scholarly journals ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations

2020 ◽  
Vol 34 (04) ◽  
pp. 5470-5477 ◽  
Author(s):  
Ekagra Ranjan ◽  
Soumya Sanyal ◽  
Partha Talukdar
Keyword(s):  
State Of The Art ◽  
Reproducible Research ◽  
Graph Classification ◽  
Cluster Assignment ◽  
Graph Representations ◽  
Average Improvement ◽  
Adaptive Structure ◽  
Soft Cluster ◽  
Graph Neural Networks ◽  
Multiple Graph

Graph Neural Networks (GNN) have been shown to work effectively for modeling graph structured data to solve tasks such as node classification, link prediction and graph classification. There has been some recent progress in defining the notion of pooling in graphs whereby the model tries to generate a graph level representation by downsampling and summarizing the information present in the nodes. Existing pooling methods either fail to effectively capture the graph substructure or do not easily scale to large graphs. In this work, we propose ASAP (Adaptive Structure Aware Pooling), a sparse and differentiable pooling method that addresses the limitations of previous graph pooling architectures. ASAP utilizes a novel self-attention network along with a modified GNN formulation to capture the importance of each node in a given graph. It also learns a sparse soft cluster assignment for nodes at each layer to effectively pool the subgraphs to form the pooled graph. Through extensive experiments on multiple datasets and theoretical analysis, we motivate our choice of the components used in ASAP. Our experimental results show that combining existing GNN architectures with ASAP leads to state-of-the-art results on multiple graph classification benchmarks. ASAP has an average improvement of 4%, compared to current sparse hierarchical state-of-the-art method. We make the source code of ASAP available to encourage reproducible research 1.

scholarly journals GSSNN: Graph Smoothing Splines Neural Networks

2020 ◽  
Vol 34 (04) ◽  
pp. 7007-7014
Author(s):  
Shichao Zhu ◽  
Lewei Zhou ◽  
Shirui Pan ◽  
Chuan Zhou ◽  
Guiying Yan ◽  
...  
Keyword(s):  
Neural Networks ◽  
State Of The Art ◽  
Representation Learning ◽  
Smoothing Splines ◽  
Graph Representation ◽  
Graph Classification ◽  
Topological Information ◽  
Graph Representations ◽  
The Arts ◽  
Graph Neural Networks

Graph Neural Networks (GNNs) have achieved state-of-the-art performance in many graph data analysis tasks. However, they still suffer from two limitations for graph representation learning. First, they exploit non-smoothing node features which may result in suboptimal embedding and degenerated performance for graph classification. Second, they only exploit neighbor information but ignore global topological knowledge. Aiming to overcome these limitations simultaneously, in this paper, we propose a novel, flexible, and end-to-end framework, Graph Smoothing Splines Neural Networks (GSSNN), for graph classification. By exploiting the smoothing splines, which are widely used to learn smoothing fitting function in regression, we develop an effective feature smoothing and enhancement module Scaled Smoothing Splines (S3) to learn graph embedding. To integrate global topological information, we design a novel scoring module, which exploits closeness, degree, as well as self-attention values, to select important node features as knots for smoothing splines. These knots can be potentially used for interpreting classification results. In extensive experiments on biological and social datasets, we demonstrate that our model achieves state-of-the-arts and GSSNN is superior in learning more robust graph representations. Furthermore, we show that S3 module is easily plugged into existing GNNs to improve their performance.

scholarly journals Coloring Graph Neural Networks for Node Disambiguation

2020 ◽  
Author(s):  
George Dasoulas ◽  
Ludovic Dos Santos ◽  
Kevin Scaman ◽  
Aladin Virmaux
Keyword(s):  
Neural Networks ◽  
Message Passing ◽  
State Of The Art ◽  
Structural Characteristics ◽  
Expressive Power ◽  
Continuous Functions ◽  
Graph Classification ◽  
Node Attributes ◽  
Graph Neural Networks ◽  
Coloring Graph

