Showing papers on "Adjacency list published in 2020"

A Set-Membership Approach to Event-Triggered Filtering for General Nonlinear Systems Over Sensor Networks

Abstract: This paper is concerned with the distributed set-membership filtering problem for a class of general discrete-time nonlinear systems under event-triggered communication protocols over sensor networks. To mitigate the communication burden, each intelligent sensing node broadcasts its measurement to the neighboring nodes only when a predetermined event-based media-access condition is satisfied. According to the interval mathematics theory, a recursive distributed set-membership scheme is designed to obtain an ellipsoid set containing the target states of interest via adequately fusing the measurements from neighboring nodes, where both the accurate estimate on Lagrange remainder and the event-based media-access condition are skillfully utilized to improve the filter performance. Furthermore, such a scheme is only dependent on neighbor information and local adjacency weights, thereby fulfilling the scalability requirement of sensor networks. In addition, an optimization algorithm is developed to minimize the trace of the estimated ellipsoid set, and the effect from the adopted event-triggered threshold is thoroughly discussed as well. Finally, a simulation example is utilized to illustrate the usefulness of the proposed distributed set-membership filtering scheme.

Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting

Abstract: Spatial-temporal data forecasting of traffic flow is a challenging task because of complicated spatial dependencies and dynamical trends of temporal pattern between different roads. Existing frameworks typically utilize given spatial adjacency graph and sophisticated mechanisms for modeling spatial and temporal correlations. However, limited representations of given spatial graph structure with incomplete adjacent connections may restrict effective spatial-temporal dependencies learning of those models. To overcome those limitations, our paper proposes Spatial-Temporal Fusion Graph Neural Networks (STFGNN) for traffic flow forecasting. SFTGNN could effectively learn hidden spatial-temporal dependencies by a novel fusion operation of various spatial and temporal graphs, which is generated by a data-driven method. Meanwhile, by integrating this fusion graph module and a novel gated convolution module into a unified layer, SFTGNN could handle long sequences. Experimental results on several public traffic datasets demonstrate that our method achieves state-of-the-art performance consistently than other baselines.

On the Universality of the Quantum Approximate Optimization Algorithm

Abstract: The quantum approximate optimization algorithm (QAOA) is considered to be one of the most promising approaches towards using near-term quantum computers for practical application. In its original form, the algorithm applies two different Hamiltonians, called the mixer and the cost Hamiltonian, in alternation with the goal being to approach the ground state of the cost Hamiltonian. Recently, it has been suggested that one might use such a set-up as a parametric quantum circuit with possibly some other goal than reaching ground states. From this perspective, a recent work (Lloyd, arXiv:1812.11075 ) argued that for one-dimensional local cost Hamiltonians, composed of nearest neighbour ZZ terms, this set-up is quantum computationally universal and provides a universal gate set, i.e. all unitaries can be reached up to arbitrary precision. In the present paper, we complement this work by giving a complete proof and the precise conditions under which such a one-dimensional QAOA might produce a universal gate set. We further generalize this type of gate-set universality for certain cost Hamiltonians with ZZ and ZZZ terms arranged according to the adjacency structure of certain graphs and hypergraphs.

Adaptive Graph Representation Learning for Video Person Re-Identification

Abstract: Recent years have witnessed the remarkable progress of applying deep learning models in video person re-identification (Re-ID) A key factor for video person Re-ID is to effectively construct discriminative and robust video feature representations for many complicated situations Part-based approaches employ spatial and temporal attention to extract representative local features While correlations between parts are ignored in the previous methods, to leverage the relations of different parts, we propose an innovative adaptive graph representation learning scheme for video person Re-ID, which enables the contextual interactions between relevant regional features Specifically, we exploit the pose alignment connection and the feature affinity connection to construct an adaptive structure-aware adjacency graph, which models the intrinsic relations between graph nodes We perform feature propagation on the adjacency graph to refine regional features iteratively, and the neighbor nodes’ information is taken into account for part feature representation To learn compact and discriminative representations, we further propose a novel temporal resolution-aware regularization, which enforces the consistency among different temporal resolutions for the same identities We conduct extensive evaluations on four benchmarks, ie iLIDS-VID, PRID2011, MARS, and DukeMTMC-VideoReID, experimental results achieve the competitive performance which demonstrates the effectiveness of our proposed method Code is available at https://githubcom/weleen/AGRLpytorch

