Yuzhou Chen

Andac Demir, Baris Coskunuzer, Ignacio Segovia-Dominguez et al.

In computer-aided drug discovery (CADD), virtual screening (VS) is used for identifying the drug candidates that are most likely to bind to a molecular target in a large library of compounds. Most VS methods to date have focused on using canonical compound representations (e.g., SMILES strings, Morgan fingerprints) or generating alternative fingerprints of the compounds by training progressively more complex variational autoencoders (VAEs) and graph neural networks (GNNs). Although VAEs and GNNs led to significant improvements in VS performance, these methods suffer from reduced performance when scaling to large virtual compound datasets. The performance of these methods has shown only incremental improvements in the past few years. To address this problem, we developed a novel method using multiparameter persistence (MP) homology that produces topological fingerprints of the compounds as multidimensional vectors. Our primary contribution is framing the VS process as a new topology-based graph ranking problem by partitioning a compound into chemical substructures informed by the periodic properties of its atoms and extracting their persistent homology features at multiple resolution levels. We show that the margin loss fine-tuning of pretrained Triplet networks attains highly competitive results in differentiating between compounds in the embedding space and ranking their likelihood of becoming effective drug candidates. We further establish theoretical guarantees for the stability properties of our proposed MP signatures, and demonstrate that our models, enhanced by the MP signatures, outperform state-of-the-art methods on benchmark datasets by a wide and highly statistically significant margin (e.g., 93% gain for Cleves-Jain and 54% gain for DUD-E Diverse dataset).

Yuzhou Chen, Yulia R. Gel

Graph neural networks (GNNs) have demonstrated a significant success in various graph learning tasks, from graph classification to anomaly detection. There recently has emerged a number of approaches adopting a graph pooling operation within GNNs, with a goal to preserve graph attributive and structural features during the graph representation learning. However, most existing graph pooling operations suffer from the limitations of relying on node-wise neighbor weighting and embedding, which leads to insufficient encoding of rich topological structures and node attributes exhibited by real-world networks. By invoking the machinery of persistent homology and the concept of landmarks, we propose a novel topological pooling layer and witness complex-based topological embedding mechanism that allow us to systematically integrate hidden topological information at both local and global levels. Specifically, we design new learnable local and global topological representations Wit-TopoPool which allow us to simultaneously extract rich discriminative topological information from graphs. Experiments on 11 diverse benchmark datasets against 18 baseline models in conjunction with graph classification tasks indicate that Wit-TopoPool significantly outperforms all competitors across all datasets.

Naheed Anjum Arafat, Debabrota Basu, Yulia Gel et al.

Capitalizing on the intuitive premise that shape characteristics are more robust to perturbations, we bridge adversarial graph learning with the emerging tools from computational topology, namely, persistent homology representations of graphs. We introduce the concept of witness complex to adversarial analysis on graphs, which allows us to focus only on the salient shape characteristics of graphs, yielded by the subset of the most essential nodes (i.e., landmarks), with minimal loss of topological information on the whole graph. The remaining nodes are then used as witnesses, governing which higher-order graph substructures are incorporated into the learning process. Armed with the witness mechanism, we design Witness Graph Topological Layer (WGTL), which systematically integrates both local and global topological graph feature representations, the impact of which is, in turn, automatically controlled by the robust regularized topological loss. Given the attacker's budget, we derive the important stability guarantees of both local and global topology encodings and the associated robust topological loss. We illustrate the versatility and efficiency of WGTL by its integration with five GNNs and three existing non-topological defense mechanisms. Our extensive experiments across six datasets demonstrate that WGTL boosts the robustness of GNNs across a range of perturbations and against a range of adversarial attacks. Our datasets and source codes are available at https://github.com/toggled/WGTL.

Sinan G. Aksoy, Ryan Bennink, Yuzhou Chen et al.

We present and discuss seven different open problems in applied combinatorics. The application areas relevant to this compilation include quantum computing, algorithmic differentiation, topological data analysis, iterative methods, hypergraph cut algorithms, and power systems.

Yuzhou Chen, Tian Jiang, Miguel Heleno et al.

