Adjacency Graph Research Articles

HeteGraph: graph learning in recommender systems via graph convolutional networks

With the explosive growth of online information, many recommendation methods have been proposed. This research direction is boosted with deep learning architectures, especially the recently proposed graph convolutional networks (GCNs). GCNs have shown tremendous potential in graph embedding learning thanks to its inductive inference property. However, most of the existing GCN-based methods focus on solving tasks in the homogeneous graph settings, and none of them considers heterogeneous graph settings. In this paper, we bridge the gap by developing a novel framework called HeteGraph based on the GCN principles. HeteGraph can handle heterogeneous graphs in the recommender systems. Specifically, we propose a sampling technique and a graph convolutional operation to learn high-quality graph’s node embeddings, which differs from the traditional GCN approaches where a full graph adjacency matrix is needed for the embedding learning. We design two models based on the HeteGraph framework to evaluate two important recommendation tasks, namely item rating prediction and diversified item recommendations. Extensive experiments show the encouraging performance of HeteGraph on the first task and the state-of-the-art performance on the second task.

Multi-community passenger demand prediction at region level based on spatio-temporal graph convolutional network

Region-level passenger demand prediction plays an important role in the coordination of travel demand and supply in the urban public transportation system. The complex urban road network structure leads to irregular shapes and arrangements of regions, which poses a challenge for capturing the spatio-temporal correlation of demand generated in different regions. In this study, we propose a multi-community spatio-temporal graph convolutional network (MC_STGCN) framework to predict passenger demand at a multi-region level by exploring spatio-temporal correlations among regions. Specifically, the gated recurrent unit (GRU) is applied to encode the temporal correlation in regions into a vector. On the other hand, the spatial correlations among regions are encoded into two graphs through the graph convolutional network (GCN): geographically adjacent graph and functional similarity graph. Then, a prediction module based on the Louvain algorithm is used to accomplish the passenger demand prediction of multi-regions. The two real-world taxi order data collected in Shenzhen City and New York City are used in model validation and comparison. The numerical results show that the MC_STGCN model outperforms both classical time-series prediction methods and deep learning approaches. Moreover, in order to better illustrate the superiority of the proposed model, we further discuss the improvement of prediction performance though spatio-temporal correlation modeling and analyzing, the effectiveness of community detection compared with random classification of regions, and the advantages of regional level prediction compared with grid-based prediction models.

TrammelGraph: visual graph abstraction for comparison

Network data, represented by graph-based structures, are used in a variety of applications such as social networks and disease complication networks. A crucial task in many applications is graph comparison, with the goal of understanding the structural differences between pairs of graphs. However, traditional graph visualization techniques, node-link diagrams, and adjacency matrices are not intrinsically designed for comparison tasks. In this paper, we present TrammelGraph, a novel visual graph abstraction technique for graph comparison. TrammelGraph uses graph embedding and node alignment methods to create a map-based representation that eliminates visual clutter and thus facilities graph comparison. The design results in a planar graph with a regularly-spaced, crossing-free layout that helps users identify high-level topological information for graph comparison tasks. To evaluate the effectiveness of TrammelGraph, we conducted a controlled user study with 20 participants that compares TrammelGraph with node-link diagrams and adjacency matrices on a variety of common graph comparison tasks. We also conducted an expert interview with a physician using the MIMIC dataset. Both the quantitative and qualitative results from the study and interview highlighted the key strengths of TrammelGraph as a tool for visual graph comparison.

TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity

This paper is concerned with polynomial optimization problems. We show how to exploit term (or monomial) sparsity of the input polynomials to obtain a new converging hierarchy of semidefinite programming relaxations. The novelty (and distinguishing feature) of such relaxations is to involve block-diagonal matrices obtained in an iterative procedure performing completion of the connected components of certain adjacency graphs. The graphs are related to the terms arising in the original data and not to the links between variables. Our theoretical framework is then applied to compute lower bounds for polynomial optimization problems either randomly generated or coming from the networked system literature.