On the generalized adjacency, Laplacian and signless Laplacian spectra of the weighted edge corona networks

Abstract: Many problems in real world, either natural or man-made, can be usefully represented by graphs or networks. Along with a complex topological structure, the weight is a vital factor in characterizing some properties of real networks. In this paper, we define a class of the weighted edge corona product networks. The generalized adjacency (resp., Laplacian and signless Laplacian) spectra with two different structures are determined. As applications, the number of spanning trees and Kirchhoff index of the weighted edge corona product networks are computed.

Deep Network Embedding for Graph Representation Learning in Signed Networks

Abstract: Network embedding has attracted an increasing attention over the past few years. As an effective approach to solve graph mining problems, network embedding aims to learn a low-dimensional feature vector representation for each node of a given network. The vast majority of existing network embedding algorithms, however, are only designed for unsigned networks, and the signed networks containing both positive and negative links, have pretty distinct properties from the unsigned counterpart. In this paper, we propose a deep network embedding model to learn the low-dimensional node vector representations with structural balance preservation for the signed networks. The model employs a semisupervised stacked auto-encoder to reconstruct the adjacency connections of a given signed network. As the adjacency connections are overwhelmingly positive in the real-world signed networks, we impose a larger penalty to make the auto-encoder focus more on reconstructing the scarce negative links than the abundant positive links. In addition, to preserve the structural balance property of signed networks, we design the pairwise constraints to make the positively connected nodes much closer than the negatively connected nodes in the embedding space. Based on the network representations learned by the proposed model, we conduct link sign prediction and community detection in signed networks. Extensive experimental results in real-world datasets demonstrate the superiority of the proposed model over the state-of-the-art network embedding algorithms for graph representation learning in signed networks.

Cross-Modality Attention with Semantic Graph Embedding for Multi-Label Classification

Abstract: Multi-label image and video classification are fundamental yet challenging tasks in computer vision. The main challenges lie in capturing spatial or temporal dependencies between labels and discovering the locations of discriminative features for each class. In order to overcome these challenges, we propose to use cross-modality attention with semantic graph embedding for multi-label classification. Based on the constructed label graph, we propose an adjacency-based similarity graph embedding method to learn semantic label embeddings, which explicitly exploit label relationships. Then our novel cross-modality attention maps are generated with the guidance of learned label embeddings. Experiments on two multi-label image classification datasets (MS-COCO and NUS-WIDE) show our method outperforms other existing state-of-the-arts. In addition, we validate our method on a large multi-label video classification dataset (YouTube-8M Segments) and the evaluation results demonstrate the generalization capability of our method.

3D Dynamic Scene Graphs: Actionable Spatial Perception with Places, Objects, and Humans

Abstract: We present a unified representation for actionable spatial perception: 3D Dynamic Scene Graphs. Scene graphs are directed graphs where nodes represent entities in the scene (e.g. objects, walls, rooms), and edges represent relations (e.g. inclusion, adjacency) among nodes. Dynamic scene graphs (DSGs) extend this notion to represent dynamic scenes with moving agents (e.g. humans, robots), and to include actionable information that supports planning and decision-making (e.g. spatio-temporal relations, topology at different levels of abstraction). Our second contribution is to provide the first fully automatic Spatial PerceptIon eNgine(SPIN) to build a DSG from visual-inertial data. We integrate state-of-the-art techniques for object and human detection and pose estimation, and we describe how to robustly infer object, robot, and human nodes in crowded scenes. To the best of our knowledge, this is the first paper that reconciles visual-inertial SLAM and dense human mesh tracking. Moreover, we provide algorithms to obtain hierarchical representations of indoor environments (e.g. places, structures, rooms) and their relations. Our third contribution is to demonstrate the proposed spatial perception engine in a photo-realistic Unity-based simulator, where we assess its robustness and expressiveness. Finally, we discuss the implications of our proposal on modern robotics applications. 3D Dynamic Scene Graphs can have a profound impact on planning and decision-making, human-robot interaction, long-term autonomy, and scene prediction. A video abstract is available at this https URL