Nowadays, it is broadly recognized in the power system community that to meet the ever expanding energy sector's needs, it is no longer possible to rely solely on physics-based models and that reliable, timely and sustainable operation of energy systems is impossible without systematic integration of artificial intelligence (AI) tools. Nevertheless, the adoption of AI in power systems is still limited, while integration of AI particularly into distribution grid investment planning is still an uncharted territory. We make the first step forward to bridge this gap by showing how graph convolutional networks coupled with the hyperstructures representation learning framework can be employed for accurate, reliable, and computationally efficient distribution grid planning with resilience objectives. We further propose a Hyperstructures Graph Convolutional Neural Networks (Hyper-GCNNs) to capture hidden higher order representations of distribution networks with attention mechanism. Our numerical experiments show that the proposed Hyper-GCNNs approach yields substantial gains in computational efficiency compared to the prevailing methodology in distribution grid planning and also noticeably outperforms seven state-of-the-art models from deep learning (DL) community.

Yuzhou Chen, Yuebing Liang, Lingqian Hu et al.

Street-view imagery (SVI) is widely used to quantify key indicators of urban environment, such as green- ery, sky, or road view indices. However, existing studies largely focus on measuring current streetscapes and rarely support the generation of alternative and non-existing urban scenarios, which is a core task in geospatial disciplines such as urban planning and design. To address this gap, we propose a gener- ative multimodal AI framework that synthesizes alternative streetscapes conditioned on targeted visual metrics, enabling direct visual exploration of urban scenarios. We first construct a multimodal dataset that aligns SVIs with textual descriptions, segmentation maps, road masks, and quantitative metrics of visual elements in Chicago and Orlando. Using this dataset, we demonstrate that diffusion models can produce realistic and semantically consistent streetscape imagery while responding to both textual and imagery controls. Our quantitative evaluations show that incorporating visual controls can improve semantic consistency, reducing the LPIPS index by approximately 6% while maintaining global visual realism. In addition, overall semantic consistency increases by 23.7% in Orlando and 46.4% in Chicago, as measured by the mIoU index, with class-wise gains exceeding even 100% improvement for building view indices. Streetscape generation can be controlled in a fine-grained manner by both visual and textual prompts, and when textual and visual controls conflict, imagery controls consistently dominate, indicating a clear control hierarchy and the importance of further developing visual controls for urban scene generation. Overall, this work establishes an important benchmark for streetscape generation us- ing SVIs and diffusion models, and illustrates how generative AI can serve as a practical, scalable, and controllable approach for urban scenario exploration.

Hao Li, Hao Wan, Yuzhou Chen et al.

Dynamic graphs evolve continuously, presenting challenges for traditional graph learning due to their changing structures and temporal dependencies. Recent advancements have shown potential in addressing these challenges by developing suitable meta-learning-based dynamic graph neural network models. However, most meta-learning approaches for dynamic graphs rely on fixed weight update parameters, neglecting the essential intrinsic complex high-order topological information of dynamically evolving graphs. We have designed Dowker Zigzag Persistence (DZP), an efficient and stable dynamic graph persistent homology representation method based on Dowker complex and zigzag persistence, to capture the high-order features of dynamic graphs. Armed with the DZP ideas, we propose TMetaNet, a new meta-learning parameter update model based on dynamic topological features. By utilizing the distances between high-order topological features, TMetaNet enables more effective adaptation across snapshots. Experiments on real-world datasets demonstrate TMetaNet's state-of-the-art performance and resilience to graph noise, illustrating its high potential for meta-learning and dynamic graph analysis. Our code is available at https://github.com/Lihaogx/TMetaNet.

Yujia Wu, Junyi Mo, Elynn Chen et al.

