Ambuj Singh

Saurabh Sharma, Yongqin Xian, Ning Yu et al.

The problem of long-tailed recognition (LTR) has received attention in recent years due to the fundamental power-law distribution of objects in the real-world. Most recent works in LTR use softmax classifiers that are biased in that they correlate classifier norm with the amount of training data for a given class. In this work, we show that learning prototype classifiers addresses the biased softmax problem in LTR. Prototype classifiers can deliver promising results simply using Nearest-Class- Mean (NCM), a special case where prototypes are empirical centroids. We go one step further and propose to jointly learn prototypes by using distances to prototypes in representation space as the logit scores for classification. Further, we theoretically analyze the properties of Euclidean distance based prototype classifiers that lead to stable gradient-based optimization which is robust to outliers. To enable independent distance scales along each channel, we enhance Prototype classifiers by learning channel-dependent temperature parameters. Our analysis shows that prototypes learned by Prototype classifiers are better separated than empirical centroids. Results on four LTR benchmarks show that Prototype classifier outperforms or is comparable to state-of-the-art methods. Our code is made available at https://github.com/saurabhsharma1993/prototype-classifier-ltr.

Mert Kosan, Zexi Huang, Sourav Medya et al.

Graph neural networks (GNNs) find applications in various domains such as computational biology, natural language processing, and computer security. Owing to their popularity, there is an increasing need to explain GNN predictions since GNNs are black-box machine learning models. One way to address this is counterfactual reasoning where the objective is to change the GNN prediction by minimal changes in the input graph. Existing methods for counterfactual explanation of GNNs are limited to instance-specific local reasoning. This approach has two major limitations of not being able to offer global recourse policies and overloading human cognitive ability with too much information. In this work, we study the global explainability of GNNs through global counterfactual reasoning. Specifically, we want to find a small set of representative counterfactual graphs that explains all input graphs. Towards this goal, we propose GCFExplainer, a novel algorithm powered by vertex-reinforced random walks on an edit map of graphs with a greedy summary. Extensive experiments on real graph datasets show that the global explanation from GCFExplainer provides important high-level insights of the model behavior and achieves a 46.9% gain in recourse coverage and a 9.5% reduction in recourse cost compared to the state-of-the-art local counterfactual explainers.

Sikun Lin, Shuyun Tang, Scott Grafton et al.

Finding an appropriate representation of dynamic activities in the brain is crucial for many downstream applications. Due to its highly dynamic nature, temporally averaged fMRI (functional magnetic resonance imaging) can only provide a narrow view of underlying brain activities. Previous works lack the ability to learn and interpret the latent dynamics in brain architectures. This paper builds an efficient graph neural network model that incorporates both region-mapped fMRI sequences and structural connectivities obtained from DWI (diffusion-weighted imaging) as inputs. We find good representations of the latent brain dynamics through learning sample-level adaptive adjacency matrices and performing a novel multi-resolution inner cluster smoothing. We also attribute inputs with integrated gradients, which enables us to infer (1) highly involved brain connections and subnetworks for each task, (2) temporal keyframes of imaging sequences that characterize tasks, and (3) subnetworks that discriminate between individual subjects. This ability to identify critical subnetworks that characterize signal states across heterogeneous tasks and individuals is of great importance to neuroscience and other scientific domains. Extensive experiments and ablation studies demonstrate our proposed method's superiority and efficiency in spatial-temporal graph signal modeling with insightful interpretations of brain dynamics.

