Showing papers on "Adjacency list published in 2021"

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 usually 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. Furthermore, existing methods were out at elbows when solving complicated spatial-temporal data: they usually utilize separate modules for spatial and temporal correlations, or they only use independent components capturing localized or global heterogeneous dependencies. To overcome those limitations, our paper proposes a novel Spatial-Temporal Fusion Graph Neural Networks (STFGNN) for traffic flow forecasting. First, a data-driven method of generating “temporal graph” is proposed to compensate several genuine correlations that spatial graph may not reflect. STFGNN could effectively learn hidden spatial-temporal dependencies by a novel fusion operation of various spatial and temporal graphs, treated for different time periods in parallel. Meanwhile, by integrating this fusion graph module and a novel gated convolution module into a unified layer parallelly, STFGNN could handle long sequences by learning more spatial-temporal dependencies with layers stacked. Experimental results on several public traffic datasets demonstrate that our method achieves state-of-the-art performance consistently than other baselines.

LF-GDPR: A Framework for Estimating Graph Metrics with Local Differential Privacy

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. To address low data utility of LDP, it optimally allocates privacy budget between the two atomic metrics during data collection. To demonstrate the usage of LF-GDPR, we show use cases on two common graph analysis tasks, namely, clustering coefficient estimation and community detection. The privacy and utility achieved by LF-GDPR are verified through theoretical analysis and extensive experimental results.

Global Consistent Graph Convolutional Network for Hyperspectral Image Classification

Abstract: 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).

Modeling Inter-station Relationships with Attentive Temporal Graph Convolutional Network for Air Quality Prediction

Abstract: Air pollution is an important environmental issue of increasing concern, which impacts human health. Accurate air quality prediction is crucial for avoiding people suffering from serious air pollution. Most of the prior works focus on capturing the temporal trend of air quality for each monitoring station. Recent deep learning based methods also model spatial dependencies among neighboring stations. However, we observe that besides geospatially adjacent stations, the stations which share similar functionalities or consistent temporal patterns could also have strong dependencies. In this paper, we propose an Attentive Temporal Graph Convolutional Network (ATGCN) to model diverse inter-station relationships for air quality prediction of citywide stations. Specifically, we first encode three types of relationships among stations including spatial adjacency, functional similarity, and temporal pattern similarity into graphs. Then we design parallel encoding modules, which respectively incorporate attentive graph convolution operations into the Gated Recurrent Units (GRUs) to iteratively aggregate features from related stations with different graphs. Furthermore, augmented with an attention-based fusion unit, decoding modules with a similar structure to the encoding modules are designed to generate multi-step predictions for all stations. The experiments on two real-world datasets demonstrate the superior performance of our model beyond state-of-the-art methods.

A Graph Convolutional Stacked Bidirectional Unidirectional-LSTM Neural Network for Metro Ridership Prediction

Abstract: Timely precise metro ridership forecasting is helpful to reveal real-time traffic demand, which is a crucial but challenging task in modern traffic management. Given the complex spatial correlation and temporal variation of riding behaviour in a metro system, deep learning algorithms have been widely applied owing to their superior performance in capturing spatio-temporal features. However, current deep learning models utilize regular convolutional operations, which can barely provide satisfactory accuracy due to either the ignorance of realistic topology of a traffic network or insufficiency in capturing representative spatiotemporal patterns. To further improve the accuracy in metro ridership prediction, this study proposes a parallel-structured deep learning model that consists of a Graph Convolution Network and a stacked Bidirectional unidirectional Long short-term Memory network (GCN-SBULSTM). The GCN module regards a metro network as a structured graph, and a K-hop matrix, which integrates the travel distance, population flow, and adjacency, is introduced to capture the dynamic spatial correlation among metro stations. The SBULSTM module considers both backward and forward states of ridership time series and can learn complex temporal features with stacked recurrent layers. Experiments are conducted on three real-life metro ridership datasets to demonstrate the effectiveness of the proposed model. Compared with state-of-the-art prediction models, GCN-SBULSTM presents better performance in multiple scenarios and largely enhances the efficiencies of training processes.