Optimization of strip-layout using graph-theoretic methodology for stamping operations on progressive die: a case study

The design of the progressive die stamping process is optimized through minimizing the number of die stamping stations in the strip layout to reduce the die cost. In order to accomplish such end, in this study, a graph-theoretic based method is implemented to model and optimize the strip layout design. This method starts with mapping stamping features into stamping operations. This step is followed by constructing two graphs to model the precedence and adjacency constraints among stamping operations based on a set of manufacturing rules. These two graphs are called: operation precedence graph and operation adjacency graph. In the next step, a topological sorting algorithm clusters the operations into partially ordered sets. Then, a graph coloring algorithm clusters the partially ordered operations sets into final sequence of operations. The graph-theoretic technique has been implemented on a part currently manufactured by laser cutting process technology in some Egyptian factory in Cairo. This study indicated that the graph-theoretic technique offers several advantages including the ease of programming and transparency in understanding the obtained strip layout design. This is besides being a systematic and logically approach to obtain an optimized strip layout design. In general, the progressive die manufacturing can increase productivity of sheet metal works in Egypt, only in situations of mass production. The limitation is that it requires considerable skill level and training for labor to conduct die strip layout design.

Fusing Node Embeddings and Incomplete Attributes by Complement‐Based Concatenation

Network embedding that learns representations of network nodes plays a critical role in network analysis, since it enables many downstream learning tasks. Although various network embedding methods have been proposed, they are mainly designed for a single network scenario. This paper considers a “multiple network” scenario by studying the problem of fusing the node embeddings and incomplete attributes from two different networks. To address this problem, we propose to complement the incomplete attributes, so as to conduct data fusion via concatenation. Specifically, we first propose a simple inductive method, in which attributes are defined as a parametric function of the given node embedding vectors. We then propose its transductive variant by adaptively learning an adjacency graph to approximate the original network structure. Additionally, we also provide a light version of this transductive variant. Experimental results on four datasets demonstrate the superiority of our methods.

Global Consistent Graph Convolutional Network for Hyperspectral Image Classification

While semisupervised methods based on graph convolutional networks (GCNs) can achieve good results in hyperspectral image (HSI) classification, their performance is limited as they rely only on spatial-spectral similarity when constructing local adjacency graphs. Moreover, relying on local adjacency graphs can limit the ability of the methods to ensure the consistency of global feature in complex hyperspectral remote sensing environments. Using the spatial-spectral information is typically not sufficient for providing a reliable similarity measurement to construct a global graph when the spectral variability is large and the spatial distance is long in intraclass pixels. To address this issue, this article presents a novel globally consistent GCN (GCGCN) for HSI classification. According to the proposed method, a local reliable initial graph is first built from inherent spatial-spectral information by considering this graph as a variable to optimize. Then, adaptive global high-order neighbors are explored to capture the underlying rich spatial contextual information by utilizing the graph topological consistent connectivity instead of the common strategy of using only the spatial-spectral similarity measurement. Finally, the adaptive global high-order graph structure and two-layer networks are combined to achieve the global feature smoothing of the same class samples and maintain high global feature consistency. The proposed GCGCN method is evaluated on three real HSI data sets to demonstrate its superiority compared to ten different classification methods. Moreover, the proposed GCGCN method achieves state-of-the-art classification results on three data sets in terms of four classification evaluation metrics, including overall accuracy (OA), kappa coefficient (KC), average accuracy (AA), and class accuracy (CA).

Learning Graph Convolutional Network for Blind Mesh Visual Quality Assessment

This paper proposes a new method for blind mesh visual quality assessment (MVQA) based on a graph convolutional network. For that, we address the node classification problem to predict the perceived visual quality. First, two matrices representing the 3D mesh are considered: a graph adjacency matrix and a feature matrix. Both matrices are used as input to a shallow graph convolutional network. The network consists of two convolutional layers followed by a max-pooling layer to provide the final feature representation. With this structure, the Softmax classifier predicts the quality score category without the reference mesh's availability. Experiments are conducted on four publicly available databases constructed explicitly for the mesh quality assessment task. We investigate several perceptual and visual features to select the most effective combination. Comparisons with the state-of-the-art alternative methods show the effectiveness of the proposed framework.