Kha-Dinh Luong, Ambuj Singh

Property prediction on molecular graphs is an important application of Graph Neural Networks. Recently, unlabeled molecular data has become abundant, which facilitates the rapid development of self-supervised learning for GNNs in the chemical domain. In this work, we propose pretraining GNNs at the fragment level, a promising middle ground to overcome the limitations of node-level and graph-level pretraining. Borrowing techniques from recent work on principal subgraph mining, we obtain a compact vocabulary of prevalent fragments from a large pretraining dataset. From the extracted vocabulary, we introduce several fragment-based contrastive and predictive pretraining tasks. The contrastive learning task jointly pretrains two different GNNs: one on molecular graphs and the other on fragment graphs, which represents higher-order connectivity within molecules. By enforcing consistency between the fragment embedding and the aggregated embedding of the corresponding atoms from the molecular graphs, we ensure that the embeddings capture structural information at multiple resolutions. The structural information of fragment graphs is further exploited to extract auxiliary labels for graph-level predictive pretraining. We employ both the pretrained molecular-based and fragment-based GNNs for downstream prediction, thus utilizing the fragment information during finetuning. Our graph fragment-based pretraining (GraphFP) advances the performances on 5 out of 8 common molecular benchmarks and improves the performances on long-range biological benchmarks by at least 11.5%. Code is available at: https://github.com/lvkd84/GraphFP.

Rhys Tracy, Haotian Xia, Alex Rasla et al.

This research aims to improve the accuracy of complex volleyball predictions and provide more meaningful insights to coaches and players. We introduce a specialized graph encoding technique to add additional contact-by-contact volleyball context to an already available volleyball dataset without any additional data gathering. We demonstrate the potential benefits of using graph neural networks (GNNs) on this enriched dataset for three different volleyball prediction tasks: rally outcome prediction, set location prediction, and hit type prediction. We compare the performance of our graph-based models to baseline models and analyze the results to better understand the underlying relationships in a volleyball rally. Our results show that the use of GNNs with our graph encoding yields a much more advanced analysis of the data, which noticeably improves prediction results overall. We also show that these baseline tasks can be significantly improved with simple adjustments, such as removing blocked hits. Lastly, we demonstrate the importance of choosing a model architecture that will better extract the important information for a certain task. Overall, our study showcases the potential strengths and weaknesses of using graph encodings in sports data analytics and hopefully will inspire future improvements in machine learning strategies across sports and applications by using graphbased encodings.

Ege Demirci, Francesco Bullo, Ananthram Swami et al.

Recovering missing flows on the edges of a network, while exactly respecting local conservation laws, is a fundamental inverse problem that arises in many systems such as transportation, energy, and mobility. We introduce FlowSymm, a novel architecture that combines (i) a group-action on divergence-free flows, (ii) a graph-attention encoder to learn feature-conditioned weights over these symmetry-preserving actions, and (iii) a lightweight Tikhonov refinement solved via implicit bilevel optimization. The method first anchors the given observation on a minimum-norm divergence-free completion. We then compute an orthonormal basis for all admissible group actions that leave the observed flows invariant and parameterize the valid solution subspace, which shows an Abelian group structure under vector addition. A stack of GATv2 layers then encodes the graph and its edge features into per-edge embeddings, which are pooled over the missing edges and produce per-basis attention weights. This attention-guided process selects a set of physics-aware group actions that preserve the observed flows. Finally, a scalar Tikhonov penalty refines the missing entries via a convex least-squares solver, with gradients propagated implicitly through Cholesky factorization. Across three real-world flow benchmarks (traffic, power, bike), FlowSymm outperforms state-of-the-art baselines in RMSE, MAE and correlation metrics.

Zichen Chen, Jianda Chen, Ambuj Singh et al.

Large Language Models (LLMs) have achieved remarkable success in natural language tasks, yet understanding their reasoning processes remains a significant challenge. We address this by introducing XplainLLM, a dataset accompanying an explanation framework designed to enhance LLM transparency and reliability. Our dataset comprises 24,204 instances where each instance interprets the LLM's reasoning behavior using knowledge graphs (KGs) and graph attention networks (GAT), and includes explanations of LLMs such as the decoder-only Llama-3 and the encoder-only RoBERTa. XplainLLM also features a framework for generating grounded explanations and the debugger-scores for multidimensional quality analysis. Our explanations include why-choose and why-not-choose components, reason-elements, and debugger-scores that collectively illuminate the LLM's reasoning behavior. Our evaluations demonstrate XplainLLM's potential to reduce hallucinations and improve grounded explanation generation in LLMs. XplainLLM is a resource for researchers and practitioners to build trust and verify the reliability of LLM outputs.