ST-Trader: A Spatial-Temporal Deep Neural Network for Modeling Stock Market Movement

Abstract: Stocks that are fundamentally connected with each other tend to move together. Considering such common trends is believed to benefit stock movement forecasting tasks. However, such signals are not trivial to model because the connections among stocks are not physically presented and need to be estimated from volatile data. Motivated by this observation, we propose a framework that incorporates the inter-connection of firms to forecast stock prices. To effectively utilize a large set of fundamental features, we further design a novel pipeline. First, we use variational autoencoder (VAE) to reduce the dimension of stock fundamental information and then cluster stocks into a graph structure (fundamentally clustering). Second, a hybrid model of graph convolutional network and long-short term memory network (GCN-LSTM) with an adjacency graph matrix (learnt from VAE) is proposed for graph-structured stock market forecasting. Experiments on minute-level U.S. stock market data demonstrate that our model effectively captures both spatial and temporal signals and achieves superior improvement over baseline methods. The proposed model is promising for other applications in which there is a possible but hidden spatial dependency to improve time-series prediction.

UV-Net: Learning from Boundary Representations

Abstract: We introduce UV-Net, a novel neural network architecture and representation designed to operate directly on Boundary representation (B-rep) data from 3D CAD models. The B-rep format is widely used in the design, simulation and manufacturing industries to enable sophisticated and precise CAD modeling operations. However, B-rep data presents some unique challenges when used with modern machine learning due to the complexity of the data structure and its support for both continuous non-Euclidean geometric entities and discrete topological entities. In this paper, we propose a unified representation for B-rep data that exploits the U and V parameter domain of curves and surfaces to model geometry, and an adjacency graph to explicitly model topology. This leads to a unique and efficient network architecture, UV-Net, that couples image and graph convolutional neural networks in a compute and memory-efficient manner To aid in future research we present a synthetic labelled B-rep dataset, SolidLetters, derived from human designed fonts with variations in both geometry and topology. Finally we demonstrate that UV-Net can generalize to supervised and unsupervised tasks on five datasets, while outperforming alternate 3D shape representations such as point clouds, voxels, and meshes.

Quantum spectral clustering

Abstract: Spectral clustering is a powerful unsupervised machine learning algorithm for clustering data with nonconvex or nested structures [A. Y. Ng, M. I. Jordan, and Y. Weiss, On spectral clustering: Analysis and an algorithm, in Advances in Neural Information Processing Systems 14: Proceedings of the 2001 Conference (MIT Press, Cambridge, MA, 2002), pp. 849--856]. With roots in graph theory, it uses the spectral properties of the Laplacian matrix to project the data in a low-dimensional space where clustering is more efficient. Despite its success in clustering tasks, spectral clustering suffers in practice from a fast-growing running time of $O({n}^{3})$, where $n$ is the number of points in the data set. In this work we propose an end-to-end quantum algorithm performing spectral clustering, extending a number of works in quantum machine learning. The quantum algorithm is composed of two parts: the first is the efficient creation of the quantum state corresponding to the projected Laplacian matrix, and the second consists of applying the existing quantum analog of the $k$-means algorithm [I. Kerenidis, J. Landman, A. Luongo, and A. Prakash, $q$-means: A quantum algorithm for unsupervised machine learning, in Advances in Neural Information Processing Systems 32: Proceedings of the 2019 Conference (Curran Associates, Red Hook, NY, 2020), pp. 4136--4146]. Both steps depend polynomially on the number of clusters, as well as precision and data parameters arising from quantum procedures, and polylogarithmically on the dimension of the input vectors. Our numerical simulations show an asymptotic linear growth with $n$ when all terms are taken into account, significantly better than the classical cubic growth. This work opens the path to other graph-based quantum machine learning algorithms, as it provides routines for efficient computation and quantum access to the incidence, adjacency, and projected Laplacian matrices of a graph.