Graph Signal Processing: Vertex Multiplication

On the Euclidean domains of classical signal processing, linking of signal samples to underlying coordinate structures is straightforward. While graph adjacency matrices totally define the quantitative associations among the underlying graph vertices, a major problem in graph signal processing is the lack of explicit association of vertices with an underlying coordinate structure. To make this link, we propose an operation, called the vertex multiplication (VM), which is defined for graphs and can operate on graph signals. VM, which generalizes the coordinate multiplication (CM) operation in time series signals, can be interpreted as an operator that assigns a coordinate structure to a graph. By using the graph domain extension of differentiation and graph Fourier transform (GFT), VM is defined such that it shows Fourier duality that differentiation and CM operations are duals of each other under Fourier transformation (FT). Numerical examples and applications are also presented.

Double gaussianization of graph spectra

The graph spectrum is the set of eigenvalues of a simple graph with n vertices. Here we fold this graph spectrum at a given pair of reference eigenvalues and then exponentiate the resulting folded graph spectrum. This process produces double Gaussianized functions of the graph adjacency matrix which give more importance to the reference eigenvalues than to the rest of the spectrum. Based on evidences from mathematical chemistry we focus here our attention on the reference eigenvalues ±1. In the examples that we have examined, they enclose most of the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) of organic molecular graphs. We prove here several results for the trace of the double Gaussianized adjacency matrix of simple graphs–the double Gaussianized Estrada index. Finally we apply this index to the classification of polycyclic aromatic hydrocarbons (PAHs) as carcinogenic or inactive ones. We discover that local indices based on the previously developed matrix function allow to classify correctly 100% of the PAHs analyzed. Such indices reflect the electron population of the HOMO/LUMO and eigenvalues close to them, in the so-called K and L regions of PAHs.

Generalized Multi-manifold Graph Ensemble Embedding for Multi-View Dimensionality Reduction

In this paper, we propose a new dimension reduction (DR) algorithm called ensemble graph-based locality preserving projections (EGLPP); to overcome the neighborhood size k sensitivity in locally preserving projections (LPP). EGLPP constructs a homogeneous ensemble of adjacency graphs by varying neighborhood size k and finally uses the integrated embedded graph to optimize the low-dimensional projections. Furthermore, to appropriately handle the intrinsic geometrical structure of the multi-view data and overcome the dimensionality curse, we propose a generalized multi-manifold graph ensemble embedding framework (MLGEE). MLGEE aims to utilize multi-manifold graphs for the adjacency estimation with automatically weight each manifold to derive the integrated heterogeneous graph. Experimental results on various computer vision databases verify the effectiveness of proposed EGLPP and MLGEE over existing comparative DR methods.

On the Role of Graph Theory Apparatus in a CAD Modeling Kernel

This paper summarizes the experience of authors in solving a broad range of CAD modeling problems where the formalism of graph theory demonstrates its expressive power. Some results reported in this paper have never been published elsewhere. The set of topological and geometric heuristics backing the subgraph isomorphism algorithm is presented to achieve decent performance in our extensible feature recognition framework. By the example of sheet metal features, we show that using wise topological and geometric heuristics speeds up the search process up to interactive performance rates. For detecting CAD part’s type, we present the connected components’ analysis in the attributed adjacency graph. Our approach allows for identifying two-sided CAD parts, such as sheet metals, tubes, and flat plates. We use the notion of face transition graph for the unfoldability analysis. The basic operations on hierarchical assembly graphs are formalized in terms of graph theory for handling CAD assemblies. We describe instance singling operation that allows for addressing unique part’s occurrences in the component tree of an assembly. The presented algorithms and ideas demonstrated their efficiency and accuracy in the bunch of industrial applications developed by our team.

