Showing papers on "Adjacency list published in 2016"

Mathematical Foundations of the GraphBLAS

Abstract: The GraphBLAS standard (this http URL) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. Mathematically the Graph- BLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, the two are easily connected by matrix mul- tiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.

Better Algorithms for Counting Triangles in Data Streams

Abstract: We present space-efficient data stream algorithms for approximating the number of triangles in a graph up to a factor 1+e. While it can be shown that determining whether a graph is triangle-free is not possible in sub-linear space, a large body of work has focused on minimizing the space required in terms of the number of triangles T (or a lower bound on this quantity) and other parameters including the number of nodes n and the number of edges m. Two models are important in the literature: the arbitrary order model in which the stream consists of the edges of the graph in arbitrary order and the adjacency list order model in which all edges incident to the same node appear consecutively. We improve over the state of the art results in both models. For the adjacency list order model, we show that ~O(e-2m/√T) space is sufficient in one pass and ~O(e-2m3/2/T) space is sufficient in two passes where the ~O(·) notation suppresses log factors. For the arbitrary order model, we show that ~O(e-2m/√T) space suffices given two passes and that ~O(e-2m3/2/T) space suffices given three passes and oracle access to the degrees. Finally, we show how to efficiently implement the "wedge sampling" approach to triangle estimation in the arbitrary order model. To do this, we develop the first algorithm for lp sampling such that multiple independent samples can be generated with O(polylog n) update time; this primitive is widely applicable and this result may be of independent interest.

Quantum homomorphisms

Abstract: A homomorphism from a graph X to a graph Y is an adjacency preserving map f : V ( X ) ? V ( Y ) . We consider a nonlocal game in which Alice and Bob are trying to convince a verifier with certainty that a graph X admits a homomorphism to Y. This is a generalization of the well-studied graph coloring game. Via systematic study of quantum homomorphisms we prove new results for graph coloring. Most importantly, we show that the Lovasz theta number of the complement is a lower bound on the quantum chromatic number, the latter of which is not known to be computable. We also show that some of our newly introduced graph parameters, namely quantum independence and clique numbers, can differ from their classical counterparts while others, namely quantum odd girth, cannot. Finally, we show that quantum homomorphisms closely relate to zero-error channel capacity. In particular, we use quantum homomorphisms to construct graphs for which entanglement-assistance increases their one-shot zero-error capacity.

Adaptive Object Detection Using Adjacency and Zoom Prediction

Abstract: State-of-the-art object detection systems rely on an accurate set of region proposals. Several recent methods use a neural network architecture to hypothesize promising object locations. While these approaches are computationally efficient, they rely on fixed image regions as anchors for predictions. In this paper we propose to use a search strategy that adaptively directs computational resources to sub-regions likely to contain objects. Compared to methods based on fixed anchor locations, our approach naturally adapts to cases where object instances are sparse and small. Our approach is comparable in terms of accuracy to the state-of-the-art Faster R-CNN approach while using two orders of magnitude fewer anchors on average. Code is publicly available.

An Automatic Faulted Line Section Location Method for Electric Power Distribution Systems Based on Multisource Information

Abstract: This paper presents an automatic faulted line section location method for distribution systems. It can be divided into two parts: faulted line section location method for medium-voltage distribution feeders and faulted area identification technique for low-voltage distribution systems. In the first part, an adjacency list that shows the adjacency relationship and status of fault indicating devices is developed. Then, an iterative search technique is devised to traverse the adjacency list to determine the faulted line section. In the second part, a relational table that shows the association relationship between smart meters, meter boxes, and distribution transformers is developed. Based on the table and the voltage of smart meters received from the customer electric information acquisition system, the faulted area can be located. Several test cases studied in a real distribution system demonstrate the effectiveness of the proposed method.

GraphJet: real-time content recommendations at twitter

Abstract: This paper presents GraphJet, a new graph-based system for generating content recommendations at Twitter. As motivation, we trace the evolution of our formulation and approach to the graph recommendation problem, embodied in successive generations of systems. Two trends can be identified: supplementing batch with real-time processing and a broadening of the scope of recommendations from users to content. Both of these trends come together in Graph-Jet, an in-memory graph processing engine that maintains a real-time bipartite interaction graph between users and tweets. The storage engine implements a simple API, but one that is sufficiently expressive to support a range of recommendation algorithms based on random walks that we have refined over the years. Similar to Cassovary, a previous graph recommendation engine developed at Twitter, GraphJet assumes that the entire graph can be held in memory on a single server. The system organizes the interaction graph into temporally-partitioned index segments that hold adjacency lists. GraphJet is able to support rapid ingestion of edges while concurrently serving lookup queries through a combination of compact edge encoding and a dynamic memory allocation scheme that exploits power-law characteristics of the graph. Each GraphJet server ingests up to one million graph edges per second, and in steady state, computes up to 500 recommendations per second, which translates into several million edge read operations per second.

