Graph machine learning, particularly using graph neural networks, heavily relies on node features. However, many real-world systems, such as social and biological networks, lack node features due to privacy concerns, incomplete data, or collection limitations. Structural and positional encoding are commonly used to address this but are constrained by the maximum values of the encoded properties, such as the highest node degree. This limitation makes them impractical for scale-free networks and applications involving large or non-categorical properties. This paper introduces PropEnc, a novel and versatile encoder to generate expressive node embedding from any graph metric. By combining histogram construction with reversed index encoding, PropEnc offers a flexible solution that supports low-dimensional representations and diverse input types, effectively mitigating sparsity issues while improving computational efficiency. Additionally, it replicates one-hot encoding or approximates indices with high accuracy, making it adaptable to a wide range of graph applications. We validate PropEnc through extensive experiments on graph classification task across several social networks lacking node features. The empirical results demonstrate that PropEnc offers an efficient mechanism for constructing node features from various graph metrics.
Graph pooling compresses graphs and summarises their topological properties and features in a vectorial representation. It is an essential part of deep graph representation learning and is indispensable in graph-level tasks like classification or regression. Current approaches pool hierarchical structures in graphs by iteratively applying shallow pooling operators up to a fixed depth. However, they disregard the interdependencies between structures at different hierarchical levels and do not adapt to datasets that contain graphs with different sizes that may require pooling with various depths. To address these issues, we propose MDL-Pool, a pooling operator based on the minimum description length (MDL) principle, whose loss formulation explicitly models the interdependencies between different hierarchical levels and facilitates a direct comparison between multiple pooling alternatives with different depths. MDP-Pool builds on the map equation, an information-theoretic objective function for community detection, which naturally implements Occam's razor and balances between model complexity and goodness-of-fit via the MDL. We demonstrate MDL-Pool's competitive performance in an empirical evaluation against various baselines across standard graph classification datasets.
Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order information, i.e., information that goes \emph{beyond} pairwise interactions. Recent work has shown that persistent homology, a tool from topological data analysis, can enrich graph neural networks with topological information that they otherwise could not capture. Calculating such features is efficient for dimension 0 (connected components) and dimension 1 (cycles). However, when it comes to higher-order structures, it does not scale well, with a complexity of $O(n^d)$, where $n$ is the number of nodes and $d$ is the order of the structures. In this work, we introduce a novel method that extracts information about higher-order structures in the graph while still using the efficient low-dimensional persistent homology algorithm. On standard benchmark datasets, we show that our method can lead to up to $31\%$ improvements in test accuracy.
Electronic Design Automation (EDA) is essential for IC design and has recently benefited from AI-based techniques to improve efficiency. Logic synthesis, a key EDA stage, transforms high-level hardware descriptions into optimized netlists. Recent research has employed machine learning to predict Quality of Results (QoR) for pairs of And-Inverter Graphs (AIGs) and synthesis recipes. However, the severe scarcity of data due to a very limited number of available AIGs results in overfitting, significantly hindering performance. Additionally, the complexity and large number of nodes in AIGs make plain GNNs less effective for learning expressive graph-level representations. To tackle these challenges, we propose MTLSO - a Multi-Task Learning approach for Logic Synthesis Optimization. On one hand, it maximizes the use of limited data by training the model across different tasks. This includes introducing an auxiliary task of binary multi-label graph classification alongside the primary regression task, allowing the model to benefit from diverse supervision sources. On the other hand, we employ a hierarchical graph representation learning strategy to improve the model's capacity for learning expressive graph-level representations of large AIGs, surpassing traditional plain GNNs. Extensive experiments across multiple datasets and against state-of-the-art baselines demonstrate the superiority of our method, achieving an average performance gain of 8.22\% for delay and 5.95\% for area.
