Showing papers on "Adjacency list published in 2019"

Spectral–Spatial Graph Convolutional Networks for Semisupervised Hyperspectral Image Classification

Abstract: Collecting labeled samples is quite costly and time-consuming for hyperspectral image (HSI) classification task. Semisupervised learning framework, which combines the intrinsic information of labeled and unlabeled samples, can alleviate the deficient labeled samples and increase the accuracy of HSI classification. In this letter, we propose a novel semisupervised learning framework that is based on spectral–spatial graph convolutional networks ( $\text{S}^{2}$ GCNs). It explicitly utilizes the adjacency nodes in graph to approximate the convolution. In the process of approximate convolution on graph, the proposed method makes full use of the spatial information of the current pixel. The experimental results on three real-life HSI data sets, i.e., Botswana Hyperion, Kennedy Space Center, and Indian Pines, show that the proposed $\text{S}^{2}$ GCN can significantly improve the classification accuracy. For instance, the overall accuracy on Indian data is increased from 66.8% (GCN) to 91.6%.

Low-rank Kernel Learning for Graph-based Clustering

Abstract: Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen kernel matrix. To address this issue, previous multiple kernel learning algorithm has been applied to learn an optimal kernel from a group of predefined kernels. This approach might be sensitive to noise and limits the representation ability of the consensus kernel. In contrast to existing methods, we propose to learn a low-rank kernel matrix which exploits the similarity nature of the kernel matrix and seeks an optimal kernel from the neighborhood of candidate kernels. By formulating graph construction and kernel learning in a unified framework, the graph and consensus kernel can be iteratively enhanced by each other. Extensive experimental results validate the efficacy of the proposed method.

Cluster adjacency and the four-loop NMHV heptagon

Abstract: We exploit the recently described property of cluster adjacency for scattering amplitudes in planar $$ \mathcal{N}=4 $$ super Yang-Mills theory to construct the symbol of the four-loop NMHV heptagon amplitude. We use a manifestly cluster adjacent ansatz and describe how the parameters of this ansatz are determined using simple physical consistency requirements. We then specialise our answer for the amplitude to the multi-Regge limit, finding agreement with previously available results up to the next-to-leading logarithm, and obtaining new predictions up to (next-to)3-leading-logarithmic accuracy.

PartNet: A Recursive Part Decomposition Network for Fine-Grained and Hierarchical Shape Segmentation

Abstract: Deep learning approaches to 3D shape segmentation are typically formulated as a multi-class labeling problem. These models are trained for a fixed set of labels, which greatly limits their flexibility and adaptivity. We opt for top-down recursive decomposition and develop the first deep learning model for hierarchical segmentation of 3D shapes, based on recursive neural networks. Starting from a full shape represented as a point cloud, our model performs recursive binary decomposition, where the decomposition network at all nodes in the hierarchy share weights. At each node, a node classifier is trained to determine the type (adjacency or symmetry) and stopping criteria of its decomposition. The features extracted in higher level nodes are recursively propagated to lower level ones. Thus, the meaningful decompositions in higher levels provide strong contextual cues constraining the segmentations in lower levels. Meanwhile, to increase the segmentation accuracy at each node, we enhance the recursive contextual feature with the shape feature extracted for the corresponding part. Our method segments a 3D shape in point cloud into an arbitrary number of parts, depending on the shape complexity, showing strong generality and flexibility. It achieves the state-of-the-art performance, both for fine-grained and semantic segmentation, on the public benchmark and a new benchmark of fine-grained segmentation proposed in this work. We also demonstrate its application for fine-grained part refinements in image-to-shape reconstruction.

On a two-truths phenomenon in spectral graph clustering.

Abstract: Clustering is concerned with coherently grouping observations without any explicit concept of true groupings. Spectral graph clustering-clustering the vertices of a graph based on their spectral embedding-is commonly approached via K-means (or, more generally, Gaussian mixture model) clustering composed with either Laplacian spectral embedding (LSE) or adjacency spectral embedding (ASE). Recent theoretical results provide deeper understanding of the problem and solutions and lead us to a "two-truths" LSE vs. ASE spectral graph clustering phenomenon convincingly illustrated here via a diffusion MRI connectome dataset: The different embedding methods yield different clustering results, with LSE capturing left hemisphere/right hemisphere affinity structure and ASE capturing gray matter/white matter core-periphery structure.