Graph contrastive learning (GCL) has emerged as a promising approach to enhance graph neural networks' (GNNs) ability to learn rich representations from unlabeled graph-structured data. However, current GCL models face challenges with computational demands and limited feature utilization, often relying only on basic graph properties like node degrees and edge attributes. This constrains their capacity to fully capture the complex topological characteristics of real-world phenomena represented by graphs. To address these limitations, we propose Tensor-Fused Multi-View Graph Contrastive Learning (TensorMV-GCL), a novel framework that integrates extended persistent homology (EPH) with GCL representations and facilitates multi-scale feature extraction. Our approach uniquely employs tensor aggregation and compression to fuse information from graph and topological features obtained from multiple augmented views of the same graph. By incorporating tensor concatenation and contraction modules, we reduce computational overhead by separating feature tensor aggregation and transformation. Furthermore, we enhance the quality of learned topological features and model robustness through noise-injected EPH. Experiments on molecular, bioinformatic, and social network datasets demonstrate TensorMV-GCL's superiority, outperforming 15 state-of-the-art methods in graph classification tasks across 9 out of 11 benchmarks while achieving comparable results on the remaining two. The code for this paper is publicly available at https://github.com/CS-SAIL/Tensor-MV-GCL.git.

Javad M Alizadeh, Genhui Zheng, Chiu C Tan et al.

People experiencing homelessness (PEH) face substantial barriers to accessing timely, accurate information about community services. DreamKG addresses this through a knowledge graph-augmented conversational system that grounds responses in verified, up-to-date data about Philadelphia organizations, services, locations, and hours. Unlike standard large language models (LLMs) prone to hallucinations, DreamKG combines Neo4j knowledge graphs with structured query understanding to handle location-aware and time-sensitive queries reliably. The system performs spatial reasoning for distance-based recommendations and temporal filtering for operating hours. Preliminary evaluation shows 59% superiority over Google Search AI on relevant queries and 84% rejection of irrelevant queries. This demonstration highlights the potential of hybrid architectures that combines LLM flexibility with knowledge graph reliability to improve service accessibility for vulnerable populations effectively.

Zihao Wang, Yuzhou Chen, Shaogang Ren

Cross-modal image translation remains brittle and inefficient. Standard diffusion approaches often rely on a single, global linear transfer between domains. We find that this shortcut forces the sampler to traverse off-manifold, high-cost regions, inflating the correction burden and inviting semantic drift. We refer to this shared failure mode as fixed-schedule domain transfer. In this paper, we embed domain-shift dynamics directly into the generative process. Our model predicts a spatially varying mixing field at every reverse step and injects an explicit, target-consistent restoration term into the drift. This in-step guidance keeps large updates on-manifold and shifts the model's role from global alignment to local residual correction. We provide a continuous-time formulation with an exact solution form and derive a practical first-order sampler that preserves marginal consistency. Empirically, across translation tasks in medical imaging, remote sensing, and electroluminescence semantic mapping, our framework improves structural fidelity and semantic consistency while converging in fewer denoising steps.

Tao Wen, Elynn Chen, Yuzhou Chen

Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems. Despite their state-of-the-art performances, existing GNNs only use local information from a very limited neighborhood around each node, suffering from loss of multi-modal information and overheads of excessive computation. To address these issues, we propose a novel Tensor-view Topological Graph Neural Network (TTG-NN), a class of simple yet effective topological deep learning built upon persistent homology, graph convolution, and tensor operations. This new method incorporates tensor learning to simultaneously capture Tensor-view Topological (TT), as well as Tensor-view Graph (TG) structural information on both local and global levels. Computationally, to fully exploit graph topology and structure, we propose two flexible TT and TG representation learning modules that disentangle feature tensor aggregation and transformation and learn to preserve multi-modal structure with less computation. Theoretically, we derive high probability bounds on both the out-of-sample and in-sample mean squared approximation errors for our proposed Tensor Transformation Layer (TTL). Real data experiments show that the proposed TTG-NN outperforms 20 state-of-the-art methods on various graph benchmarks.

Yujia Wu, Bo Yang, Yang Zhao et al.