Identifying structures in common forms the basis for networked systems design and optimization. However, real structures represented by graphs are often of varying sizes, leading to the low accuracy of traditional graph classification methods. These graphs are called cross-scale graphs. To overcome this limitation, in this study, we propose GSpect, an advanced spectral graph filtering model for cross-scale graph classification tasks. Compared with other methods, we use graph wavelet neural networks for the convolution layer of the model, which aggregates multi-scale messages to generate graph representations. We design a spectral-pooling layer which aggregates nodes to one node to reduce the cross-scale graphs to the same size. We collect and construct the cross-scale benchmark data set, MSG (Multi Scale Graphs). Experiments reveal that, on open data sets, GSpect improves the performance of classification accuracy by 1.62% on average, and for a maximum of 3.33% on PROTEINS. On MSG, GSpect improves the performance of classification accuracy by 15.55% on average. GSpect fills the gap in cross-scale graph classification studies and has potential to provide assistance in application research like diagnosis of brain disease by predicting the brain network's label and developing new drugs with molecular structures learned from their counterparts in other systems.
Graph distillation has emerged as a solution for reducing large graph datasets to smaller, more manageable, and informative ones. Existing methods primarily target node classification, involve computationally intensive processes, and fail to capture the true distribution of the full graph dataset. To address these issues, we introduce Graph Distillation with Structural Attention Matching (GSTAM), a novel method for condensing graph classification datasets. GSTAM leverages the attention maps of GNNs to distill structural information from the original dataset into synthetic graphs. The structural attention-matching mechanism exploits the areas of the input graph that GNNs prioritize for classification, effectively distilling such information into the synthetic graphs and improving overall distillation performance. Comprehensive experiments demonstrate GSTAM's superiority over existing methods, achieving 0.45% to 6.5% better performance in extreme condensation ratios, highlighting its potential use in advancing distillation for graph classification tasks (Code available at https://github.com/arashrasti96/GSTAM).
Data augmentation is widely used for training a neural network given little labeled data. A common practice of augmentation training is applying a composition of multiple transformations sequentially to the data. Existing augmentation methods such as RandAugment randomly sample from a list of pre-selected transformations, while methods such as AutoAugment apply advanced search to optimize over an augmentation set of size $k^d$, which is the number of transformation sequences of length $d$, given a list of $k$ transformations. In this paper, we design efficient algorithms whose running time complexity is much faster than the worst-case complexity of $O(k^d)$, provably. We propose a new algorithm to search for a binary tree-structured composition of $k$ transformations, where each tree node corresponds to one transformation. The binary tree generalizes sequential augmentations, such as the SimCLR augmentation scheme for contrastive learning. Using a top-down, recursive search procedure, our algorithm achieves a runtime complexity of $O(2^d k)$, which is much faster than $O(k^d)$ as $k$ increases above $2$. We apply our algorithm to tackle data distributions with heterogeneous subpopulations by searching for one tree in each subpopulation and then learning a weighted combination, resulting in a forest of trees. We validate our proposed algorithms on numerous graph and image datasets, including a multi-label graph classification dataset we collected. The dataset exhibits significant variations in the sizes of graphs and their average degrees, making it ideal for studying data augmentation. We show that our approach can reduce the computation cost by 43% over existing search methods while improving performance by 4.3%. The tree structures can be used to interpret the relative importance of each transformation, such as identifying the important transformations on small vs. large graphs.
Graph classification is a challenging problem owing to the difficulty in quantifying the similarity between graphs or representing graphs as vectors, though there have been a few methods using graph kernels or graph neural networks (GNNs). Graph kernels often suffer from computational costs and manual feature engineering, while GNNs commonly utilize global pooling operations, risking the loss of structural or semantic information. This work introduces Graph Reference Distribution Learning (GRDL), an efficient and accurate graph classification method. GRDL treats each graph's latent node embeddings given by GNN layers as a discrete distribution, enabling direct classification without global pooling, based on maximum mean discrepancy to adaptively learned reference distributions. To fully understand this new model (the existing theories do not apply) and guide its configuration (e.g., network architecture, references' sizes, number, and regularization) for practical use, we derive generalization error bounds for GRDL and verify them numerically. More importantly, our theoretical and numerical results both show that GRDL has a stronger generalization ability than GNNs with global pooling operations. Experiments on moderate-scale and large-scale graph datasets show the superiority of GRDL over the state-of-the-art, emphasizing its remarkable efficiency, being at least 10 times faster than leading competitors in both training and inference stages.