Inference for multiple heterogeneous networks with a common invariant subspace

Abstract: The development of models for multiple heterogeneous network data is of critical importance both in statistical network theory and across multiple application domains. Although single-graph inference 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 (COSIE) 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 COSIE 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 (MASE) - leads, in a COSIE model, to simultaneous consistent estimation of underlying parameters for each graph. Under mild additional assumptions, MASE estimates satisfy asymptotic normality and yield improvements for graph eigenvalue estimation and hypothesis testing. In both simulated and real data, the COSIE model and the MASE embedding can be deployed for a number of subsequent network inference tasks, including dimensionality reduction, classification, hypothesis testing and community detection. Specifically, when MASE is applied to a dataset of connectomes constructed through diffusion magnetic resonance imaging, the result is an accurate classification of brain scans by patient and a meaningful determination of heterogeneity across scans of different subjects.

A Joint 3D UNet-Graph Neural Network-Based Method for Airway Segmentation from Chest CTs

Abstract: We present an end-to-end deep learning segmentation method by combining a 3D UNet architecture with a graph neural network (GNN) model. In this approach, the convolutional layers at the deepest level of the UNet are replaced by a GNN-based module with a series of graph convolutions. The dense feature maps at this level are transformed into a graph input to the GNN module. The incorporation of graph convolutions in the UNet provides nodes in the graph with information that is based on node connectivity, in addition to the local features learnt through the downsampled paths. This information can help improve segmentation decisions. By stacking several graph convolution layers, the nodes can access higher order neighbourhood information without substantial increase in computational expense. We propose two types of node connectivity in the graph adjacency: (i) one predefined and based on a regular node neighbourhood, and (ii) one dynamically computed during training and using the nearest neighbour nodes in the feature space. We have applied this method to the task of segmenting the airway tree from chest CT scans. Experiments have been performed on 32 CTs from the Danish Lung Cancer Screening Trial dataset. We evaluate the performance of the UNet-GNN models with two types of graph adjacency and compare it with the baseline UNet.

Weisfeiler and Leman go sparse: Towards scalable higher-order graph embeddings

Abstract: Graph kernels based on the $1$-dimensional Weisfeiler-Leman algorithm and corresponding neural architectures recently emerged as powerful tools for (supervised) learning with graphs. However, due to the purely local nature of the algorithms, they might miss essential patterns in the given data and can only handle binary relations. The $k$-dimensional Weisfeiler-Leman algorithm addresses this by considering $k$-tuples, defined over the set of vertices, and defines a suitable notion of adjacency between these vertex tuples. Hence, it accounts for the higher-order interactions between vertices. However, it does not scale and may suffer from overfitting when used in a machine learning setting. Hence, it remains an important open problem to design WL-based graph learning methods that are simultaneously expressive, scalable, and non-overfitting. Here, we propose local variants and corresponding neural architectures, which consider a subset of the original neighborhood, making them more scalable, and less prone to overfitting. The expressive power of (one of) our algorithms is strictly higher than the original algorithm, in terms of ability to distinguish non-isomorphic graphs. Our experimental study confirms that the local algorithms, both kernel and neural architectures, lead to vastly reduced computation times, and prevent overfitting. The kernel version establishes a new state-of-the-art for graph classification on a wide range of benchmark datasets, while the neural version shows promising performance on large-scale molecular regression tasks.

Cluster adjacency beyond MHV

Abstract: We explore further the notion of cluster adjacency, focussing on non-MHV amplitudes. We extend the notion of adjacency to the BCFW decomposition of tree-level amplitudes. Adjacency controls the appearance of poles, both physical and spurious, in individual BCFW terms. We then discuss how this notion of adjacency is connected to the adjacency already observed at the level of symbols of scattering amplitudes which controls the appearance of branch cut singularities. Poles and symbols become intertwined by cluster adjacency and we discuss the relation of this property to the $$ \overline{Q} $$ -equation which imposes constraints on the derivatives of the transcendental functions appearing in loop amplitudes.

Open problems in the spectral theory of signed graphs

Abstract: Signed graphs are graphs whose edges get a sign +1 or −1 (the signature). Signed graphs can be studied by means of graph matrices extended to signed graphs in a natural way. Recently, the spectra of signed graphs have attracted much attention from graph spectra specialists. One motivation is that the spectral theory of signed graphs elegantly generalizes the spectral theories of unsigned graphs. On the other hand, unsigned graphs do not disappear completely, since their role can be taken by the special case of balanced signed graphs. Therefore, spectral problems defined and studied for unsigned graphs can be considered in terms of signed graphs, and sometimes such generalization shows nice properties which cannot be appreciated in terms of (unsigned) graphs. Here, we survey some general results on the adjacency spectra of signed graphs, and we consider some spectral problems which are inspired from the spectral theory of (unsigned) graphs.