Geometrically consistent plane extraction for dense indoor 3D maps segmentation

Abstract: Modern SLAM systems with a depth sensor are able to reliably reconstruct dense 3D geometric maps of indoor scenes. Representing these maps in terms of meaningful entities is a step towards building semantic maps for autonomous robots. One approach is to segment the 3D maps into semantic objects using Conditional Random Fields (CRF), which requires large 3D ground truth datasets to train the classification model. Additionally, the CRF inference is often computationally expensive. In this paper, we present an unsupervised geometric-based approach for the segmentation of 3D point clouds into objects and meaningful scene structures. We approximate an input point cloud by an adjacency graph over surface patches, whose edges are then classified as being either on or off. We devise an effective classifier which utilises both global planar surfaces and local surface convexities for edge classification. More importantly, we propose a novel global plane extraction algorithm for robustly discovering the underlying planes in the scene. Our algorithm is able to enforce the extracted planes to be mutually orthogonal or parallel which conforms usually with human-made indoor environments. We reconstruct 654 3D indoor scenes from NYUv2 sequences to validate the efficiency and effectiveness of our segmentation method.

Large-Scale Aerial Image Categorization Using a Multitask Topological Codebook

Abstract: Fast and accurately categorizing the millions of aerial images on Google Maps is a useful technique in pattern recognition. Existing methods cannot handle this task successfully due to two reasons: 1) the aerial images’ topologies are the key feature to distinguish their categories, but they cannot be effectively encoded by a conventional visual codebook and 2) it is challenging to build a realtime image categorization system, as some geo-aware Apps update over 20 aerial images per second. To solve these problems, we propose an efficient aerial image categorization algorithm. It focuses on learning a discriminative topological codebook of aerial images under a multitask learning framework. The pipeline can be summarized as follows. We first construct a region adjacency graph (RAG) that describes the topology of each aerial image. Naturally, aerial image categorization can be formulated as RAG-to-RAG matching. According to graph theory, RAG-to-RAG matching is conducted by enumeratively comparing all their respective graphlets (i.e., small subgraphs). To alleviate the high time consumption, we propose to learn a codebook containing topologies jointly discriminative to multiple categories. The learned topological codebook guides the extraction of the discriminative graphlets. Finally, these graphlets are integrated into an AdaBoost model for predicting aerial image categories. Experimental results show that our approach is competitive to several existing recognition models. Furthermore, over 24 aerial images are processed per second, demonstrating that our approach is ready for real-world applications.

Eigenvalue Outliers of Non-Hermitian Random Matrices with a Local Tree Structure

Abstract: Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graphs. Eigenvalue outliers in the spectrum are of particular interest, since they determine the stationary state and the stability of dynamical processes. We present a general and exact theory for the eigenvalue outliers of random matrices with a local tree structure. For adjacency and Laplacian matrices of oriented random graphs, we derive analytical expressions for the eigenvalue outliers, the first moments of the distribution of eigenvector elements associated with an outlier, the support of the spectral density, and the spectral gap. We show that these spectral observables obey universal expressions, which hold for a broad class of oriented random matrices.

A Modified Locality-Preserving Projection Approach for Hyperspectral Image Classification

Abstract: Locality-preserving projection (LPP) is a typical manifold-based dimensionality reduction (DR) method, which has been successfully applied to some pattern recognition tasks. However, LPP depends on an underlying adjacency graph, which has several problems when it is applied to hyperspectral image (HSI) processing. The adjacency graph is artificially created in advance, which may not be suitable for the following DR and classification. It is also difficult to determine an appropriate neighborhood size in graph construction. Additionally, only the information of local neighboring data points is considered in LPP, which is limited for improving classification accuracy. To address these problems, a modified version of the original LPP called MLPP is proposed for hyperspectral remote-sensing image classification. The idea is to select a different number of nearest neighbors for each data point adaptively and to focus on maximizing the distance between nonnearest neighboring points. This not only preserves the intrinsic geometric structure of the data but also increases the separability among ground objects with different spectral characteristics. Moreover, MLPP does not depend on any parameters or prior knowledge. Experiments on two real HSIs from different sensors demonstrate that MLPP is remarkably superior to other conventional DR methods in enhancing classification performance.