Theoretical studies on the representation power of GNNs have been centered around understanding the equivalence of GNNs, using WL-Tests for detecting graph isomorphism. In this paper, we argue that such equivalence ignores the accompanying optimization issues and does not provide a holistic view of the GNN learning process. We illustrate these gaps between representation and optimization with examples and experiments. We also explore the existence of an implicit inductive bias (e.g. fully connected networks prefer to learn low frequency functions in their input space) in GNNs, in the context of graph classification tasks. We further prove theoretically that the message-passing layers in the graph, have a tendency to search for either discriminative subgraphs, or a collection of discriminative nodes dispersed across the graph, depending on the different global pooling layers used. We empirically verify this bias through experiments over real-world and synthetic datasets. Finally, we show how our work can help in incorporating domain knowledge via attention based architectures, and can evince their capability to discriminate coherent subgraphs.
Persistent homology, a fundamental technique within Topological Data Analysis (TDA), captures structural and shape characteristics of graphs, yet encounters computational difficulties when applied to dynamic directed graphs. This paper introduces the Dynamic Neural Dowker Network (DNDN), a novel framework specifically designed to approximate the results of dynamic Dowker filtration, aiming to capture the high-order topological features of dynamic directed graphs. Our approach creatively uses line graph transformations to produce both source and sink line graphs, highlighting the shared neighbor structures that Dowker complexes focus on. The DNDN incorporates a Source-Sink Line Graph Neural Network (SSLGNN) layer to effectively capture the neighborhood relationships among dynamic edges. Additionally, we introduce an innovative duality edge fusion mechanism, ensuring that the results for both the sink and source line graphs adhere to the duality principle intrinsic to Dowker complexes. Our approach is validated through comprehensive experiments on real-world datasets, demonstrating DNDN's capability not only to effectively approximate dynamic Dowker filtration results but also to perform exceptionally in dynamic graph classification tasks.
Graph Transformers (GTs) have recently achieved significant success in the graph domain by effectively capturing both long-range dependencies and graph inductive biases. However, these methods face two primary challenges: (1) multi-view chaos, which results from coupling multi-view information (positional, structural, attribute), thereby impeding flexible usage and the interpretability of the propagation process. (2) local-global chaos, which arises from coupling local message passing with global attention, leading to issues of overfitting and over-globalizing. To address these challenges, we propose a high-level decoupled perspective of GTs, breaking them down into three components and two interaction levels: positional attention, structural attention, and attribute attention, alongside local and global interaction. Based on this decoupled perspective, we design a decoupled graph triple attention network named DeGTA, which separately computes multi-view attentions and adaptively integrates multi-view local and global information. This approach offers three key advantages: enhanced interpretability, flexible design, and adaptive integration of local and global information. Through extensive experiments, DeGTA achieves state-of-the-art performance across various datasets and tasks, including node classification and graph classification. Comprehensive ablation studies demonstrate that decoupling is essential for improving performance and enhancing interpretability. Our code is available at: https://github.com/wangxiaotang0906/DeGTA
The increasing prevalence of graph-structured data across various domains has intensified greater interest in graph classification tasks. While numerous sophisticated graph learning methods have emerged, their complexity often hinders practical implementation. In this article, we address this challenge by proposing a method that constructs feature vectors based on fundamental graph structural properties. We demonstrate that these features, despite their simplicity, are powerful enough to capture the intrinsic characteristics of graphs within the same class. We explore the efficacy of our approach using three distinct machine learning methods, highlighting how our feature-based classification leverages the inherent structural similarities of graphs within the same class to achieve accurate classification. A key advantage of our approach is its simplicity, which makes it accessible and adaptable to a broad range of applications, including social network analysis, bioinformatics, and cybersecurity. Furthermore, we conduct extensive experiments to validate the performance of our method, showing that it not only reveals a competitive performance but in some cases surpasses the accuracy of more complex, state-of-the-art techniques. Our findings suggest that a focus on fundamental graph features can provide a robust and efficient alternative for graph classification, offering significant potential for both research and practical applications.