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.

The Sklyanin Bracket and Cluster Adjacency at All Multiplicity

Abstract: We argue that the Sklyanin Poisson bracket on Gr(4, n) can be used to efficiently test whether an amplitude in planar $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory satisfies cluster adjacency. We use this test to show that cluster adjacency is satisfied by all one- and two-loop MHV amplitudes in this theory, once suitably regulated. Using this technique we also demonstrate that cluster adjacency implies the extended Steinmann relations at all particle multiplicities.

TSSOS: A Moment-SOS hierarchy that exploits term sparsity

Abstract: 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 systems literature.

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, i.e. iLIDS-VID, PRID2011, MARS, and DukeMTMC-VideoReID, experimental results achieve the competitive performance which demonstrates the effectiveness of our proposed method. The code is available at this https URL.

Analysis of spectral clustering algorithms for community detection: the general bipartite setting

Abstract: We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or Laplacian matrix (2) a form of spectral truncation and (3) a k-means type algorithm in the reduced spectral domain. We focus on the adjacency-based spectral clustering and for the first step, propose a new data-driven regularization that can restore the concentration of the adjacency matrix even for the sparse networks. This result is based on recent work on regularization of random binary matrices, but avoids using unknown population level parameters, and instead estimates the necessary quantities from the data. We also propose and study a novel variation of the spectral truncation step and show how this variation changes the nature of the misclassification rate in a general SBM. We then show how the consistency results can be extended to models beyond SBMs, such as inhomogeneous random graph models with approximate clusters, including a graphon clustering problem, as well as general sub-Gaussian biclustering. A theme of the paper is providing a better understanding of the analysis of spectral methods for community detection and establishing consistency results, under fairly general clustering models and for a wide regime of degree growths, including sparse cases where the average expected degree grows arbitrarily slowly.

On Distance-Based Topological Descriptors of Subdivision Vertex-Edge Join of Three Graphs

Abstract: The analysis of networks and graphs through topological descriptors carries out a useful role to derive their underlying topologies. This process has been widely used in biomedicine, cheminformatics, and bioinformatics, where assessments based on graph invariants have been made available for effectively communicating with the various challenging schemes. In the studies of quantitative structure-activity relationships (QSARs) and quantitative structure-property relationships (QSPRs), graph invariants are used to approximate the biological activities and properties of chemical compounds. In this paper, we give the results related to the eccentric-connectivity index, connective eccentricity index, total-eccentricity index, average eccentricity index, Zagreb eccentricity indices, eccentric geometric-arithmetic index, eccentric atom-bond connectivity index, eccentric adjacency index, modified eccentric-connectivity index, eccentric distance sum, Wiener index, Harary index, hyper-Wiener index and degree distance index of a new graph operation named as “subdivision vertex-edge join” of three graphs.

Small Object Sensitive Segmentation of Urban Street Scene With Spatial Adjacency Between Object Classes

Abstract: Recent advancements in deep learning have shown an exciting promise in the urban street scene segmentation. However, many objects, such as poles and sign symbols, are relatively small, and they usually cannot be accurately segmented, since the larger objects usually contribute more to the segmentation loss. In this paper, we propose a new boundary-based metric that measures the level of spatial adjacency between each pair of object classes and find that this metric is robust against object size-induced biases. We develop a new method to enforce this metric into the segmentation loss. We propose a network, which starts with a segmentation network, followed by a new encoder to compute the proposed boundary-based metric, and then trains this network in an end-to-end fashion. In deployment, we only use the trained segmentation network, without the encoder, to segment new unseen images. Experimentally, we evaluate the proposed method using CamVid and CityScapes data sets and achieve a favorable overall performance improvement and a substantial improvement in segmenting small objects.

Fast and Accurate Graph Stream Summarization

Abstract: A graph stream is a continuous sequence of data items, in which each item indicates an edge, including its two endpoints and edge weight. It forms a dynamic graph that changes with every item. Graph streams play important roles in cyber security, social networks, cloud troubleshooting systems and more. Due to the vast volume and high update speed of graph streams, traditional data structures for graph storage such as the adjacency matrix and the adjacency list are no longer sufficient. However, prior art of graph stream summarization, like CM sketches, gSketches, TCM and gMatrix, either supports limited kinds of queries or suffers from poor accuracy of query results. In this paper, we propose a novel Graph Stream Sketch (GSS for short) to summarize the graph streams, which has linear space cost O(|E|) (E is the edge set of the graph) and constant update time cost (O(1)) and supports most kinds of queries over graph streams with the controllable errors. Both theoretical analysis and experiment results confirm the superiority of our solution with regard to the time/space complexity and query results’ precision compared with the state-of-the-art.