In this paper, we show that a simple coloring scheme can improve, both theoretically and empirically, the expressive power of Message Passing Neural Networks (MPNNs). More specifically, we introduce a graph neural network called Colored Local Iterative Procedure (CLIP) that uses colors to disambiguate identical node attributes, and show that this representation is a universal approximator of continuous functions on graphs with node attributes. Our method relies on separability, a key topological characteristic that allows to extend well-chosen neural networks into universal representations. Finally, we show experimentally that CLIP is capable of capturing structural characteristics that traditional MPNNs fail to distinguish, while being state-of-the-art on benchmark graph classification datasets.

scholarly journals Deep Graph Mapper: Seeing Graphs Through the Neural Lens

2021 ◽  
Vol 4 ◽  
Author(s):  
Cristian Bodnar ◽  
Cătălina Cangea ◽  
Pietro Liò
Keyword(s):  
Neural Networks ◽  
Complex Networks ◽  
State Of The Art ◽  
Expressive Power ◽  
Max Pooling ◽  
Empirical Success ◽  
Topological Framework ◽  
Graph Summarization ◽  
Soft Cluster ◽  
Graph Neural Networks

Graph summarization has received much attention lately, with various works tackling the challenge of defining pooling operators on data regions with arbitrary structures. These contrast the grid-like ones encountered in image inputs, where techniques such as max-pooling have been enough to show empirical success. In this work, we merge the Mapper algorithm with the expressive power of graph neural networks to produce topologically grounded graph summaries. We demonstrate the suitability of Mapper as a topological framework for graph pooling by proving that Mapper is a generalization of pooling methods based on soft cluster assignments. Building upon this, we show how easy it is to design novel pooling algorithms that obtain competitive results with other state-of-the-art methods. Additionally, we use our method to produce GNN-aided visualisations of attributed complex networks.

scholarly journals Graph convolutional and attention models for entity classification in multilayer networks

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Lorenzo Zangari ◽  
Roberto Interdonato ◽  
Antonio Calió ◽  
Andrea Tagarelli
Keyword(s):  
State Of The Art ◽  
Structural Characteristics ◽  
Representation Learning ◽  
Efficient Solutions ◽  
Single Type ◽  
Graph Classification ◽  
Multilayer Networks ◽  
Attention Networks ◽  
Convolutional Networks ◽  
Graph Neural Networks

AbstractGraph Neural Networks (GNNs) are powerful tools that are nowadays reaching state of the art performances in a plethora of different tasks such as node classification, link prediction and graph classification. A challenging aspect in this context is to redefine basic deep learning operations, such as convolution, on graph-like structures, where nodes generally have unordered neighborhoods of varying size. State-of-the-art GNN approaches such as Graph Convolutional Networks (GCNs) and Graph Attention Networks (GATs) work on monoplex networks only, i.e., on networks modeling a single type of relation among an homogeneous set of nodes. The aim of this work is to generalize such approaches by proposing a GNN framework for representation learning and semi-supervised classification in multilayer networks with attributed entities, and arbitrary number of layers and intra-layer and inter-layer connections between nodes. We instantiate our framework with two new formulations of GAT and GCN models, namely and , specifically devised for general, attributed multilayer networks. The proposed approaches are evaluated on an entity classification task on nine widely used real-world network datasets coming from different domains and with different structural characteristics. Results show that both our proposed and methods provide effective and efficient solutions to the problem of entity classification in multilayer attributed networks, being faster to learn and offering better accuracy than the competitors. Furthermore, results show how our methods are able to take advantage of the presence of real attributes for the entities, in addition to arbitrary inter-layer connections between the nodes in the various layers.

scholarly journals Path integral based convolution and pooling for graph neural networks*