Unsupervised Dimensionality Reduction for Hyperspectral Imagery via Local Geometric Structure Feature Learning

Abstract: Hyperspectral images (HSIs) possess a large number of spectral bands, which easily lead to the curse of dimensionality. To improve the classification performance, a huge challenge is how to reduce the number of spectral bands and preserve the valuable intrinsic information in the HSI. In this letter, we propose a novel unsupervised dimensionality reduction method called local neighborhood structure preserving embedding (LNSPE) for HSI classification. At first, LNSPE reconstructs each sample with its spectral neighbors and obtains the optimal weights for constructing the adjacency graph by modifying its loss function. Then, to discover the scatter information of the training samples, LNSPE minimizes the scatter between the pixels and the corresponding neighbors and maximizes the total scatter of the HSI data. Finally, it incorporates the scatter information and the dual graph structure to enhance the aggregation of the HSI. As a result, LNSPE can effectively reveal the intrinsic structure and improve the classification performance of the HSI data. The experimental results on two real hyperspectral data sets exhibit the efficiency and superiority of LNSPE to some state-of-the-art methods.

House-GAN: Relational Generative Adversarial Networks for Graph-constrained House Layout Generation

Abstract: This paper proposes a novel graph-constrained generative adversarial network, whose generator and discriminator are built upon relational architecture. The main idea is to encode the constraint into the graph structure of its relational networks. We have demonstrated the proposed architecture for a new house layout generation problem, whose task is to take an architectural constraint as a graph (i.e., the number and types of rooms with their spatial adjacency) and produce a set of axis-aligned bounding boxes of rooms. We measure the quality of generated house layouts with the three metrics: the realism, the diversity, and the compatibility with the input graph constraint. Our qualitative and quantitative evaluations over 117,000 real floorplan images demonstrate that the proposed approach outperforms existing methods and baselines. We will publicly share all our code and data.

Encoding word order in complex embeddings

Abstract: Sequential word order is important when processing text. Currently, neural networks (NNs) address this by modeling word position using position embeddings. The problem is that position embeddings capture the position of individual words, but not the ordered relationship (e.g., adjacency or precedence) between individual word positions. We present a novel and principled solution for modeling both the global absolute positions of words and their order relationships. Our solution generalizes word embeddings, previously defined as independent vectors, to continuous word functions over a variable (position). The benefit of continuous functions over variable positions is that word representations shift smoothly with increasing positions. Hence, word representations in different positions can correlate with each other in a continuous function. The general solution of these functions can be extended to complex-valued variants. We extend CNN, RNN and Transformer NNs to complex-valued versions to incorporate our complex embedding (we make all code available). Experiments on text classification, machine translation and language modeling show gains over both classical word embeddings and position-enriched word embeddings. To our knowledge, this is the first work in NLP to link imaginary numbers in complex-valued representations to concrete meanings (i.e., word order).

House-GAN: Relational Generative Adversarial Networks for Graph-Constrained House Layout Generation

Abstract: This paper proposes a novel graph-constrained generative adversarial network, whose generator and discriminator are built upon relational architecture. The main idea is to encode the constraint into the graph structure of its relational networks. We have demonstrated the proposed architecture for a new house layout generation problem, whose task is to take an architectural constraint as a graph (i.e., the number and types of rooms with their spatial adjacency) and produce a set of axis-aligned bounding boxes of rooms. We measure the quality of generated house layouts with the three metrics: the realism, the diversity, and the compatibility with the input graph constraint. Our qualitative and quantitative evaluations over 117,000 real floorplan images demonstrate that the proposed approach outperforms existing methods and baselines. We will publicly share all our code and data.