Graph Neural Networks (GNNs) have become the de facto standard for analyzing graph-structured data, leveraging message-passing techniques to capture both structural and node feature information. However, recent studies have raised concerns about the statistical reliability of uncertainty estimates produced by GNNs. This paper addresses this crucial challenge by introducing a novel technique for quantifying uncertainty in non-exchangeable graph-structured data, while simultaneously reducing the size of label prediction sets in graph classification tasks. We propose Conformalized Tensor-based Topological Neural Networks (CF-T2NN), a new approach for rigorous prediction inference over graphs. CF-T2NN employs tensor decomposition and topological knowledge learning to navigate and interpret the inherent uncertainty in decision-making processes. This method enables a more nuanced understanding and handling of prediction uncertainties, enhancing the reliability and interpretability of neural network outcomes. Our empirical validation, conducted across 10 real-world datasets, demonstrates the superiority of CF-T2NN over a wide array of state-of-the-art methods on various graph benchmarks. This work not only enhances the GNN framework with robust uncertainty quantification capabilities but also sets a new standard for reliability and precision in graph-structured data analysis.

Yujia Wu, Bo Yang, Elynn Chen et al.

Graph classification in medical imaging and drug discovery requires accuracy and robust uncertainty quantification. To address this need, we introduce Conditional Prediction ROC (CP-ROC) bands, offering uncertainty quantification for ROC curves and robustness to distributional shifts in test data. Although developed for Tensorized Graph Neural Networks (TGNNs), CP-ROC is adaptable to general Graph Neural Networks (GNNs) and other machine learning models. We establish statistically guaranteed coverage for CP-ROC under a local exchangeability condition. This addresses uncertainty challenges for ROC curves under non-iid setting, ensuring reliability when test graph distributions differ from training data. Empirically, to establish local exchangeability for TGNNs, we introduce a data-driven approach to construct local calibration sets for graphs. Comprehensive evaluations show that CP-ROC significantly improves prediction reliability across diverse tasks. This method enhances uncertainty quantification efficiency and reliability for ROC curves, proving valuable for real-world applications with non-iid objects.

Javad M Alizadeh, Jay S Patel, Gabriel Tajeu et al.

Over 30 million Americans are affected by Type II diabetes (T2D), a treatable condition with significant health risks. This study aims to develop and validate predictive models using machine learning (ML) techniques to estimate emergency department (ED) visits among patients with T2D. Data for these patients was obtained from the HealthShare Exchange (HSX), focusing on demographic details, diagnoses, and vital signs. Our sample contained 34,151 patients diagnosed with T2D which resulted in 703,065 visits overall between 2017 and 2021. A workflow integrated EMR data with SDoH for ML predictions. A total of 87 out of 2,555 features were selected for model construction. Various machine learning algorithms, including CatBoost, Ensemble Learning, K-nearest Neighbors (KNN), Support Vector Classification (SVC), Random Forest, and Extreme Gradient Boosting (XGBoost), were employed with tenfold cross-validation to predict whether a patient is at risk of an ED visit. The ROC curves for Random Forest, XGBoost, Ensemble Learning, CatBoost, KNN, and SVC, were 0.82, 0.82, 0.82, 0.81, 0.72, 0.68, respectively. Ensemble Learning and Random Forest models demonstrated superior predictive performance in terms of discrimination, calibration, and clinical applicability. These models are reliable tools for predicting risk of ED visits among patients with T2D. They can estimate future ED demand and assist clinicians in identifying critical factors associated with ED utilization, enabling early interventions to reduce such visits. The top five important features were age, the difference between visitation gaps, visitation gaps, R10 or abdominal and pelvic pain, and the Index of Concentration at the Extremes (ICE) for income.

Zihao Wang, Yingyu Yang, Yuzhou Chen et al.

Cross-modality image segmentation aims to segment the target modalities using a method designed in the source modality. Deep generative models can translate the target modality images into the source modality, thus enabling cross-modality segmentation. However, a vast body of existing cross-modality image translation methods relies on supervised learning. In this work, we aim to address the challenge of zero-shot learning-based image translation tasks (extreme scenarios in the target modality is unseen in the training phase). To leverage generative learning for zero-shot cross-modality image segmentation, we propose a novel unsupervised image translation method. The framework learns to translate the unseen source image to the target modality for image segmentation by leveraging the inherent statistical consistency between different modalities for diffusion guidance. Our framework captures identical cross-modality features in the statistical domain, offering diffusion guidance without relying on direct mappings between the source and target domains. This advantage allows our method to adapt to changing source domains without the need for retraining, making it highly practical when sufficient labeled source domain data is not available. The proposed framework is validated in zero-shot cross-modality image segmentation tasks through empirical comparisons with influential generative models, including adversarial-based and diffusion-based models.