Mert Kosan, Samidha Verma, Burouj Armgaan et al.

Numerous explainability methods have been proposed to shed light on the inner workings of GNNs. Despite the inclusion of empirical evaluations in all the proposed algorithms, the interrogative aspects of these evaluations lack diversity. As a result, various facets of explainability pertaining to GNNs, such as a comparative analysis of counterfactual reasoners, their stability to variational factors such as different GNN architectures, noise, stochasticity in non-convex loss surfaces, feasibility amidst domain constraints, and so forth, have yet to be formally investigated. Motivated by this need, we present a benchmarking study on perturbation-based explainability methods for GNNs, aiming to systematically evaluate and compare a wide range of explainability techniques. Among the key findings of our study, we identify the Pareto-optimal methods that exhibit superior efficacy and stability in the presence of noise. Nonetheless, our study reveals that all algorithms are affected by stability issues when faced with noisy data. Furthermore, we have established that the current generation of counterfactual explainers often fails to provide feasible recourses due to violations of topological constraints encoded by domain-specific considerations. Overall, this benchmarking study empowers stakeholders in the field of GNNs with a comprehensive understanding of the state-of-the-art explainability methods, potential research problems for further enhancement, and the implications of their application in real-world scenarios.

Wanjing Huang, Weixiang Yan, Zhen Zhang et al.

Large Language Models (LLMs) demonstrate strong reasoning and task planning capabilities but remain fundamentally limited in physical interaction modeling. Existing approaches integrate perception via Vision-Language Models (VLMs) or adaptive decision-making through Reinforcement Learning (RL), but they fail to capture dynamic object interactions or require task-specific training, limiting their real-world applicability. We introduce APEX (Anticipatory Physics-Enhanced Execution), a framework that equips LLMs with physics-driven foresight for real-time task planning. APEX constructs structured graphs to identify and model the most relevant dynamic interactions in the environment, providing LLMs with explicit physical state updates. Simultaneously, APEX provides low-latency forward simulations of physically feasible actions, allowing LLMs to select optimal strategies based on predictive outcomes rather than static observations. We evaluate APEX on three benchmarks designed to assess perception, prediction, and decision-making: (1) Physics Reasoning Benchmark, testing causal inference and object motion prediction; (2) Tetris, evaluating whether physics-informed prediction enhances decision-making performance in long-horizon planning tasks; (3) Dynamic Obstacle Avoidance, assessing the immediate integration of perception and action feasibility analysis. APEX significantly outperforms standard LLMs and VLM-based models, demonstrating the necessity of explicit physics reasoning for bridging the gap between language-based intelligence and real-world task execution. The source code and experiment setup are publicly available at https://github.com/hwj20/APEX_EXP .

Danqing Wang, Antonis Antoniades, Kha-Dinh Luong et al.

Counterfactual explanations of Graph Neural Networks (GNNs) offer a powerful way to understand data that can naturally be represented by a graph structure. Furthermore, in many domains, it is highly desirable to derive data-driven global explanations or rules that can better explain the high-level properties of the models and data in question. However, evaluating global counterfactual explanations is hard in real-world datasets due to a lack of human-annotated ground truth, which limits their use in areas like molecular sciences. Additionally, the increasing scale of these datasets provides a challenge for random search-based methods. In this paper, we develop a novel global explanation model RLHEX for molecular property prediction. It aligns the counterfactual explanations with human-defined principles, making the explanations more interpretable and easy for experts to evaluate. RLHEX includes a VAE-based graph generator to generate global explanations and an adapter to adjust the latent representation space to human-defined principles. Optimized by Proximal Policy Optimization (PPO), the global explanations produced by RLHEX cover 4.12% more input graphs and reduce the distance between the counterfactual explanation set and the input set by 0.47% on average across three molecular datasets. RLHEX provides a flexible framework to incorporate different human-designed principles into the counterfactual explanation generation process, aligning these explanations with domain expertise. The code and data are released at https://github.com/dqwang122/RLHEX.