GraphOne: A Data Store for Real-time Analytics on Evolving Graphs

Abstract: There is a growing need to perform a diverse set of real-time analytics (batch and stream analytics) on evolving graphs to deliver the values of big data to users. The key requirement from such applications is to have a data store to support their diverse data access efficiently, while concurrently ingesting fine-grained updates at a high velocity. Unfortunately, current graph systems, either graph databases or analytics engines, are not designed to achieve high performance for both operations; rather, they excel in one area that keeps a private data store in a specialized way to favor their operations only. To address this challenge, we have designed and developed GraphOne, a graph data store that abstracts the graph data store away from the specialized systems to solve the fundamental research problems associated with the data store design. It combines two complementary graph storage formats (edge list and adjacency list) and uses dual versioning to decouple graph computations from updates. Importantly, it presents a new data abstraction, GraphView, to enable data access at two different granularities of data ingestions (called data visibility) for concurrent execution of diverse classes of real-time graph analytics with only a small data duplication. Experimental results show that GraphOne is able to deliver 11.40× and 5.36× average speedup in ingestion rate against LLAMA and Stinger, the two state-of-the-art dynamic graph systems, respectively. Further, they achieve an average speedup of 8.75× and 4.14× against LLAMA and 12.80× and 3.18× against Stinger for BFS and PageRank analytics (batch version), respectively. GraphOne also gains over 2,000× speedup against Kickstarter, a state-of-the-art stream analytics engine in ingesting the streaming edges and performing streaming BFS when treating first half as a base snapshot and rest as streaming edge in a synthetic graph. GraphOne also achieves an ingestion rate of two to three orders of magnitude higher than graph databases. Finally, we demonstrate that it is possible to run concurrent stream analytics from the same data store.

3D Dynamic Scene Graphs: Actionable Spatial Perception with Places, Objects, and Humans.

Abstract: We present a unified representation for actionable spatial perception: 3D Dynamic Scene Graphs. Scene graphs are directed graphs where nodes represent entities in the scene (e.g. objects, walls, rooms), and edges represent relations (e.g. inclusion, adjacency) among nodes. Dynamic scene graphs (DSGs) extend this notion to represent dynamic scenes with moving agents (e.g. humans, robots), and to include actionable information that supports planning and decision-making (e.g. spatio-temporal relations, topology at different levels of abstraction). Our second contribution is to provide the first fully automatic Spatial PerceptIon eNgine(SPIN) to build a DSG from visual-inertial data. We integrate state-of-the-art techniques for object and human detection and pose estimation, and we describe how to robustly infer object, robot, and human nodes in crowded scenes. To the best of our knowledge, this is the first paper that reconciles visual-inertial SLAM and dense human mesh tracking. Moreover, we provide algorithms to obtain hierarchical representations of indoor environments (e.g. places, structures, rooms) and their relations. Our third contribution is to demonstrate the proposed spatial perception engine in a photo-realistic Unity-based simulator, where we assess its robustness and expressiveness. Finally, we discuss the implications of our proposal on modern robotics applications. 3D Dynamic Scene Graphs can have a profound impact on planning and decision-making, human-robot interaction, long-term autonomy, and scene prediction. A video abstract is available at this https URL

Learning Unsupervised Hierarchical Part Decomposition of 3D Objects From a Single RGB Image