Graph product structure for non-minor-closed classes

Abstract: Dujmovic et al. (FOCS 2019) recently proved that every planar graph is a subgraph of the strong product of a graph of bounded treewidth and a path. Analogous results were obtained for graphs of bounded Euler genus or apex-minor-free graphs. These tools have been used to solve longstanding problems on queue layouts, non-repetitive colouring, $p$-centered colouring, and adjacency labelling. This paper proves analogous product structure theorems for various non-minor-closed classes. One noteable example is $k$-planar graphs (those with a drawing in the plane in which each edge is involved in at most $k$ crossings). We prove that every $k$-planar graph is a subgraph of the strong product of a graph of treewidth $O(k^5)$ and a path. This is the first result of this type for a non-minor-closed class of graphs. It implies, amongst other results, that $k$-planar graphs have non-repetitive chromatic number upper-bounded by a function of $k$. All these results generalise for drawings of graphs on arbitrary surfaces. In fact, we work in a much more general setting based on so-called shortcut systems that are of independent interest. This leads to analogous results for map graphs, string graphs, graph powers, and nearest neighbour graphs.

PartNet: A Recursive Part Decomposition Network for Fine-grained and Hierarchical Shape Segmentation

Abstract: Deep learning approaches to 3D shape segmentation are typically formulated as a multi-class labeling problem. Existing models are trained for a fixed set of labels, which greatly limits their flexibility and adaptivity. We opt for top-down recursive decomposition and develop the first deep learning model for hierarchical segmentation of 3D shapes, based on recursive neural networks. Starting from a full shape represented as a point cloud, our model performs recursive binary decomposition, where the decomposition network at all nodes in the hierarchy share weights. At each node, a node classifier is trained to determine the type (adjacency or symmetry) and stopping criteria of its decomposition. The features extracted in higher level nodes are recursively propagated to lower level ones. Thus, the meaningful decompositions in higher levels provide strong contextual cues constraining the segmentations in lower levels. Meanwhile, to increase the segmentation accuracy at each node, we enhance the recursive contextual feature with the shape feature extracted for the corresponding part. Our method segments a 3D shape in point cloud into an unfixed number of parts, depending on the shape complexity, showing strong generality and flexibility. It achieves the state-of-the-art performance, both for fine-grained and semantic segmentation, on the public benchmark and a new benchmark of fine-grained segmentation proposed in this work. We also demonstrate its application for fine-grained part refinements in image-to-shape reconstruction.

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.

Prediction of atomization energy using graph kernel and active learning.

Abstract: Data-driven prediction of molecular properties presents unique challenges to the design of machine learning methods concerning data structure/dimensionality, symmetry adaption, and confidence management. In this paper, we present a kernel-based pipeline that can learn and predict the atomization energy of molecules with high accuracy. The framework employs Gaussian process regression to perform predictions based on the similarity between molecules, which is computed using the marginalized graph kernel. To apply the marginalized graph kernel, a spatial adjacency rule is first employed to convert molecules into graphs whose vertices and edges are labeled by elements and interatomic distances, respectively. We then derive formulas for the efficient evaluation of the kernel. Specific functional components for the marginalized graph kernel are proposed, while the effects of the associated hyperparameters on accuracy and predictive confidence are examined. We show that the graph kernel is particularly suitable for predicting extensive properties because its convolutional structure coincides with that of the covariance formula between sums of random variables. Using an active learning procedure, we demonstrate that the proposed method can achieve a mean absolute error of 0.62 ± 0.01 kcal/mol using as few as 2000 training samples on the QM7 dataset.

The Complexity of Counting Cycles in the Adjacency List Streaming Model

Abstract: We study the problem of counting cycles in the adjacency list streaming model, fully resolving in which settings there exist sublinear space algorithms. Our main upper bound is a two-pass algorithm for estimating triangles that uses $\wtO (m/T^2/3 )$ space, where m is the edge count and T is the triangle count of the graph. On the other hand, we show that no sublinear space multipass algorithm exists for counting $\ell$-cycles for $\ell \geq 5$. Finally, we show that counting 4-cycles is intermediate: sublinear space algorithms exist in multipass but not single-pass settings.