A Property Encoder for Graph Neural Networks

Graph machine learning, particularly using graph neural networks, fundamentally relies on node features. Nevertheless, numerous real-world systems, such as social and biological networks, often lack node features due to various reasons, including privacy concerns, incomplete or missing data, and limitations in data collection. In such scenarios, researchers typically resort to methods like structural and positional encoding to construct node features. However, the length of such features is contingent on the maximum value within the property being encoded, for example, the highest node degree, which can be exceedingly large in applications like scale-free networks. Furthermore, these encoding schemes are limited to categorical data and might not be able to encode metrics returning other type of values. In this paper, we introduce a novel, universally applicable encoder, termed PropEnc, which constructs expressive node embedding from any given graph metric. PropEnc leverages histogram construction combined with reverse index encoding, offering a flexible method for node features initialization. It supports flexible encoding in terms of both dimensionality and type of input, demonstrating its effectiveness across diverse applications. PropEnc allows encoding metrics in low-dimensional space which effectively avoids the issue of sparsity and enhances the efficiency of the models. We show that \emph{PropEnc} can construct node features that either exactly replicate one-hot encoding or closely approximate indices under various settings. Our extensive evaluations in graph classification setting across multiple social networks that lack node features support our hypothesis. The empirical results conclusively demonstrate that PropEnc is both an efficient and effective mechanism for constructing node features from diverse set of graph metrics.

Improving Graph Machine Learning Performance Through Feature Augmentation Based on Network Control Theory

Network control theory (NCT) offers a robust analytical framework for understanding the influence of network topology on dynamic behaviors, enabling researchers to decipher how certain patterns of external control measures can steer system dynamics towards desired states. Distinguished from other structure-function methodologies, NCT's predictive capabilities can be coupled with deploying Graph Neural Networks (GNNs), which have demonstrated exceptional utility in various network-based learning tasks. However, the performance of GNNs heavily relies on the expressiveness of node features, and the lack of node features can greatly degrade their performance. Furthermore, many real-world systems may lack node-level information, posing a challenge for GNNs.To tackle this challenge, we introduce a novel approach, NCT-based Enhanced Feature Augmentation (NCT-EFA), that assimilates average controllability, along with other centrality indices, into the feature augmentation pipeline to enhance GNNs performance. Our evaluation of NCT-EFA, on six benchmark GNN models across two experimental setting. solely employing average controllability and in combination with additional centrality metrics. showcases an improved performance reaching as high as 11%. Our results demonstrate that incorporating NCT into feature enrichment can substantively extend the applicability and heighten the performance of GNNs in scenarios where node-level information is unavailable.

Control-based Graph Embeddings with Data Augmentation for Contrastive Learning

In this paper, we study the problem of unsupervised graph representation learning by harnessing the control properties of dynamical networks defined on graphs. Our approach introduces a novel framework for contrastive learning, a widely prevalent technique for unsupervised representation learning. A crucial step in contrastive learning is the creation of 'augmented' graphs from the input graphs. Though different from the original graphs, these augmented graphs retain the original graph's structural characteristics. Here, we propose a unique method for generating these augmented graphs by leveraging the control properties of networks. The core concept revolves around perturbing the original graph to create a new one while preserving the controllability properties specific to networks and graphs. Compared to the existing methods, we demonstrate that this innovative approach enhances the effectiveness of contrastive learning frameworks, leading to superior results regarding the accuracy of the classification tasks. The key innovation lies in our ability to decode the network structure using these control properties, opening new avenues for unsupervised graph representation learning.

Enhanced Graph Neural Networks with Ego-Centric Spectral Subgraph Embeddings Augmentation

Graph Neural Networks (GNNs) have shown remarkable merit in performing various learning-based tasks in complex networks. The superior performance of GNNs often correlates with the availability and quality of node-level features in the input networks. However, for many network applications, such node-level information may be missing or unreliable, thereby limiting the applicability and efficacy of GNNs. To address this limitation, we present a novel approach denoted as Ego-centric Spectral subGraph Embedding Augmentation (ESGEA), which aims to enhance and design node features, particularly in scenarios where information is lacking. Our method leverages the topological structure of the local subgraph to create topology-aware node features. The subgraph features are generated using an efficient spectral graph embedding technique, and they serve as node features that capture the local topological organization of the network. The explicit node features, if present, are then enhanced with the subgraph embeddings in order to improve the overall performance. ESGEA is compatible with any GNN-based architecture and is effective even in the absence of node features. We evaluate the proposed method in a social network graph classification task where node attributes are unavailable, as well as in a node classification task where node features are corrupted or even absent. The evaluation results on seven datasets and eight baseline models indicate up to a 10% improvement in AUC and a 7% improvement in accuracy for graph and node classification tasks, respectively.

NeuroGraph: Benchmarks for Graph Machine Learning in Brain Connectomics

Machine learning provides a valuable tool for analyzing high-dimensional functional neuroimaging data, and is proving effective in predicting various neurological conditions, psychiatric disorders, and cognitive patterns. In functional Magnetic Resonance Imaging (MRI) research, interactions between brain regions are commonly modeled using graph-based representations. The potency of graph machine learning methods has been established across myriad domains, marking a transformative step in data interpretation and predictive modeling. Yet, despite their promise, the transposition of these techniques to the neuroimaging domain remains surprisingly under-explored due to the expansive preprocessing pipeline and large parameter search space for graph-based datasets construction. In this paper, we introduce NeuroGraph, a collection of graph-based neuroimaging datasets that span multiple categories of behavioral and cognitive traits. We delve deeply into the dataset generation search space by crafting 35 datasets within both static and dynamic contexts, running in excess of 15 baseline methods for benchmarking. Additionally, we provide generic frameworks for learning on dynamic as well as static graphs. Our extensive experiments lead to several key observations. Notably, using correlation vectors as node features, incorporating larger number of regions of interest, and employing sparser graphs lead to improved performance. To foster further advancements in graph-based data driven Neuroimaging, we offer a comprehensive open source Python package that includes the datasets, baseline implementations, model training, and standard evaluation. The package is publicly accessible at https://anwar-said.github.io/anwarsaid/neurograph.html .