Abstract: Humans perceive the 3D world as a set of distinct objects that are characterized by various low-level (geometry, reflectance) and high-level (connectivity, adjacency, symmetry) properties. Recent methods based on convolutional neural networks (CNNs) demonstrated impressive progress in 3D reconstruction, even when using a single 2D image as input. However, the majority of these methods focuses on recovering the local 3D geometry of an object without considering its part-based decomposition or relations between parts. We address this challenging problem by proposing a novel formulation that allows to jointly recover the geometry of a 3D object as a set of primitives as well as their latent hierarchical structure without part-level supervision. Our model recovers the higher level structural decomposition of various objects in the form of a binary tree of primitives, where simple parts are represented with fewer primitives and more complex parts are modeled with more components. Our experiments on the ShapeNet and D-FAUST datasets demonstrate that considering the organization of parts indeed facilitates reasoning about 3D geometry.

Adjacency Labelling for Planar Graphs (and Beyond)

Abstract: We show that there exists an adjacency labelling scheme for planar graphs where each vertex of an $n$-vertex planar graph $G$ is assigned a $(1+o(1))\log_2 n$-bit label and the labels of two vertices $u$ and $v$ are sufficient to determine if $uv$ is an edge of $G$. This is optimal up to the lower order term and is the first such asymptotically optimal result. An alternative, but equivalent, interpretation of this result is that, for every $n$, there exists a graph $U_n$ with $n^{1+o(1)}$ vertices such that every $n$-vertex planar graph is an induced subgraph of $U_n$. These results generalize to bounded genus graphs, apex-minor-free graphs, bounded-degree graphs from minor closed families, and $k$-planar graphs.

Privacy-Preserving Approach PBCN in Social Network With Differential Privacy

Abstract: Currently, lots of real social relations in social networks force users to face the potential risk of privacy leakage. Consequently, data holders would like to disturbor anonymize their individual data before publishing them, for the purpose of privacy protection. Due to the characteristics of high sensitivity and large volume data of social network graph structure, it is difficult for privacy protection schemes to enable a reasonable allocation of noises while keeping desirable data availability and execution efficiency. On the basis of differential privacy model, combining with clustering and randomization algorithms, a privacy protection approach PBCN (Privacy Preserving Approach Based on Clustering and Noise) is proposed. This proposal is composed of five algorithms including random disturbance based on clustering, graph reconstruction after disturbing degree sequence and noise nodes generation, etc. Furthermore, a privacy measure algorithm based on adjacency degree is put forward in order to objectively evaluate the privacy-preserving strength of various schemes against graph structure and degree attacks. Simulation experiments are conducted to achieve performance comparisons between PBCN, Spctr Add/Del, Spctr Switch, DER and HPDP. The experimental results show that PBCN realizes more satisfactory data availability and execution efficiency. Finally, parameters utility analysis demonstrates PBCN can achieve a “trade-off” between data availability and privacy protection level.

Graph Sequence Recurrent Neural Network for Vision-Based Freezing of Gait Detection

Abstract: Freezing of gait (FoG) is one of the most common symptoms of Parkinson’s disease (PD), a neurodegenerative disorder which impacts millions of people around the world. Accurate assessment of FoG is critical for the management of PD and to evaluate the efficacy of treatments. Currently, the assessment of FoG requires well-trained experts to perform time-consuming annotations via vision-based observations. Thus, automatic FoG detection algorithms are needed. In this study, we formulate vision-based FoG detection, as a fine-grained graph sequence modelling task, by representing the anatomic joints in each temporal segment with a directed graph, since FoG events can be observed through the motion patterns of joints. A novel deep learning method is proposed, namely graph sequence recurrent neural network (GS-RNN), to characterize the FoG patterns by devising graph recurrent cells, which take graph sequences of dynamic structures as inputs. For the cases of which prior edge annotations are not available, a data-driven based adjacency estimation method is further proposed. To the best of our knowledge, this is one of the first studies on vision-based FoG detection using deep neural networks designed for graph sequences of dynamic structures. Experimental results on more than 150 videos collected from 45 patients demonstrated promising performance of the proposed GS-RNN for FoG detection with an AUC value of 0.90.