Assembly-based conceptual 3D modeling with unlabeled components using probabilistic factor graph

Abstract: This work presents a novel and intuitive assembly based 3D modeling interface to support conceptual design exploration activities. In the presented modeling interface, unlabeled segmented components of the objects are assembled to create new 3D models. The development of the interface is motivated by two aspects. First, the focus is on novice users since they stand to gain the most from intuitive interfaces. Second, the intent is on creative reuse of a growing number and variety of 3D models available on vast online repositories like Turbosquid and Trimble 3D warehouse. Specifically, we have devised an automated component suggestion algorithm based on a probabilistic factor graph. This algorithm helps the user to easily browse and select components from a database that are most compatible with the current state of 3D models being assembled. The component suggestion algorithm incorporates various aspects such as shape similarity, repetitions of shapes, and adjacency relationships. Our new suggestive interface overcomes several limitations of traditional CAD interfaces by helping the users to quickly create and explore new conceptual designs. We present results on the conceptual design of several products. We present a novel 3D CAD tool for conceptual design exploration.Interactive concept exploration through assembly-based 3D modeling paradigm.Automated component suggestion algorithm based on probabilistic factor graph.Creative reuse of 3D models available on vast online repositories.

Planar Matching in Streams Revisited

Abstract: We present data stream algorithms for estimating the size or weight of the maximum matching in low arboricity graphs. A large body of work has focused on improving the constant approximation factor for general graphs when the data stream algorithm is permitted O(n polylog n) space where n is the number of nodes. This space is necessary if the algorithm must return the matching. Recently, Esfandiari et al. (SODA 2015) showed that it was possible to estimate the maximum cardinality of a matching in a planar graph up to a factor of 24+epsilon using O(epsilon^{-2} n^{2/3} polylog n) space. We first present an algorithm (with a simple analysis) that improves this to a factor 5+epsilon using the same space. We also improve upon the previous results for other graphs with bounded arboricity. We then present a factor 12.5 approximation for matching in planar graphs that can be implemented using O(log n) space in the adjacency list data stream model where the stream is a concatenation of the adjacency lists of the graph. The main idea behind our results is finding "local" fractional matchings, i.e., fractional matchings where the value of any edge e is solely determined by the edges sharing an endpoint with e. Our work also improves upon the results for the dynamic data stream model where the stream consists of a sequence of edges being inserted and deleted from the graph. We also extend our results to weighted graphs, improving over the bounds given by Bury and Schwiegelshohn (ESA 2015), via a reduction to the unweighted problem that increases the approximation by at most a factor of two.

Towards a theory without adjacency: hyper-contextual VI-rules

Abstract: It has been proposed that allomorphy and suppletion is restricted not only by (various conceptions of) cyclic locality, but also by adjacency of elements. Embick (2010) proposes that two elements can only enter into an relationship of allomorphy if they are linearly adjacent to each other, whereas Adger et al. (2003) and Bobaljik (2012) argue that elements must be structurally adjacent.

Hyperbolic mapping of complex networks based on community information

Abstract: To improve the hyperbolic mapping methods both in terms of accuracy and running time, a novel mapping method called Community and Hyperbolic Mapping ( CHM ) is proposed based on community information in this paper. Firstly, an index called Community Intimacy ( CI ) is presented to measure the adjacency relationship between the communities, based on which a community ordering algorithm is introduced. According to the proposed Community-Sector hypothesis, which supposes that most nodes of one community gather in a same sector in hyperbolic space, CHM maps the ordered communities into hyperbolic space, and then the angular coordinates of nodes are randomly initialized within the sector that they belong to. Therefore, all the network nodes are so far mapped to hyperbolic space, and then the initialized angular coordinates can be optimized by employing the information of all nodes, which can greatly improve the algorithm precision. By applying the proposed dual-layer angle sampling method in the optimization procedure, CHM reduces the time complexity to O ( n 2 ) . The experiments show that our algorithm outperforms the state-of-the-art methods.

Spectral directed hypergraph theory via tensors

Abstract: In this paper, we show that each of the adjacency tensor, the Laplacian tensor and the signless Laplacian tensor of a uniform directed hypergraph has n linearly independent H-eigenvectors. Some lower and upper bounds for the largest and smallest adjacency, Laplacian and signless Laplacian H-eigenvalues of a uniform directed hypergraph are given. For a uniform directed hypergraph, the smallest Laplacian H-eigenvalue is 0. On the other hand, the upper bound of the largest adjacency and signless Laplacian H-eigenvalues are achieved if and only if it is a complete directed hypergraph. For a uniform directed hyperstar, all adjacency H-eigenvalues are 0. At the same time, we make some conjectures about the nonnegativity of one H-eigenvector corresponding to the largest H-eigenvalue, and raise some questions about whether the Laplacian and signless Laplacian tensors are positive semi-definite for a uniform directed hypergraph.

Measuring accuracy of semantic graphs with exogenous datasets

Abstract: Provided is a process including: obtaining a semantic similarity graph having nodes corresponding to documents in an analyzed corpus and edges indicating semantic similarity between pairs of the documents; for at least a plurality of nodes in the graph, evaluating accuracy of the edges based on neighboring nodes and an external corpus by performing operations including: identifying the neighboring nodes based on adjacency to the respective node in the graph; selecting documents from an external corpus based on references in the selected documents to entities mentioned in the documents of the neighboring nodes; and determining how semantically similar the respective node is to the selected documents.