Graph Based Method for Lathe Machining Part Model

Process planning is about bridging design to manufacturing in an effective way. Although many methods can be used to recognize CAD and manufacturing feature, one way to do it is by Graph-based Method. Attributed Adjacency Graph (AAG) is develop for each feature of a part model in this case to ease of planning the machining of the part. Each machining feature will have a unique constructive sub-graph (CG). This paper proposes CG for lathe machining feature. The proposed CG is useful for future development of a generative process planning system of a lathe machining.

Les vedettes du Dictionnaire Électronique des Synonymes et les relations d’adjacence entre leurs synonymes

The Dictionnaire Électronique des Synonymes of CRISCO (DES, Université de Caen-Normandie) has acquired an undisputed reputation over the last twenty years. The synonymic links that originally originated from 7 source dictionaries have been progressively completed by tens of thousands of proposals from Internet users, whose relevance has been tested and validated by the successive engineers and webmasters of the DES. The present study deals with the utilization of the adjacency graph between all registered synonyms, their distribution into two or more sets of interconnected synonyms, and especially the question of the numerous isolated synonymic links whose integration into an interrelated component is being tested using an original method of exploiting second-order synonymic links. This method, which delivers a high integration rate (between 70% and 80%, irreducible links being removed), will allow an appreciable cleaning of the synonymic network of the DES.

Sparsity-Based Clustering for Large Hyperspectral Remote Sensing Images

Hyperspectral image (HSI) clustering is extremely challenging because of the complexity of the image structure. Recently, the subspace clustering algorithms have achieved competitive performance for HSIs. However, these methods generally are computationally complex and time-and-memory-consuming, given their reliance on large-scale adjacency matrix learning and graph segmentation, which limits their application to large HSIs and reduces their attractiveness in real applications. In this article, in view of this, two novel sparsity-based clustering algorithms are proposed for large HSIs, named sparse coding-based clustering (SCC) and joint SCC (JSCC). To the best of our knowledge, we are the first to use the sparse representation recovery residual to cluster HSIs. Based on a structured dictionary constructed by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -means and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -nearest neighbor (KNN), an SCC model is constructed to cluster HSIs according to the recovery residual minimization criterion. By dealing with a pixel-wise sparse recovery problem instead of the large-scale graph optimization problem of the whole image, the computational complexity and the time-and-memory cost are reduced to a large degree, which makes sense for practical applications. Then, by introducing the super-pixel neighborhood, a JSCC model is constructed to better explore the interpixel correlation of HSIs and further improve the clustering performance. The proposed algorithms were verified on three widely used HSIs. All the three experiments confirm the effectiveness of the proposed algorithms, which can be considered as competitive tools for use with large HSIs.

Balanced Graph-based regularized semi-supervised extreme learning machine for EEG classification

Machine learning algorithms play a critical role in electroencephalograpy (EEG)-based brain-computer interface (BCI) systems. However, collecting labeled samples for classifier training and calibration is still difficult and time-consuming, especially for patients. As a promising alternative way to address the problem, semi-supervised learning has attracted much attention by exploiting both labeled and unlabeled samples in the training process. Nowadays, semi-supervised extreme learning machine (SS-ELM) is widely used in EEG classification due to its fast training speed and good generalization performance. However, the classification performance of SS-ELM largely depends on the quality of sample graph. The graphs of most semi-supervised algorithms are constructed by the similarity between labeled and unlabeled data called manifold graph. The more similar the structural information between samples, the greater probability they belong to the same class. In this paper, the label-consistency graph (LCG) and sample-similarity graph (SSG) are combined to constrain the model output. When the SSG is not accurate enough, the weight of LCG needs to be increased, and vice versa. The weight ratio of two graphs is optimized to obtain an optimal adjacency graph, and finally the best output weight vector is achieved. To verify the effectiveness of the proposed algorithm, it was validated and compared with several existing methods on two real datasets: BCI Competition IV Dataset 2a and BCI Competition III Dataset 4a. Experimental results show that our algorithm has achieved the promising results, especially when the number of labeled samples is small.