Fangyi Cao, Bin Ren, Zihao Wang et al.

With over 1,000,000 images from more than 10,000 exposures using state-of-the-art high-contrast imagers (e.g., Gemini Planet Imager, VLT/SPHERE) in the search for exoplanets, can artificial intelligence (AI) serve as a transformative tool in imaging Earth-like exoplanets in the coming decade? In this paper, we introduce a benchmark and explore this question from a polarimetric image representation learning perspective. Despite extensive investments over the past decade, only a few new exoplanets have been directly imaged. Existing imaging approaches rely heavily on labor-intensive labeling of reference stars, which serve as background to extract circumstellar objects (disks or exoplanets) around target stars. With our POLARIS (POlarized Light dAta for total intensity Representation learning of direct Imaging of exoplanetary Systems) dataset, we classify reference star and circumstellar disk images using the full public SPHERE/IRDIS polarized-light archive since 2014, requiring less than 10 percent manual labeling. We evaluate a range of models including statistical, generative, and large vision-language models and provide baseline performance. We also propose an unsupervised generative representation learning framework that integrates these models, achieving superior performance and enhanced representational power. To our knowledge, this is the first uniformly reduced, high-quality exoplanet imaging dataset, rare in astrophysics and machine learning. By releasing this dataset and baselines, we aim to equip astrophysicists with new tools and engage data scientists in advancing direct exoplanet imaging, catalyzing major interdisciplinary breakthroughs.

Tao Wen, Elynn Chen, Yuzhou Chen et al.

Graph Neural Networks (GNNs) have recently become the predominant tools for studying graph data. Despite state-of-the-art performance on graph classification tasks, GNNs are overwhelmingly trained in a single domain under supervision, thus necessitating a prohibitively high demand for labels and resulting in poorly transferable representations. To address this challenge, we propose the Label-Propagation Tensor Graph Neural Network (LP-TGNN) framework to bridge the gap between graph data and traditional domain adaptation methods. It extracts graph topological information holistically with a tensor architecture and then reduces domain discrepancy through label propagation. It is readily compatible with general GNNs and domain adaptation techniques with minimal adjustment through pseudo-labeling. Experiments on various real-world benchmarks show that our LP-TGNN outperforms baselines by a notable margin. We also validate and analyze each component of the proposed framework in the ablation study.

Linghang Kong, Elynn Chen, Yuzhou Chen et al.

Multi-dimensional time series data, such as matrix and tensor-variate time series, are increasingly prevalent in fields such as economics, finance, and climate science. Traditional Transformer models, though adept with sequential data, do not effectively preserve these multi-dimensional structures, as their internal operations in effect flatten multi-dimensional observations into vectors, thereby losing critical multi-dimensional relationships and patterns. To address this, we introduce the Tensor-Augmented Transformer (TEAFormer), a novel method that incorporates tensor expansion and compression within the Transformer framework to maintain and leverage the inherent multi-dimensional structures, thus reducing computational costs and improving prediction accuracy. The core feature of the TEAFormer, the Tensor-Augmentation (TEA) module, utilizes tensor expansion to enhance multi-view feature learning and tensor compression for efficient information aggregation and reduced computational load. The TEA module is not just a specific model architecture but a versatile component that is highly compatible with the attention mechanism and the encoder-decoder structure of Transformers, making it adaptable to existing Transformer architectures. Our comprehensive experiments, which integrate the TEA module into three popular time series Transformer models across three real-world benchmarks, show significant performance enhancements, highlighting the potential of TEAFormers for cutting-edge time series forecasting.