Learning Unsupervised Hierarchical Part Decomposition of 3D Objects from a Single RGB Image

Abstract: Humans perceive the 3D world as a set of distinct objects that are characterized by various low-level (geometry, reflectance) and high-level (connectivity, adjacency, symmetry) properties. Recent methods based on convolutional neural networks (CNNs) demonstrated impressive progress in 3D reconstruction, even when using a single 2D image as input. However, the majority of these methods focuses on recovering the local 3D geometry of an object without considering its part-based decomposition or relations between parts. We address this challenging problem by proposing a novel formulation that allows to jointly recover the geometry of a 3D object as a set of primitives as well as their latent hierarchical structure without part-level supervision. Our model recovers the higher level structural decomposition of various objects in the form of a binary tree of primitives, where simple parts are represented with fewer primitives and more complex parts are modeled with more components. Our experiments on the ShapeNet and D-FAUST datasets demonstrate that considering the organization of parts indeed facilitates reasoning about 3D geometry.

Chordal-TSSOS: a moment-SOS hierarchy that exploits term sparsity with chordal extension

Abstract: This work is a follow-up and a complement to arXiv:1912.08899 [math.OC] for solving polynomial optimization problems (POPs). The chordal-TSSOS hierarchy that we propose is a new sparse moment-SOS framework based on term-sparsity and chordal extension. By exploiting term-sparsity of the input polynomials we obtain a two-level hierarchy of semidefinite programming relaxations. The novelty and distinguishing feature of such relaxations is to obtain quasi block-diagonal matrices obtained in an iterative procedure that performs chordal extension of certain adjacency graphs. The graphs are related to the terms arising in the original data and not to the links between variables. Various numerical examples demonstrate the efficiency and the scalability of this new hierarchy for both unconstrained and constrained POPs. The two hierarchies are complementary. While the former TSSOS arXiv:1912.08899 [math.OC] has a theoretical convergence guarantee, the chordal-TSSOS has superior performance but lacks this theoretical guarantee.

Arc Adjacency Matrix-Based Fast Ellipse Detection

Abstract: Fast and accurate ellipse detection is critical in certain computer vision tasks. In this paper, we propose an arc adjacency matrix-based ellipse detection (AAMED) method to fulfill this requirement. At first, after segmenting the edges into elliptic arcs, the digraph-based arc adjacency matrix (AAM) is constructed to describe their triple sequential adjacency states. Curvature and region constraints are employed to make the AAM sparse. Secondly, through bidirectionally searching the AAM, we can get all arc combinations which are probably true ellipse candidates. The cumulative-factor (CF) based cumulative matrices (CM) are worked out simultaneously. CF is irrelative to the image context and can be pre-calculated. CM is related to the arcs or arc combinations and can be calculated by the addition or subtraction of CF. Then the ellipses are efficiently fitted from these candidates through twice eigendecomposition of CM using Jacobi method. Finally, a comprehensive validation score is proposed to eliminate false ellipses effectively. The score is mainly influenced by the constraints about adaptive shape, tangent similarity, distribution compensation. Experiments show that our method outperforms the 12 state-of-the-art methods on 9 datasets as a whole, with reference to recall, precision, F-measure, and time-consumption.

LiveGraph: a transactional graph storage system with purely sequential adjacency list scans

Abstract: The specific characteristics of graph workloads make it hard to design a one-size-fits-all graph storage system. Systems that support transactional updates use data structures with poor data locality, which limits the efficiency of analytical workloads or even simple edge scans. Other systems run graph analytics workloads efficiently, but cannot properly support transactions.This paper presents LiveGraph, a graph storage system that outperforms both the best graph transactional systems and the best solutions for real-time graph analytics on fresh data. LiveGraph achieves this by ensuring that adjacency list scans, a key operation in graph workloads, are purely sequential: they never require random accesses even in presence of concurrent transactions. Such pure-sequential operations are enabled by combining a novel graph-aware data structure, the Transactional Edge Log (TEL), with a concurrency control mechanism that leverages TEL's data layout. Our evaluation shows that LiveGraph significantly outperforms state-of-the-art (graph) database solutions on both transactional and real-time analytical workloads.

