating nodes We assume that the nodes are fixed (though their geographic locations are not necessarily known), and that each node can communicate wirelessly with some of its geographic neighbors - a common scenario in sensor networks We develop a protocol which in a preprocessing phase discovers the global topology of the sensor field and, as a byproduct, partitions the nodes into routable tiles - regions where the node placement is sufficiently dense and regular that local greedy methods can work well Such global topology includes not just connectivity but also higher order topological features, such as the presence of holes We address each node by the name of the tile containing it and a set of local coordinates derived from connectivity graph distances between the node and certain landmark nodes associated with its own and neighboring tiles We use the tile adjacency graph for global route planning and the local coordinates for realizing actual inter- and intra-tile routes We show that efficient load-balanced global routing can be implemented quite simply using such a scheme

Collecting the internet AS-level topology

Abstract: At the inter-domain level, the Internet topology can be represented by a graph with Autonomous Systems (ASes) as nodes and AS peerings as links. This AS-level topology graph has been widely used in a variety of research efforts. Conventionally this topology graph is derived from routing tables collected by Route Views or RIPE RIS. In this work, we assemble the most complete AS-level topology by extending the conventional method along two dimensions. First, in addition to using data from RouteViews and RIPE RIS, we also collect data from many other sources, including route servers, looking glasses, and routing registries. Second, in addition to using routing tables, we also accumulate topological information from routing updates over time. The resulting topology graph on a recent day contains 44% more links and 3% more nodes than that from using RouteViews routing tables alone. Our data collection and topology generation process have been automated, and we publish the latest topology on the web on a daily basis.

Service selection algorithms for Web services with end-to-end QoS constraints

Abstract: Web services are new forms of Internet software that can be universally deployed and invoked using standard protocols. Services from different providers can be integrated into a composite service regardless of their locations, platforms, and/or execution speeds to implement complex business processes and transactions. In this paper, we study the end-to-end QoS issues of composite services by utilizing a QoS broker that is responsible for selecting and coordinating the individual service component. We design the service selection algorithms used by QoS brokers to construct the optimal composite service. The objective of the algorithms is to maximize the user-defined utility function value while meeting the end-to-end delay constraint. We propose two solution approaches to the service selection problem: the combinatorial approach, by modeling the problem as the Multiple Choice Knapsack Problem (MCKP), and the graph approach, by modeling the problem as the constrained shortest path problem in the graph theory. We study efficient solutions for each approach.

Beyond pairwise clustering

Abstract: We consider the problem of clustering in domains where the affinity relations are not dyadic (pairwise), but rather triadic, tetradic or higher. The problem is an instance of the hypergraph partitioning problem. We propose a two-step algorithm for solving this problem. In the first step we use a novel scheme to approximate the hypergraph using a weighted graph. In the second step a spectral partitioning algorithm is used to partition the vertices of this graph. The algorithm is capable of handling hyperedges of all orders including order two, thus incorporating information of all orders simultaneously. We present a theoretical analysis that relates our algorithm to an existing hypergraph partitioning algorithm and explain the reasons for its superior performance. We report the performance of our algorithm on a variety of computer vision problems and compare it to several existing hypergraph partitioning algorithms.

Detection and representation of scenes in videos

Abstract: This paper presents a method to perform a high-level segmentation of videos into scenes. A scene can be defined as a subdivision of a play in which either the setting is fixed, or when it presents continuous action in one place. We exploit this fact and propose a novel approach for clustering shots into scenes by transforming this task into a graph partitioning problem. This is achieved by constructing a weighted undirected graph called a shot similarity graph (SSG), where each node represents a shot and the edges between the shots are weighted by their similarity based on color and motion information. The SSG is then split into subgraphs by applying the normalized cuts for graph partitioning. The partitions so obtained represent individual scenes in the video. When clustering the shots, we consider the global similarities of shots rather than the individual shot pairs. We also propose a method to describe the content of each scene by selecting one representative image from the video as a scene key-frame. Recently, DVDs have become available with a chapter selection option where each chapter is represented by one image. Our algorithm automates this objective which is useful for applications such as video-on-demand, digital libraries, and the Internet. Experiments are presented with promising results on several Hollywood movies and one sitcom.