2021 ◽  
Vol 2021 (12) ◽  
pp. 124011
Author(s):  
Zheng Ma ◽  
Junyu Xuan ◽  
Yu Guang Wang ◽  
Ming Li ◽  
Pietro Liò
Keyword(s):  
Neural Networks ◽  
Path Integral ◽  
State Of The Art ◽  
Graph Laplacian ◽  
Maximal Entropy ◽  
Optimized Design ◽  
Graph Classification ◽  
Physical Sciences ◽  
Special Cases ◽  
Graph Neural Networks

Abstract Graph neural networks (GNNs) extend the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we propose path integral-based GNNs (PAN) for classification and regression tasks on graphs. Specifically, we consider a convolution operation that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. It generalizes the graph Laplacian to a new transition matrix that we call the maximal entropy transition (MET) matrix derived from a path integral formalism. Importantly, the diagonal entries of the MET matrix are directly related to the subgraph centrality, thus leading to a natural and adaptive pooling mechanism. PAN provides a versatile framework that can be tailored for different graph data with varying sizes and structures. We can view most existing GNN architectures as special cases of PAN. Experimental results show that PAN achieves state-of-the-art performance on various graph classification/regression tasks, including a new benchmark dataset from statistical mechanics that we propose to boost applications of GNN in physical sciences.

scholarly journals Hierarchical Pooling in Graph Neural Networks to Enhance Classification Performance in Large Datasets

Sensors ◽  
2021 ◽  
Vol 21 (18) ◽  
pp. 6070
Author(s):  
Hai Van Pham ◽  
Dat Hoang Thanh ◽  
Philip Moore
Keyword(s):  
Neural Networks ◽  
Classification Performance ◽  
Graph Representation ◽  
Alternative Methods ◽  
Effective Control ◽  
Cluster Assignment ◽  
Training Time ◽  
Interesting Approach ◽  
Soft Cluster ◽  
Graph Neural Networks

Deep learning methods predicated on convolutional neural networks and graph neural networks have enabled significant improvement in node classification and prediction when applied to graph representation with learning node embedding to effectively represent the hierarchical properties of graphs. An interesting approach (DiffPool) utilises a differentiable graph pooling technique which learns ‘differentiable soft cluster assignment’ for nodes at each layer of a deep graph neural network with nodes mapped on sets of clusters. However, effective control of the learning process is difficult given the inherent complexity in an ‘end-to-end’ model with the potential for a large number parameters (including the potential for redundant parameters). In this paper, we propose an approach termed FPool, which is a development of the basic method adopted in DiffPool (where pooling is applied directly to node representations). Techniques designed to enhance data classification have been created and evaluated using a number of popular and publicly available sensor datasets. Experimental results for FPool demonstrate improved classification and prediction performance when compared to alternative methods considered. Moreover, FPool shows a significant reduction in the training time over the basic DiffPool framework.

scholarly journals Graph Representations for Higher-Order Logic and Theorem Proving

2020 ◽  
Vol 34 (03) ◽  
pp. 2967-2974
Author(s):  
Aditya Paliwal ◽  
Sarah Loos ◽  
Markus Rabe ◽  
Kshitij Bansal ◽  
Christian Szegedy
Keyword(s):  
Theorem Proving ◽  
State Of The Art ◽  
Higher Order ◽  
Order Logic ◽  
Established Method ◽  
Higher Order Logic ◽  
Graph Representations ◽  
Significant Challenge ◽  
Proof Search ◽  
Graph Neural Networks

This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain. Interactive, higher-order theorem provers allow for the formalization of most mathematical theories and have been shown to pose a significant challenge for deep learning. Higher-order logic is highly expressive and, even though it is well-structured with a clearly defined grammar and semantics, there still remains no well-established method to convert formulas into graph-based representations. In this paper, we consider several graphical representations of higher-order logic and evaluate them against the HOList benchmark for higher-order theorem proving.

scholarly journals K-plex cover pooling for graph neural networks

2021 ◽  
Author(s):  
Davide Bacciu ◽  
Alessio Conte ◽  
Roberto Grossi ◽  
Francesco Landolfi ◽  
Andrea Marino
Keyword(s):  
Neural Networks ◽  
Graph Theory ◽  
State Of The Art ◽  
Graph Classification ◽  
Topological Information ◽  
Community Discovery ◽  
Connectivity Patterns ◽  
Graph Neural Networks ◽  
Pruning Heuristics ◽  
Non Parametric