SAR image segmentation with parallel region merging

In this paper, a parallel region merging strategy is proposed for partitioning Synthetic Aperture Radar (SAR) images into several disjoint regions, based on the region adjacency graph (RAG) of an initial partition and the nearest neighbor graph (NNG) produced from the RAG. Developed from the multi-direction ratio edge detector, a multi-scale-multi-direction (MSMD) one is used to extract edge strength map (ESM) of an initial SAR image, feeded into watershed transform to generate an initial partition result of the initial SAR image. Considering local image properties, which makes the generated NNG center around bi-node circles situated in interiors of homogeneous regions, many of which are independently located in different homogeneous regions, the predication of the parallelizability for bi-node circles is proposed to make the proposed parallel region merging strategy. The proposed parallel merging strategy simultaneously merges bi-node circles far away from boundaries of regions, characterized by the length of path from a node to the bi-node circle in the NNG. The performance of the proposed parallel merging strategy is analyzed theoretically and experimentally, and our experiments show that the proposed method outweighs other compared methods.

Searching and describing objects in satellite images on the basis of modeling reasoning

The article presents an approach to a problem of contextual search and description of objects in raster satellite images, which consists in modeling reasoning on the basis of structured cases. As a result of image processing, an adjacency graph of color regions is constructed. The object is characterized by color, attributes of the form of segments of the border and the shape of the object as a whole. A structured case is represented in the form of a beam graph, whose arcs are ordered according to a positive bypass of the region boundaries. Using a graph matching algorithm, occurrences of cases stored in the system database are detected in the analyzed image. When the occurrence is detected, a case-based inference rule is applied. The degree to which an object belongs to a certain class depends not only on the properties of the object itself, but also on the reliability of the surrounding objects. The contextual search strategy contains stages of recursion and iteration. In contrast to neural network technologies, the proposed approach allows one not only to classify image objects, but also to form their structured descriptions. In addition, the classification decision issued by the system has a reasoned justification. The results of the experiment show that reasoning based on structured cases allows refining the results of classification and increasing the reliability of object recognition in satellite images.

Spectral-Based Directed Graph Network for Malware Detection

As a kind of behavioral-feature based malware detection approach, spectral graph-based deep learning has attracted considerable research efforts with the fast growth of threats of malicious programs. However, previous spectral based graph neural networks can hardly be applied to directed graphs due to the asymmetrical nature of the graph adjacency matrix. In order to address the issues of existing techniques, we propose a Spectral-based Directed Graph Network (SDGNet) architecture to classify directed graphs. In SDGNet, the weighted graph matrix normalization methods transform the graph adjacency matrix into three symmetrical graph matrices that describe different aspects of node information interaction. Then, the SDGNet extracts graph representations with different layers of multi-aspect directed GCN. On each layer, three node embeddings learned from the symmetrical graph matrices are fused together for a graph representation. The multi-layer graph representations are further concatenated together to form a comprehensive representation for classification with a combined loss function. We evaluate the proposed algorithm on a public benchmark data, and the experimental results show that it outperforms state-of-the-art algorithms.

Shape correspondence based on Kendall shape space and RAG for 2D animation

We introduce a 2D vectorized shape correspondence method based on Kendall shape space and region adjacency graph. We regard shape correspondence in 2D animation as a weighted bipartite graph matching problem and optimize it by means of various weights, including geometric attribute, local topological information, and global topological information in 2D animation drawing. The measuring method in Kendall shape space is introduced to determine similarity between two regions and a local adjacent region matching method is presented to associate the vicinity of the corresponding region by utilizing local topology information. Ultimately, we propose a globally optimal shape matching method, which exploits the global topological information to get the final result of the shape correspondence. Our approach can efficiently match associated regions that have exaggerated deformation and unstable topology between two shapes in 2D animation. It is also robust to the similarity transformation of shapes.