Early detection of dementia, such as Alzheimer's disease (AD) or mild cognitive impairment (MCI), is essential to enable timely intervention and potential treatment. Accurate detection of AD/MCI is challenging due to the high complexity, cost, and often invasive nature of current diagnostic techniques, which limit their suitability for large-scale population screening. Given the shared embryological origins and physiological characteristics of the retina and brain, retinal imaging is emerging as a potentially rapid and cost-effective alternative for the identification of individuals with or at high risk of AD. In this paper, we present a novel PolarNet+ that uses retinal optical coherence tomography angiography (OCTA) to discriminate early-onset AD (EOAD) and MCI subjects from controls. Our method first maps OCTA images from Cartesian coordinates to polar coordinates, allowing approximate sub-region calculation to implement the clinician-friendly early treatment of diabetic retinopathy study (ETDRS) grid analysis. We then introduce a multi-view module to serialize and analyze the images along three dimensions for comprehensive, clinically useful information extraction. Finally, we abstract the sequence embedding into a graph, transforming the detection task into a general graph classification problem. A regional relationship module is applied after the multi-view module to excavate the relationship between the sub-regions. Such regional relationship analyses validate known eye-brain links and reveal new discriminative patterns.
This paper addresses the challenge of out-of-distribution (OOD) generalization in graph machine learning, a field rapidly advancing yet grappling with the discrepancy between source and target data distributions. Traditional graph learning algorithms, based on the assumption of uniform distribution between training and test data, falter in real-world scenarios where this assumption fails, resulting in suboptimal performance. A principal factor contributing to this suboptimal performance is the inherent simplicity bias of neural networks trained through Stochastic Gradient Descent (SGD), which prefer simpler features over more complex yet equally or more predictive ones. This bias leads to a reliance on spurious correlations, adversely affecting OOD performance in various tasks such as image recognition, natural language understanding, and graph classification. Current methodologies, including subgraph-mixup and information bottleneck approaches, have achieved partial success but struggle to overcome simplicity bias, often reinforcing spurious correlations. To tackle this, we propose DIVE, training a collection of models to focus on all label-predictive subgraphs by encouraging the models to foster divergence on the subgraph mask, which circumvents the limitation of a model solely focusing on the subgraph corresponding to simple structural patterns. Specifically, we employs a regularizer to punish overlap in extracted subgraphs across models, thereby encouraging different models to concentrate on distinct structural patterns. Model selection for robust OOD performance is achieved through validation accuracy. Tested across four datasets from GOOD benchmark and one dataset from DrugOOD benchmark, our approach demonstrates significant improvement over existing methods, effectively addressing the simplicity bias and enhancing generalization in graph machine learning.
Graph learning methods have been extensively applied in diverse application areas. However, what kind of inherent graph properties e.g. graph proximity, graph structural information has been encoded into graph representation learning for downstream tasks is still under-explored. In this paper, we propose a novel graph probing framework (GraphProbe) to investigate and interpret whether the family of graph learning methods has encoded different levels of knowledge in graph representation learning. Based on the intrinsic properties of graphs, we design three probes to systematically investigate the graph representation learning process from different perspectives, respectively the node-wise level, the path-wise level, and the structural level. We construct a thorough evaluation benchmark with nine representative graph learning methods from random walk based approaches, basic graph neural networks and self-supervised graph methods, and probe them on six benchmark datasets for node classification, link prediction and graph classification. The experimental evaluation verify that GraphProbe can estimate the capability of graph representation learning. Remaking results have been concluded: GCN and WeightedGCN methods are relatively versatile methods achieving better results with respect to different tasks.
Graph out-of-distribution (OOD) generalization remains a major challenge in graph learning since graph neural networks (GNNs) often suffer from severe performance degradation under distribution shifts. Invariant learning, aiming to extract invariant features across varied distributions, has recently emerged as a promising approach for OOD generation. Despite the great success of invariant learning in OOD problems for Euclidean data (i.e., images), the exploration within graph data remains constrained by the complex nature of graphs. Existing studies, such as data augmentation or causal intervention, either suffer from disruptions to invariance during the graph manipulation process or face reliability issues due to a lack of supervised signals for causal parts. In this work, we propose a novel framework, called Invariant Graph Learning based on Information bottleneck theory (InfoIGL), to extract the invariant features of graphs and enhance models' generalization ability to unseen distributions. Specifically, InfoIGL introduces a redundancy filter to compress task-irrelevant information related to environmental factors. Cooperating with our designed multi-level contrastive learning, we maximize the mutual information among graphs of the same class in the downstream classification tasks, preserving invariant features for prediction to a great extent. An appealing feature of InfoIGL is its strong generalization ability without depending on supervised signal of invariance. Experiments on both synthetic and real-world datasets demonstrate that our method achieves state-of-the-art performance under OOD generalization for graph classification tasks. The source code is available at https://github.com/maowenyu-11/InfoIGL.