Towards Locally Differentially Private Generic Graph Metric Estimation

Abstract: Local differential privacy (LDP) is an emerging technique for privacy-preserving data collection without a trusted collector. Despite its strong privacy guarantee, LDP cannot be easily applied to real-world graph analysis tasks such as community detection and centrality analysis due to its high implementation complexity and low data utility. In this paper, we address these two issues by presenting LF-GDPR, the first LDP-enabled graph metric estimation framework for graph analysis. It collects two atomic graph metrics — the adjacency bit vector and node degree — from each node locally. LF-GDPR simplifies the job of implementing LDP-related steps (e.g., local perturbation, aggregation and calibration) for a graph metric estimation task by providing either a complete or a parameterized algorithm for each step.

Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms

Abstract: We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters. We prove finite-sample guarantees on the performance of clustering with respect to this metric when random samples are drawn from multiple intrinsically low-dimensional clusters in high-dimensional space, in the presence of a large number of high-dimensional outliers. By combining these results with spectral clustering with respect to LLPD, we provide conditions under which the Laplacian eigengap statistic correctly determines the number of clusters for a large class of data sets, and prove guarantees on the labeling accuracy of the proposed algorithm. Our methods are quite general and provide performance guarantees for spectral clustering with any ultrametric. We also introduce an efficient, easy to implement approximation algorithm for the LLPD based on a multiscale analysis of adjacency graphs, which allows for the runtime of LLPD spectral clustering to be quasilinear in the number of data points.

Superpixel Image Classification with Graph Attention Networks

Abstract: This paper presents a methodology for image classification using Graph Neural Network (GNN) models. We transform the input images into region adjacency graphs (RAGs), in which regions are superpixels and edges connect neighboring superpixels. Our experiments suggest that Graph Attention Networks (GATs), which combine graph convolutions with self-attention mechanisms, outperforms other GNN models. Although raw image classifiers perform better than GATs due to in-formation loss during the RAG generation, our methodology opens an interesting avenue of research on deep learning beyond rectangular-gridded images, such as 360-degree field of view panoramas. Traditional convolutional kernels of current state-of-the-art methods cannot handle panoramas, whereas the adapted superpixel algorithms and the resulting region adjacency graphs can naturally feed a GNN, without topology issues.

Incorporating Dynamicity of Transportation Network With Multi-Weight Traffic Graph Convolutional Network for Traffic Forecasting

Abstract: Traffic forecasting problem remains a challenging task in the intelligent transportation system due to its spatio-temporal complexity. Although temporal dependency has been well studied and discussed, spatial dependency is relatively less explored due to its large variations, especially in the urban environment. In this study, a novel graph convolutional network model, Multi-Weight Traffic Graph Convolutional (MW-TGC) network, is proposed and applied to two urban networks with contrasting geometric constraints. The model conducts graph convolution operations on speed data with multi-weighted adjacency matrices to combine the features, including speed limit, distance, and angle. The spatially isolated dimension reduction operation is conducted on the combined features to learn the dependencies among the features and reduce the size of the output to a computationally feasible level. The output of multi-weight graph convolution is applied to the sequence-to-sequence model with Long Short-Term Memory units to learn temporal dependencies. When applied to two urban sites, urban-core and urban-mix, MW-TGC network not only outperformed the comparative models in both sites but also reduced variance in the heterogeneous urban-mix network. We conclude that MW-TGC network can provide a robust traffic forecasting performance across the variations in spatial complexity, which can be a strong advantage in urban traffic forecasting.