On the adjacency dimension of graphs

Abstract: In this article we study the problem of finding the k-adjacency dimension of a graph. We give some necessary and sufficient conditions for the existence of a k-adjacency basis of an arbitrary graph G and we obtain general results on the k-adjacency dimension, including general bounds and closed formulae for some families of graphs.

DeepGraph: Graph Structure Predicts Network Growth.

Abstract: The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted structural features. These representations either fail to highlight local and global properties of the graph or suffer from a severe loss of structural information. There lacks an effective graph representation, which hinges the realization of the predictive power of network structures. In this study, we propose to learn the represention of a graph, or the topological structure of a network, through a deep learning model. This end-to-end prediction model, named DeepGraph, takes the input of the raw adjacency matrix of a real-world network and outputs a prediction of the growth of the network. The adjacency matrix is first represented using a graph descriptor based on the heat kernel signature, which is then passed through a multi-column, multi-resolution convolutional neural network. Extensive experiments on five large collections of real-world networks demonstrate that the proposed prediction model significantly improves the effectiveness of existing methods, including linear or nonlinear regressors that use hand-crafted features, graph kernels, and competing deep learning methods.

Linear Spatial Spectral Mixture Model

Abstract: Spectral unmixing is the process of decomposing the measured spectrum of a mixed pixel into a set of pure spectral signatures called endmembers and their corresponding abundances, which indicate the fractional area coverage of each endmember present in the pixel. A substantial number of spectral unmixing studies rely on a spectral mixture model which assumes that spectral mixing only occurs within the extent of a pixel. However, due to adjacency effect, the spectral measurement of the pixel may be contaminated by radiance from materials in neighboring pixels. In this paper, a linear spatial spectral mixture model that incorporates an adjacency effect in abundance estimation is proposed. We extend the classic linear mixture model by including a spatial term that expresses for each pixel the spectral contributions from its nearby pixels. An iterative optimization algorithm is developed to estimate fractional abundances of endmembers and a coefficient representing the overall intensity of the adjacency effect in the image. Our experimental results, with both synthetic and real hyperspectral images, demonstrate the effectiveness of the proposed model.

Robust Vertex Classification

Abstract: For random graphs distributed according to stochastic blockmodels, a special case of latent position graphs, adjacency spectral embedding followed by appropriate vertex classification is asymptotically Bayes optimal; but this approach requires knowledge of and critically depends on the model dimension In this paper, we propose a sparse representation vertex classifier which does not require information about the model dimension This classifier represents a test vertex as a sparse combination of the vertices in the training set and uses the recovered coefficients to classify the test vertex We prove consistency of our proposed classifier for stochastic blockmodels, and demonstrate that the sparse representation classifier can predict vertex labels with higher accuracy than adjacency spectral embedding approaches via both simulation studies and real data experiments Our results demonstrate the robustness and effectiveness of our proposed vertex classifier when the model dimension is unknown

Image Co-segmentation Using Maximum Common Subgraph Matching and Region Co-growing

Abstract: We propose a computationally efficient graph based image co-segmentation algorithm where we extract objects with similar features from an image pair or a set of images. First we build a region adjacency graph (RAG) for each image by representing image superpixels as nodes. Then we compute the maximum common subgraph (MCS) between the RAGs using the minimum vertex cover of a product graph obtained from the RAG. Next using MCS outputs as the seeds, we iteratively co-grow the matched regions obtained from the MCS in each of the constituent images by using a weighted measure of inter-image feature similarities among the already matched regions and their neighbors that have not been matched yet. Upon convergence, we obtain the co-segmented objects. The MCS based algorithm allows multiple, similar objects to be co-segmented and the region co-growing stage helps to extract different sized, similar objects. Superiority of the proposed method is demonstrated by processing images containing different sized objects and multiple objects.

An Efficient Approach for Tackling Large Real World Qualitative Spatial Networks

Abstract: We improve the state-of-the-art method for checking the consistency of large qualitative spatial networks that appear in the Web of Data by exploiting the scale-free-like structure observed in their constraint graphs. We propose an implementation scheme that triangulates the constraint graphs of the input networks and uses a hash table based adjacency list to efficiently represent and reason with them. We generate random scale-free-like qualitative spatial networks using the Barabasi-Albert (BA) model with a preferential attachment mechanism. We test our approach on the already existing random datasets that have been extensively used in the literature for evaluating the performance of qualitative spatial reasoners, our own generated random scale-free-like spatial networks, and real spatial datasets that have been made available as Linked Data. The analysis and experimental evaluation of our method presents significant improvements over the state-of-the-art approach, and establishes our implementation as t...