Inference for Multiple Heterogeneous Networks with a Common Invariant Subspace

Abstract: The development of models and methodology for the analysis of data from multiple heterogeneous networks is of importance both in statistical network theory and across a wide spectrum of application domains. Although single-graph analysis is well-studied, multiple graph inference is largely unexplored, in part because of the challenges inherent in appropriately modeling graph differences and yet retaining sufficient model simplicity to render estimation feasible. This paper addresses exactly this gap, by introducing a new model, the common subspace independent-edge multiple random graph model, which describes a heterogeneous collection of networks with a shared latent structure on the vertices but potentially different connectivity patterns for each graph. The model encompasses many popular network representations, including the stochastic blockmodel. The model is both flexible enough to meaningfully account for important graph differences, and tractable enough to allow for accurate inference in multiple networks. In particular, a joint spectral embedding of adjacency matrices-the multiple adjacency spectral embedding-leads to simultaneous consistent estimation of underlying parameters for each graph. Under mild additional assumptions, the estimates satisfy asymptotic normality and yield improvements for graph eigenvalue estimation. In both simulated and real data, the model and the embedding can be deployed for a number of subsequent network inference tasks, including dimensionality reduction, classification, hypothesis testing, and community detection. Specifically, when the embedding is applied to a data set of connectomes constructed through diffusion magnetic resonance imaging, the result is an accurate classification of brain scans by human subject and a meaningful determination of heterogeneity across scans of different individuals.

Ordered multiplicity inverse eigenvalue problem for graphs on six vertices

Abstract: For a graph $G$, we associate a family of real symmetric matrices, $\mathcal{S}(G)$, where for any $M \in \mathcal{S}(G)$, the location of the nonzero off-diagonal entries of $M$ is governed by the adjacency structure of $G$. The ordered multiplicity Inverse Eigenvalue Problem of a Graph (IEPG) is concerned with finding all attainable ordered lists of eigenvalue multiplicities for matrices in $\mathcal{S}(G)$. For connected graphs of order six, we offer significant progress on the IEPG, as well as a complete solution to the ordered multiplicity IEPG. We also show that while $K_{m,n}$ with $\min(m,n)\ge 3$ attains a particular ordered multiplicity list, it cannot do so with arbitrary spectrum.

Isotopy and energy of physical networks

Abstract: While the structural characteristics of a network are uniquely determined by its adjacency matrix1–3, in physical networks, such as the brain or the vascular system, the network’s three-dimensional layout also affects the system’s structure and function. We lack, however, the tools to distinguish physical networks with identical wiring but different geometrical layouts. To address this need, here we introduce the concept of network isotopy, representing different network layouts that can be transformed into one another without link crossings, and show that a single quantity, the graph linking number, captures the entangledness of a layout, defining distinct isotopy classes. We find that a network’s elastic energy depends linearly on the graph linking number, indicating that each local tangle offers an independent contribution to the total energy. This finding allows us to formulate a statistical model for the formation of tangles in physical networks. We apply the developed framework to a diverse set of real physical networks, finding that the mouse connectome is more entangled than expected based on optimal wiring. Recently, a framework was introduced to model three-dimensional physical networks, such as brain or vascular ones, in a way that does not allow link crossings. Here the authors combine concepts from knot theory and statistical mechanics to be able to distinguish between physical networks with identical wiring but different layouts.

Graph2Net: Perceptually-Enriched Graph Learning for Skeleton-Based Action Recognition

Abstract: Skeleton representation has attracted a great deal of attention recently as an extremely robust feature for human action recognition. However, its non-Euclidean structural characteristics raise new challenges for conventional solutions. Recent studies have shown that there is a native superiority in modeling spatiotemporal skeleton information with a Graph Convolutional Network (GCN). Nevertheless, the skeleton graph modeling normally focuses on the physical adjacency of the elements of the human skeleton sequence, which contrasts with the requirement to provide a perceptually meaningful representation. To address this problem, in this paper, we propose a perceptually-enriched graph learning method by introducing innovative features to spatial and temporal skeleton graph modeling. For the spatial information modeling, we incorporate a Local-Global Graph Convolutional Network (LG-GCN) that builds a multifaceted spatial perceptual representation. This helps to overcome the limitations caused by over-reliance on the spatial adjacency relationships in the skeleton. For temporal modeling, we present a Region-Aware Graph Convolutional Network (RA-GCN), which directly embeds the regional relationships conveyed by a skeleton sequence into a temporal graph model. This innovation mitigates the deficiency of the original skeleton graph models. In addition, we strengthened the ability of the proposed channel modeling methods to extract multi-scale representations. These innovations result in a lightweight graph convolutional model, referred to as Graph2Net, that simultaneously extends the spatial and temporal perceptual fields, and thus enhances the capacity of the graph model to represent skeleton sequences. We conduct extensive experiments on NTU-RGB+D 60&120, Northwestern-UCLA, and Kinetics-400 datasets to show that our results surpass the performance of several mainstream methods while limiting the model complexity and computational overhead.