In this paper, we introduce AutoRDF2GML, a framework designed to convert RDF data into data representations tailored for graph machine learning tasks. AutoRDF2GML enables, for the first time, the creation of both content-based features -- i.e., features based on RDF datatype properties -- and topology-based features -- i.e., features based on RDF object properties. Characterized by automated feature extraction, AutoRDF2GML makes it possible even for users less familiar with RDF and SPARQL to generate data representations ready for graph machine learning tasks, such as link prediction, node classification, and graph classification. Furthermore, we present four new benchmark datasets for graph machine learning, created from large RDF knowledge graphs using our framework. These datasets serve as valuable resources for evaluating graph machine learning approaches, such as graph neural networks. Overall, our framework effectively bridges the gap between the Graph Machine Learning and Semantic Web communities, paving the way for RDF-based machine learning applications.
The experiments at the Large Hadron Collider at CERN generate vast amounts of complex data from high-energy particle collisions. This data presents significant challenges due to its volume and complex reconstruction, necessitating the use of advanced analysis techniques for analysis. Recent advancements in deep learning, particularly Graph Neural Networks, have shown promising results in addressing the challenges but remain computationally expensive. The study presented in this paper uses a simulated particle collision dataset to integrate influence analysis inside the graph classification pipeline aiming at improving the accuracy and efficiency of collision event prediction tasks. By using a Graph Neural Network for initial training, we applied a gradient-based data influence method to identify influential training samples and then we refined the dataset by removing non-contributory elements: the model trained on this new reduced dataset can achieve good performances at a reduced computational cost. The method is completely agnostic to the specific influence method: different influence modalities can be easily integrated into our methodology. Moreover, by analyzing the discarded elements we can provide further insights about the event classification task. The novelty of integrating data attribution techniques together with Graph Neural Networks in high-energy physics tasks can offer a robust solution for managing large-scale data problems, capturing critical patterns, and maximizing accuracy across several high-data demand domains.
Graphs are crucial for representing interrelated data and aiding predictive modeling by capturing complex relationships. Achieving high-quality graph representation is important for identifying linked patterns, leading to improvements in Graph Neural Networks (GNNs) to better capture data structures. However, challenges such as data scarcity, high collection costs, and ethical concerns limit progress. As a result, generative models and data augmentation have become more and more popular. This study explores using generated graphs for data augmentation, comparing the performance of combining generated graphs with real graphs, and examining the effect of different quantities of generated graphs on graph classification tasks. The experiments show that balancing scalability and quality requires different generators based on graph size. Our results introduce a new approach to graph data augmentation, ensuring consistent labels and enhancing classification performance.
Graph classification is a critical task in numerous multimedia applications, where graphs are employed to represent diverse types of multimedia data, including images, videos, and social networks. Nevertheless, in real-world scenarios, labeled graph data can be limited or scarce. To address this issue, we focus on the problem of semi-supervised graph classification, which involves both supervised and unsupervised models learning from labeled and unlabeled data. In contrast to recent approaches that transfer the entire knowledge from the unsupervised model to the supervised one, we argue that an effective transfer should only retain the relevant semantics that align well with the supervised task. In this paper, we propose a novel framework named DisenSemi, which learns disentangled representation for semi-supervised graph classification. Specifically, a disentangled graph encoder is proposed to generate factor-wise graph representations for both supervised and unsupervised models. Then we train two models via supervised objective and mutual information (MI)-based constraints respectively. To ensure the meaningful transfer of knowledge from the unsupervised encoder to the supervised one, we further define an MI-based disentangled consistency regularization between two models and identify the corresponding rationale that aligns well with the current graph classification task. Experimental results on a range of publicly accessible datasets reveal the effectiveness of our DisenSemi.