Saurabh Sharma, Ambuj Singh

The problem of maximizing the adoption of a product through viral marketing in social networks has been studied heavily through postulated network models. We present a novel data-driven formulation of the problem. We use Graph Neural Networks (GNNs) to model the adoption of products by utilizing both topological and attribute information. The resulting Dynamic Viral Marketing (DVM) problem seeks to find the minimum budget and minimal set of dynamic topological and attribute changes in order to attain a specified adoption goal. We show that DVM is NP-Hard and is related to the existing influence maximization problem. Motivated by this connection, we develop the idea of Dynamic Gradient Influencing (DGI) that uses gradient ranking to find optimal perturbations and targets low-budget and high influence non-adopters in discrete steps. We use an efficient strategy for computing node budgets and develop the ''Meta-Influence'' heuristic for assessing a node's downstream influence. We evaluate DGI against multiple baselines and demonstrate gains on average of 24% on budget and 37% on AUC on real-world attributed networks. Our code is publicly available at https://github.com/saurabhsharma1993/dynamic_viral_marketing.

Aritra Bhowmick, Mert Kosan, Zexi Huang et al.

Graph clustering is a fundamental and challenging task in the field of graph mining where the objective is to group the nodes into clusters taking into consideration the topology of the graph. It has several applications in diverse domains spanning social network analysis, recommender systems, computer vision, and bioinformatics. In this work, we propose a novel method, DGCluster, which primarily optimizes the modularity objective using graph neural networks and scales linearly with the graph size. Our method does not require the number of clusters to be specified as a part of the input and can also leverage the availability of auxiliary node level information. We extensively test DGCluster on several real-world datasets of varying sizes, across multiple popular cluster quality metrics. Our approach consistently outperforms the state-of-the-art methods, demonstrating significant performance gains in almost all settings.

Abed K. Musaffar, Ambuj Singh, Francesco Bullo

Large language models (LLMs) are increasingly deployed in human-AI teams as support agents for complex tasks such as information retrieval, programming, and decision-making assistance. While these agents' autonomy and contextual knowledge enables them to be useful, it also exposes them to a broad range of attacks, including data poisoning, prompt injection, and even prompt engineering. Through these attack vectors, malicious actors can manipulate an LLM agent to provide harmful information, potentially manipulating human agents to make harmful decisions. While prior work has focused on LLMs as attack targets or adversarial actors, this paper studies their potential role as defensive supervisors within mixed human-AI teams. Using a dataset consisting of multi-party conversations and decisions for a real human-AI team over a 25 round horizon, we formulate the problem of malicious behavior detection from interaction traces. We find that LLMs are capable of identifying malicious behavior in real-time, and without task-specific information, indicating the potential for task-agnostic defense. Moreover, we find that the malicious behavior of interest is not easily identified using simple heuristics, further suggesting the introduction of LLM defenders could render human teams more robust to certain classes of attack.

Saurabh Sharma, Ambuj Singh

Understanding how complex behaviors, opinions, and innovations spread in online social networks remains a central challenge in computational social science. Existing models of complex contagion typically rely on stylized threshold mechanisms based solely on the number of infected neighbors and do not account for the interaction between individual preferences, local social influence, and global sentiment. Moreover, the emergence of virality through phase transitions and tipping points remains poorly characterized. In this paper, we propose a unified propagation cascade model in which notions propagate as high-dimensional vectors in the same feature space as network nodes. Node activations are governed by a unified decision function that integrates propagation affinity, local influence, and global influence. The resulting dynamics induce a stochastic, Markovian cascade process that enables efficient MCMC sampling of propagation outcomes. Using preferential attachment networks, we systematically study spread distributions, incubation dynamics, parameter sensitivity, and phase transition behavior. Our results show that balanced interactions between local reinforcement and global activation are critical for successful cascades and that early-stage growth patterns provide reliable signals of impending phase transitions.