On mining cross-graph quasi-cliques

Abstract: Joint mining of multiple data sets can often discover interesting, novel, and reliable patterns which cannot be obtained solely from any single source. For example, in cross-market customer segmentation, a group of customers who behave similarly in multiple markets should be considered as a more coherent and more reliable cluster than clusters found in a single market. As another example, in bioinformatics, by joint mining of gene expression data and protein interaction data, we can find clusters of genes which show coherent expression patterns and also produce interacting proteins. Such clusters may be potential pathways.In this paper, we investigate a novel data mining problem, mining cross-graph quasi-cliques, which is generalized from several interesting applications such as cross-market customer segmentation and joint mining of gene expression data and protein interaction data. We build a general model for mining cross-graph quasi-cliques, show why the complete set of cross-graph quasi-cliques cannot be found by previous data mining methods, and study the complexity of the problem. While the problem is difficult, we develop an efficient algorithm, Crochet, which exploits several interesting and effective techniques and heuristics to efficaciously mine cross-graph quasi-cliques. A systematic performance study is reported on both synthetic and real data sets. We demonstrate some interesting and meaningful cross-graph quasi-cliques in bioinformatics. The experimental results also show that algorithm Crochet is efficient and scalable.

Algorithmic aspects of topology control problems for ad hoc networks

Abstract: Topology control problems are concerned with the assignment of power values to the nodes of an ad hoc network so that the power assignment leads to a graph topology satisfying some specified properties. This paper considers such problems under several optimization objectives, including minimizing the maximum power and minimizing the total power. A general approach leading to a polynomial algorithm is presented for minimizing maximum power for a class of graph properties called monotone properties. The difficulty of generalizing the approach to properties that are not monotone is discussed. Problems involving the minimization of total power are known to be NP-complete even for simple graph properties. A general approach that leads to an approximation algorithm for minimizing the total power for some monotone properties is presented. Using this approach, a new approximation algorithm for the problem of minimizing the total power for obtaining a 2-node-connected graph is developed. It is shown that this algorithm provides a constant performance guarantee. Experimental results from an implementation of the approximation algorithm are also presented.

Identifiability of path-specific effects

Abstract: Counterfactual quantities representing path-specific effects arise in cases where we are interested in computing the effect of one variable on another only along certain causal paths in the graph (in other words by excluding a set of edges from consideration). A recent paper [Pearl, 2001] details a method by which such an exclusion can be specified formally by fixing the value of the parent node of each excluded edge. In this paper we derive simple, graphical conditions for experimental identifiability of path-specific effects, namely, conditions under which path-specific effects can be estimated consistently from data obtained from controlled experiments.

TRICLUSTER: an effective algorithm for mining coherent clusters in 3D microarray data

Abstract: In this paper we introduce a novel algorithm called TRICLUSTER, for mining coherent clusters in three-dimensional (3D) gene expression datasets. TRICLUSTER can mine arbitrarily positioned and overlapping clusters, and depending on different parameter values, it can mine different types of clusters, including those with constant or similar values along each dimension, as well as scaling and shifting expression patterns. TRICLUSTER relies on graph-based approach to mine all valid clusters. For each time slice, i.e., a gene×sample matrix, it constructs the range multigraph, a compact representation of all similar value ranges between any two sample columns. It then searches for constrained maximal cliques in this multigraph to yield the set of bi-clusters for this time slice. Then TRICLUSTER constructs another graph using the biclusters (as vertices) from each time slice; mining cliques from this graph yields the final set of triclusters. Optionally, TRICLUSTER merges/deletes some clusters having large overlaps. We present a useful set of metrics to evaluate the clustering quality, and we show that TRICLUSTER can find significant triclusters in the real microarray datasets.

A novel layered graph model for topology formation and routing in dynamic spectrum access networks

Abstract: This paper studies a fundamental problem in dynamic spectrum access (DSA) networks: given a set of detected spectrum bands that can be temporarily used by each node in a DSA network, how to form a topology by selecting spectrum bands for each radio interface of each node, called topology formation in this paper. We propose a novel layered graph to model the temporarily available spectrum bands, called spectrum opportunities (SOPs) in this paper, and use this layered graph model to develop effective and efficient routing and interface assignment algorithms to form near-optimal topologies for DSA networks. We have evaluated the performance of our layered graph approach and compared it to a sequential interface assignment algorithm. The numerical results show that the layered graph approach significantly outperforms the sequential interface assignment