AbstractGraph pooling methods provide mechanisms for structure reduction that are intended to ease the diffusion of context between nodes further in the graph, and that typically leverage community discovery mechanisms or node and edge pruning heuristics. In this paper, we introduce a novel pooling technique which borrows from classical results in graph theory that is non-parametric and generalizes well to graphs of different nature and connectivity patterns. Our pooling method, named KPlexPool, builds on the concepts of graph covers and k-plexes, i.e. pseudo-cliques where each node can miss up to k links. The experimental evaluation on benchmarks on molecular and social graph classification shows that KPlexPool achieves state of the art performances against both parametric and non-parametric pooling methods in the literature, despite generating pooled graphs based solely on topological information.

scholarly journals RLC-GNN: An Improved Deep Architecture for Spatial-Based Graph Neural Network with Application to Fraud Detection

2021 ◽  
Vol 11 (12) ◽  
pp. 5656
Author(s):  
Yufan Zeng ◽  
Jiashan Tang
Keyword(s):  
Numerical Experiments ◽  
State Of The Art ◽  
Single Layer ◽  
Fraud Detection ◽  
Layer By Layer ◽  
Residual Structure ◽  
Detection Algorithms ◽  
Deep Architecture ◽  
Graph Neural Networks ◽  
Node Embeddings

Graph neural networks (GNNs) have been very successful at solving fraud detection tasks. The GNN-based detection algorithms learn node embeddings by aggregating neighboring information. Recently, CAmouflage-REsistant GNN (CARE-GNN) is proposed, and this algorithm achieves state-of-the-art results on fraud detection tasks by dealing with relation camouflages and feature camouflages. However, stacking multiple layers in a traditional way defined by hop leads to a rapid performance drop. As the single-layer CARE-GNN cannot extract more information to fix the potential mistakes, the performance heavily relies on the only one layer. In order to avoid the case of single-layer learning, in this paper, we consider a multi-layer architecture which can form a complementary relationship with residual structure. We propose an improved algorithm named Residual Layered CARE-GNN (RLC-GNN). The new algorithm learns layer by layer progressively and corrects mistakes continuously. We choose three metrics—recall, AUC, and F1-score—to evaluate proposed algorithm. Numerical experiments are conducted. We obtain up to 5.66%, 7.72%, and 9.09% improvements in recall, AUC, and F1-score, respectively, on Yelp dataset. Moreover, we also obtain up to 3.66%, 4.27%, and 3.25% improvements in the same three metrics on the Amazon dataset.

scholarly journals SketchGNN: Semantic Sketch Segmentation with Graph Neural Networks

2021 ◽  
Vol 40 (3) ◽  
pp. 1-13
Author(s):  
Lumin Yang ◽  
Jiajie Zhuang ◽  
Hongbo Fu ◽  
Xiangzhi Wei ◽  
Kun Zhou ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Architecture ◽  
Large Scale ◽  
State Of The Art ◽  
Semantic Segmentation ◽  
Structure Information ◽  
Graph Neural Networks ◽  
Node Labels ◽  
Point Level

We introduce SketchGNN , a convolutional graph neural network for semantic segmentation and labeling of freehand vector sketches. We treat an input stroke-based sketch as a graph with nodes representing the sampled points along input strokes and edges encoding the stroke structure information. To predict the per-node labels, our SketchGNN uses graph convolution and a static-dynamic branching network architecture to extract the features at three levels, i.e., point-level, stroke-level, and sketch-level. SketchGNN significantly improves the accuracy of the state-of-the-art methods for semantic sketch segmentation (by 11.2% in the pixel-based metric and 18.2% in the component-based metric over a large-scale challenging SPG dataset) and has magnitudes fewer parameters than both image-based and sequence-based methods.

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