Sean Jaffe, Alexander Davydov, Deniz Lapsekili et al.

Global stability and robustness guarantees in learned dynamical systems are essential to ensure well-behavedness of the systems in the face of uncertainty. We present Extended Linearized Contracting Dynamics (ELCD), the first neural network-based dynamical system with global contractivity guarantees in arbitrary metrics. The key feature of ELCD is a parametrization of the extended linearization of the nonlinear vector field. In its most basic form, ELCD is guaranteed to be (i) globally exponentially stable, (ii) equilibrium contracting, and (iii) globally contracting with respect to some metric. To allow for contraction with respect to more general metrics in the data space, we train diffeomorphisms between the data space and a latent space and enforce contractivity in the latent space, which ensures global contractivity in the data space. We demonstrate the performance of ELCD on the high dimensional LASA, multi-link pendulum, and Rosenbrock datasets.

João Mattos, Zexi Huang, Mert Kosan et al.

Link prediction is a fundamental problem in graph data. In its most realistic setting, the problem consists of predicting missing or future links between random pairs of nodes from the set of disconnected pairs. Graph Neural Networks (GNNs) have become the predominant framework for link prediction. GNN-based methods treat link prediction as a binary classification problem and handle the extreme class imbalance -- real graphs are very sparse -- by sampling (uniformly at random) a balanced number of disconnected pairs not only for training but also for evaluation. However, we show that the reported performance of GNNs for link prediction in the balanced setting does not translate to the more realistic imbalanced setting and that simpler topology-based approaches are often better at handling sparsity. These findings motivate Gelato, a similarity-based link-prediction method that applies (1) graph learning based on node attributes to enhance a topological heuristic, (2) a ranking loss for addressing class imbalance, and (3) a negative sampling scheme that efficiently selects hard training pairs via graph partitioning. Experiments show that Gelato outperforms existing GNN-based alternatives.

Christos Zangos, Danish Ebadulla, Thomas Christopher Sprague et al.

This work introduces a novel approach to fMRI-based visual image reconstruction using a subject-agnostic common representation space. We show that the brain signals of the subjects can be aligned in this common space during training to form a semantically aligned common brain. This is leveraged to demonstrate that aligning subject-specific lightweight modules to a reference subject is significantly more efficient than traditional end-to-end training methods. Our approach excels in low-data scenarios. We evaluate our methods on different datasets, demonstrating that the common space is subject and dataset-agnostic.

Danish Ebadulla, Aditya Gulati, Ambuj Singh

We introduce a manifold analysis technique for neural network representations. Normalized Space Alignment (NSA) compares pairwise distances between two point clouds derived from the same source and having the same size, while potentially possessing differing dimensionalities. NSA can act as both an analytical tool and a differentiable loss function, providing a robust means of comparing and aligning representations across different layers and models. It satisfies the criteria necessary for both a similarity metric and a neural network loss function. We showcase NSA's versatility by illustrating its utility as a representation space analysis metric, a structure-preserving loss function, and a robustness analysis tool. NSA is not only computationally efficient but it can also approximate the global structural discrepancy during mini-batching, facilitating its use in a wide variety of neural network training paradigms.

Kha-Dinh Luong, Mert Kosan, Arlei Lopes Da Silva et al.

Explaining the decisions made by machine learning models for high-stakes applications is critical for increasing transparency and guiding improvements to these decisions. This is particularly true in the case of models for graphs, where decisions often depend on complex patterns combining rich structural and attribute data. While recent work has focused on designing so-called post-hoc explainers, the broader question of what constitutes a good explanation remains open. One intuitive property is that explanations should be sufficiently informative to reproduce the predictions given the data. In other words, a good explainer can be repurposed as a predictor. Post-hoc explainers do not achieve this goal as their explanations are highly dependent on fixed model parameters (e.g., learned GNN weights). To address this challenge, we propose RAGE (Robust Ante-hoc Graph Explainer), a novel and flexible ante-hoc explainer designed to discover explanations for graph neural networks using bilevel optimization, with a focus on the chemical domain. RAGE can effectively identify molecular substructures that contain the full information needed for prediction while enabling users to rank these explanations in terms of relevance. Our experiments on various molecular classification tasks show that RAGE explanations are better than existing post-hoc and ante-hoc approaches.