AAGCN: Adjacency-aware Graph Convolutional Network for person re-identification

Abstract: Person re-identification (ReID) is an important topic of computer vision. Existing works in this field focus primarily on learning a feature extractor that maps the pedestrian images into a feature space, in which feature vectors corresponding to the same identity are close to each other. In this paper, we propose the adjacency-aware Graph Convolutional Network (AAGCN) to smooth the intra-class features and thus reduce the intra-class variance. Specifically, our AAGCN takes the features learned by a backbone as the input nodes; it first establishes the connections or adjacency relations for the intra-class features, then the adjacent nodes (i.e., the intra-class features) would be smoothed thanks to the property of low-pass filtering of Graph Convolutional Network (GCN). In this paper, we propose two methods, i.e., the Mahalanobis Neighborhood Adjacency (MNA) and Non-Linear Mapping (NLM), to learn the adjacency relations for the intra-class features. The MNA defines the adjacency weight between two nodes as the negative exponent of the Mahalanobis distance between their corresponding features, therefore it aims to learn a small Mahalanobis distance between the intra-class features and a large Mahalanobis distance between the inter-class ones. The NLM enables the non-linear mapping from the features of the nodes to their corresponding adjacency weights. The experimental results on both visible ReID and visual-infrared ReID verify the effectiveness of our method, for instance, our model achieves 95.7% rank-1 and 93.1% mAP on Market1501, as well as 58.6% rank-1 and 60.0% mAP on SYSU.

FeederGAN: Synthetic Feeder Generation via Deep Graph Adversarial Nets

Abstract: This article presents a novel, automated, generative adversarial networks (GAN) based synthetic feeder generation mechanism, abbreviated as FeederGAN. FeederGAN digests real feeder models represented by directed graphs via a deep learning framework powered by GAN and graph convolutional networks (GCN). Information of a distribution feeder circuit is extracted from its model input files so that the device connectivity is mapped onto the adjacency matrix and the device characteristics, such as circuit types (i.e., 3-phase, 2-phase, and 1-phase) and component attributes (e.g., length and current ratings), are mapped onto the attribute matrix. Then, Wasserstein distance is used to optimize the GAN and GCN is used to discriminate the generated graphs from the actual ones. A greedy method based on graph theory is developed to reconstruct the feeder using the generated adjacency and attribute matrices. Our results show that the GAN generated feeders resemble the actual feeder in both topology and attributes verified by visual inspection and by empirical statistics obtained from actual distribution feeders.

DC-STGCN: Dual-Channel Based Graph Convolutional Networks for Network Traffic Forecasting

Abstract: Network traffic forecasting is essential for efficient network management and planning. Accurate long-term forecasting models are also essential for proactive control of upcoming congestion events. Due to the complex spatial-temporal dependencies between traffic flows, traditional time series forecasting models are often unable to fully extract the spatial-temporal characteristics between the traffic flows. To address this issue, we propose a novel dual-channel based graph convolutional network (DC-STGCN) model. The proposed model consists of two temporal components that characterize the daily and weekly correlation of the network traffic. Each of these two components contains a spatial-temporal characteristics extraction module consisting of a dual-channel graph convolutional network (DCGCN) and a gated recurrent unit (GRU). The DCGCN further consists of an adjacency feature extraction module (AGCN) and a correlation feature extraction module (PGCN) to capture the connectivity between nodes and the proximity correlation, respectively. The GRU further extracts the temporal characteristics of the traffic. The experimental results based on real network data sets show that the prediction accuracy of the DC-STGCN model overperforms the existing baseline and is capable of making long-term predictions.

Iterative graph attention memory network for cross-modal retrieval

Abstract: How to eliminate the semantic gap between multi-modal data and effectively fuse multi-modal data is the key problem of cross-modal retrieval. The abstractness of semantics makes semantic representation one-sided. In order to obtain complementary semantic information for samples with the same semantics, we construct a local graph for each instance and utilize a graph feature extractor (GFE) to reconstruct the sample representation based on the adjacency relationship between the sample itself and its neighbors. Owing to the problem that some cross-modal methods only focus on the learning of paired samples and cannot integrate more cross-modal information from the other modalities, we propose a cross-modal graph attention strategy to generate the graph attention representation for each sample from the local graph of its corresponding paired sample. In order to eliminate heterogeneous gap between modalities, we fuse the features of the two modalities using a recurrent gated memory network to choose prominent features from other modalities and filter out unimportant information to obtain a more discriminative feature representation in the common latent space. Experiments on four benchmark datasets demonstrate the superiority of our proposed model compared with state-of-the-art cross-modal methods.