Yuzhou Chen, Jose Frias, Yulia R. Gel

Graph contrastive learning (GCL) has recently emerged as a new concept which allows for capitalizing on the strengths of graph neural networks (GNNs) to learn rich representations in a wide variety of applications which involve abundant unlabeled information. However, existing GCL approaches largely tend to overlook the important latent information on higher-order graph substructures. We address this limitation by introducing the concepts of topological invariance and extended persistence on graphs to GCL. In particular, we propose a new contrastive mode which targets topological representations of the two augmented views from the same graph, yielded by extracting latent shape properties of the graph at multiple resolutions. Along with the extended topological layer, we introduce a new extended persistence summary, namely, extended persistence landscapes (EPL) and derive its theoretical stability guarantees. Our extensive numerical results on biological, chemical, and social interaction graphs show that the new Topological Graph Contrastive Learning (TopoGCL) model delivers significant performance gains in unsupervised graph classification for 11 out of 12 considered datasets and also exhibits robustness under noisy scenarios.

Ignacio Segovia-Dominguez, Yuzhou Chen, Cuneyt G. Akcora et al.

Topological data analysis (TDA) is gaining prominence across a wide spectrum of machine learning tasks that spans from manifold learning to graph classification. A pivotal technique within TDA is persistent homology (PH), which furnishes an exclusive topological imprint of data by tracing the evolution of latent structures as a scale parameter changes. Present PH tools are confined to analyzing data through a single filter parameter. However, many scenarios necessitate the consideration of multiple relevant parameters to attain finer insights into the data. We address this issue by introducing the Effective Multidimensional Persistence (EMP) framework. This framework empowers the exploration of data by simultaneously varying multiple scale parameters. The framework integrates descriptor functions into the analysis process, yielding a highly expressive data summary. It seamlessly integrates established single PH summaries into multidimensional counterparts like EMP Landscapes, Silhouettes, Images, and Surfaces. These summaries represent data's multidimensional aspects as matrices and arrays, aligning effectively with diverse ML models. We provide theoretical guarantees and stability proofs for EMP summaries. We demonstrate EMP's utility in graph classification tasks, showing its effectiveness. Results reveal that EMP enhances various single PH descriptors, outperforming cutting-edge methods on multiple benchmark datasets.

Baris Coskunuzer, Ignacio Segovia-Dominguez, Yuzhou Chen et al.

Learning time-evolving objects such as multivariate time series and dynamic networks requires the development of novel knowledge representation mechanisms and neural network architectures, which allow for capturing implicit time-dependent information contained in the data. Such information is typically not directly observed but plays a key role in the learning task performance. In turn, lack of time dimension in knowledge encoding mechanisms for time-dependent data leads to frequent model updates, poor learning performance, and, as a result, subpar decision-making. Here we propose a new approach to a time-aware knowledge representation mechanism that notably focuses on implicit time-dependent topological information along multiple geometric dimensions. In particular, we propose a new approach, named \textit{Temporal MultiPersistence} (TMP), which produces multidimensional topological fingerprints of the data by using the existing single parameter topological summaries. The main idea behind TMP is to merge the two newest directions in topological representation learning, that is, multi-persistence which simultaneously describes data shape evolution along multiple key parameters, and zigzag persistence to enable us to extract the most salient data shape information over time. We derive theoretical guarantees of TMP vectorizations and show its utility, in application to forecasting on benchmark traffic flow, Ethereum blockchain, and electrocardiogram datasets, demonstrating the competitive performance, especially, in scenarios of limited data records. In addition, our TMP method improves the computational efficiency of the state-of-the-art multipersistence summaries up to 59.5 times.

Yuzhou Chen, Yulia R. Gel, H. Vincent Poor

Simplicial neural networks (SNN) have recently emerged as the newest direction in graph learning which expands the idea of convolutional architectures from node space to simplicial complexes on graphs. Instead of pre-dominantly assessing pairwise relations among nodes as in the current practice, simplicial complexes allow us to describe higher-order interactions and multi-node graph structures. By building upon connection between the convolution operation and the new block Hodge-Laplacian, we propose the first SNN for link prediction. Our new Block Simplicial Complex Neural Networks (BScNets) model generalizes the existing graph convolutional network (GCN) frameworks by systematically incorporating salient interactions among multiple higher-order graph structures of different dimensions. We discuss theoretical foundations behind BScNets and illustrate its utility for link prediction on eight real-world and synthetic datasets. Our experiments indicate that BScNets outperforms the state-of-the-art models by a significant margin while maintaining low computation costs. Finally, we show utility of BScNets as the new promising alternative for tracking spread of infectious diseases such as COVID-19 and measuring the effectiveness of the healthcare risk mitigation strategies.