Shorter labeling schemes for planar graphs

Abstract: An adjacency labeling scheme for a given class of graphs is an algorithm that for every graph G from the class, assigns bit strings (labels) to vertices of G so that for any two vertices u, v, whether u and v are adjacent can be determined by a fixed procedure that examines only their labels. It is known that planar graphs with n vertices admit a labeling scheme with labels of bit length (2 + o(1)) log n. In this work we improve this bound by designing a labeling scheme with labels of bit length [MATH HERE]. In graph-theoretical terms, this implies an explicit construction of a graph on n4/3+o(1) vertices that contains all planar graphs on n vertices as induced subgraphs, improving the previous best upper bound of n2+o(1). Our scheme generalizes to graphs of bounded Euler genus with the same label length up to a second-order term. All the labels of the input graph can be computed in polynomial time, while adjacency can be decided from the labels in constant time.

Generating Adjacency-Constrained Subgoals in Hierarchical Reinforcement Learning.

Abstract: Goal-conditioned hierarchical reinforcement learning (HRL) is a promising approach for scaling up reinforcement learning (RL) techniques. However, it often suffers from training inefficiency as the action space of the high-level, i.e., the goal space, is often large. Searching in a large goal space poses difficulties for both high-level subgoal generation and low-level policy learning. In this paper, we show that this problem can be effectively alleviated by restricting the high-level action space from the whole goal space to a $k$-step adjacent region of the current state using an adjacency constraint. We theoretically prove that the proposed adjacency constraint preserves the optimal hierarchical policy in deterministic MDPs, and show that this constraint can be practically implemented by training an adjacency network that can discriminate between adjacent and non-adjacent subgoals. Experimental results on discrete and continuous control tasks show that incorporating the adjacency constraint improves the performance of state-of-the-art HRL approaches in both deterministic and stochastic environments.

Line Graph Enhanced AMR-to-Text Generation with Mix-Order Graph Attention Networks

Abstract: Efficient structure encoding for graphs with labeled edges is an important yet challenging point in many graph-based models. This work focuses on AMR-to-text generation -- A graph-to-sequence task aiming to recover natural language from Abstract Meaning Representations (AMR). Existing graph-to-sequence approaches generally utilize graph neural networks as their encoders, which have two limitations: 1) The message propagation process in AMR graphs is only guided by the first-order adjacency information. 2) The relationships between labeled edges are not fully considered. In this work, we propose a novel graph encoding framework which can effectively explore the edge relations. We also adopt graph attention networks with higher-order neighborhood information to encode the rich structure in AMR graphs. Experiment results show that our approach obtains new state-of-the-art performance on English AMR benchmark datasets. The ablation analyses also demonstrate that both edge relations and higher-order information are beneficial to graph-to-sequence modeling.

Generalized Spectral Clustering via Gromov-Wasserstein Learning

Abstract: We establish a bridge between spectral clustering and Gromov-Wasserstein Learning (GWL), a recent optimal transport-based approach to graph partitioning. This connection both explains and improves upon the state-of-the-art performance of GWL. The Gromov-Wasserstein framework provides probabilistic correspondences between nodes of source and target graphs via a quadratic programming relaxation of the node matching problem. Our results utilize and connect the observations that the GW geometric structure remains valid for any rank-2 tensor, in particular the adjacency, distance, and various kernel matrices on graphs, and that the heat kernel outperforms the adjacency matrix in producing stable and informative node correspondences. Using the heat kernel in the GWL framework provides new multiscale graph comparisons without compromising theoretical guarantees, while immediately yielding improved empirical results. A key insight of the GWL framework toward graph partitioning was to compute GW correspondences from a source graph to a template graph with isolated, self-connected nodes. We show that when comparing against a two-node template graph using the heat kernel at the infinite time limit, the resulting partition agrees with the partition produced by the Fiedler vector. This in turn yields a new insight into the $k$-cut graph partitioning problem through the lens of optimal transport. Our experiments on a range of real-world networks achieve comparable results to, and in many cases outperform, the state-of-the-art achieved by GWL.