Spectra of adjacency and Laplacian matrices of inhomogeneous Erdős–Rényi random graphs

Abstract: This paper considers inhomogeneous Erdős–Renyi random graphs 𝔾N on N vertices in the non-sparse non-dense regime. The edge between the pair of vertices {i,j} is retained with probability 𝜀Nf( i N, ...

Learning from Pixel-Level Label Noise: A New Perspective for Semi-Supervised Semantic Segmentation.

Abstract: This paper addresses semi-supervised semantic segmentation by exploiting a small set of images with pixel-level annotations (strong supervisions) and a large set of images with only image-level annotations (weak supervisions). Most existing approaches aim to generate accurate pixel-level labels from weak supervisions. However, we observe that those generated labels still inevitably contain noisy labels. Motivated by this observation, we present a novel perspective and formulate this task as a problem of learning with pixel-level label noise. Existing noisy label methods, nevertheless, mainly aim at image-level tasks, which can not capture the relationship between neighboring labels in one image. Therefore, we propose a graph based label noise detection and correction framework to deal with pixel-level noisy labels. In particular, for the generated pixel-level noisy labels from weak supervisions by Class Activation Map (CAM), we train a clean segmentation model with strong supervisions to detect the clean labels from these noisy labels according to the cross-entropy loss. Then, we adopt a superpixel-based graph to represent the relations of spatial adjacency and semantic similarity between pixels in one image. Finally we correct the noisy labels using a Graph Attention Network (GAT) supervised by detected clean labels. We comprehensively conduct experiments on PASCAL VOC 2012, PASCAL-Context and MS-COCO datasets. The experimental results show that our proposed semi supervised method achieves the state-of-the-art performances and even outperforms the fully-supervised models on PASCAL VOC 2012 and MS-COCO datasets in some cases.

Succinct Encodings for Families of Interval Graphs

Abstract: We consider the problem of designing succinct data structures for interval graphs with n vertices while supporting degree, adjacency, neighborhood and shortest path queries in optimal time. Towards showing succinctness, we first show that at least $$n\log _2{n} - 2n\log _2\log _2 n - O(n)$$ bits are necessary to represent any unlabeled interval graph G with n vertices, answering an open problem of Yang and Pippenger (Proc Am Math Soc Ser B 4(1):1–3, 2017). This is augmented by a data structure of size $$n\log _2{n} +O(n)$$ bits while supporting not only the above queries optimally but also capable of executing various combinatorial algorithms (like proper coloring, maximum independent set etc.) on interval graphs efficiently. Finally, we extend our ideas to other variants of interval graphs, for example, proper/unit interval graphs, k-improper interval graphs, and circular-arc graphs, and design succinct data structures for these graph classes as well along with supporting queries on them efficiently.

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

Abstract: 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.

Digraph Signal Processing With Generalized Boundary Conditions

Abstract: Signal processing on directed graphs (digraphs) is problematic, since the graph shift, and thus associated filters, are in general not diagonalizable. Furthermore, the Fourier transform in this case is now obtained from the Jordan decomposition, which may not be computable at all for larger graphs. We propose a novel and general solution for this problem based on matrix perturbation theory: We design an algorithm that adds a small number of edges to a given digraph to destroy nontrivial Jordan blocks. The obtained digraph is then diagonalizable and yields, as we show, an approximate eigenbasis and Fourier transform for the original digraph. We explain why and how this construction can be viewed as generalized form of boundary conditions, a common practice in signal processing. Our experiments with random and real world graphs show that we can scale to graphs with a few thousands nodes, and obtain Fourier transforms that are close to orthogonal while still diagonalizing an intuitive notion of convolution. Our method works with adjacency and Laplacian shift and can be used as preprocessing step to enable further processing as we show with a prototypical Wiener filter application.

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...