Yuzhou Chen, Baris Coskunuzer, Yulia R. Gel

Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these challenges, we propose a novel topological neural framework of topological relational inference (TRI) which allows for integrating higher-order graph information to GNNs and for systematically learning a local graph structure. The key idea is to rewire the original graph by using the persistent homology of the small neighborhoods of nodes and then to incorporate the extracted topological summaries as the side information into the local algorithm. As a result, the new framework enables us to harness both the conventional information on the graph structure and information on the graph higher order topological properties. We derive theoretical stability guarantees for the new local topological representation and discuss their implications on the graph algebraic connectivity. The experimental results on node classification tasks demonstrate that the new TRI-GNN outperforms all 14 state-of-the-art baselines on 6 out 7 graphs and exhibit higher robustness to perturbations, yielding up to 10\% better performance under noisy scenarios.

Ignacio Segovia-Dominguez, Huikyo Lee, Zhiwei Zhen et al.

As multiple adverse events in 2021 illustrated, virtually all aspects of our societal functioning -- from water and food security to energy supply to healthcare -- more than ever depend on the dynamics of environmental factors. Nevertheless, the social dimensions of weather and climate are noticeably less explored by the machine learning community, largely, due to the lack of reliable and easy access to use data. Here we present a unique not yet broadly available NASA's satellite dataset on aerosol optical depth (AOD), temperature and relative humidity and discuss the utility of these new data for COVID-19 biosurveillance. In particular, using the geometric deep learning models for semi-supervised classification on a county-level basis over the contiguous United States, we investigate the pressing societal question whether atmospheric variables have considerable impact on COVID-19 clinical severity.

Yuzhou Chen, Ignacio Segovia-Dominguez, Yulia R. Gel

There recently has been a surge of interest in developing a new class of deep learning (DL) architectures that integrate an explicit time dimension as a fundamental building block of learning and representation mechanisms. In turn, many recent results show that topological descriptors of the observed data, encoding information on the shape of the dataset in a topological space at different scales, that is, persistent homology of the data, may contain important complementary information, improving both performance and robustness of DL. As convergence of these two emerging ideas, we propose to enhance DL architectures with the most salient time-conditioned topological information of the data and introduce the concept of zigzag persistence into time-aware graph convolutional networks (GCNs). Zigzag persistence provides a systematic and mathematically rigorous framework to track the most important topological features of the observed data that tend to manifest themselves over time. To integrate the extracted time-conditioned topological descriptors into DL, we develop a new topological summary, zigzag persistence image, and derive its theoretical stability guarantees. We validate the new GCNs with a time-aware zigzag topological layer (Z-GCNETs), in application to traffic forecasting and Ethereum blockchain price prediction. Our results indicate that Z-GCNET outperforms 13 state-of-the-art methods on 4 time series datasets.

Yuzhou Chen, Yulia R. Gel, Konstantin Avrachenkov

Due to high utility in many applications, from social networks to blockchain to power grids, deep learning on non-Euclidean objects such as graphs and manifolds, coined Geometric Deep Learning (GDL), continues to gain an ever increasing interest. We propose a new Lévy Flights Graph Convolutional Networks (LFGCN) method for semi-supervised learning, which casts the Lévy Flights into random walks on graphs and, as a result, allows both to accurately account for the intrinsic graph topology and to substantially improve classification performance, especially for heterogeneous graphs. Furthermore, we propose a new preferential P-DropEdge method based on the Girvan-Newman argument. That is, in contrast to uniform removing of edges as in DropEdge, following the Girvan-Newman algorithm, we detect network periphery structures using information on edge betweenness and then remove edges according to their betweenness centrality. Our experimental results on semi-supervised node classification tasks demonstrate that the LFGCN coupled with P-DropEdge accelerates the training task, increases stability and further improves predictive accuracy of learned graph topology structure. Finally, in our case studies we bring the machinery of LFGCN and other deep networks tools to analysis of power grid networks - the area where the utility of GDL remains untapped.