Zexi Huang, Mert Kosan, Arlei Silva et al.

Link prediction, which consists of predicting edges based on graph features, is a fundamental task in many graph applications. As for several related problems, Graph Neural Networks (GNNs), which are based on an attribute-centric message-passing paradigm, have become the predominant framework for link prediction. GNNs have consistently outperformed traditional topology-based heuristics, but what contributes to their performance? Are there simpler approaches that achieve comparable or better results? To answer these questions, we first identify important limitations in how GNN-based link prediction methods handle the intrinsic class imbalance of the problem -- due to the graph sparsity -- in their training and evaluation. Moreover, we propose Gelato, a novel topology-centric framework that applies a topological heuristic to a graph enhanced by attribute information via graph learning. Our model is trained end-to-end with an N-pair loss on an unbiased training set to address class imbalance. Experiments show that Gelato is 145% more accurate, trains 11 times faster, infers 6,000 times faster, and has less than half of the trainable parameters compared to state-of-the-art GNNs for link prediction.

Wei Ye, Zexi Huang, Yunqi Hong et al.

Graph Convolutional Networks (GCN) is a pioneering model for graph-based semi-supervised learning. However, GCN does not perform well on sparsely-labeled graphs. Its two-layer version cannot effectively propagate the label information to the whole graph structure (i.e., the under-smoothing problem) while its deep version over-smoothens and is hard to train (i.e., the over-smoothing problem). To solve these two issues, we propose a new graph neural network called GND-Nets (for Graph Neural Diffusion Networks) that exploits the local and global neighborhood information of a vertex in a single layer. Exploiting the shallow network mitigates the over-smoothing problem while exploiting the local and global neighborhood information mitigates the under-smoothing problem. The utilization of the local and global neighborhood information of a vertex is achieved by a new graph diffusion method called neural diffusions, which integrate neural networks into the conventional linear and nonlinear graph diffusions. The adoption of neural networks makes neural diffusions adaptable to different datasets. Extensive experiments on various sparsely-labeled graphs verify the effectiveness and efficiency of GND-Nets compared to state-of-the-art approaches.

Zexi Huang, Arlei Silva, Ambuj Singh

Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify opportunities to advance the state-of-the-art. Meanwhile, existing work has left several fundamental questions -- such as how embeddings capture different structural scales and how they should be applied for effective link prediction -- unanswered. This paper addresses these challenges with an analytical framework for random-walk based graph embedding that consists of three components: a random-walk process, a similarity function, and an embedding algorithm. Our framework not only categorizes many existing approaches but naturally motivates new ones. With it, we illustrate novel ways to incorporate embeddings at multiple scales to improve downstream task performance. We also show that embeddings based on autocovariance similarity, when paired with dot product ranking for link prediction, outperform state-of-the-art methods based on Pointwise Mutual Information similarity by up to 100%.

Mert Kosan, Arlei Silva, Sourav Medya et al.

Event detection is a critical task for timely decision-making in graph analytics applications. Despite the recent progress towards deep learning on graphs, event detection on dynamic graphs presents particular challenges to existing architectures. Real-life events are often associated with sudden deviations of the normal behavior of the graph. However, existing approaches for dynamic node embedding are unable to capture the graph-level dynamics related to events. In this paper, we propose DyGED, a simple yet novel deep learning model for event detection on dynamic graphs. DyGED learns correlations between the graph macro dynamics -- i.e. a sequence of graph-level representations -- and labeled events. Moreover, our approach combines structural and temporal self-attention mechanisms to account for application-specific node and time importances effectively. Our experimental evaluation, using a representative set of datasets, demonstrates that DyGED outperforms competing solutions in terms of event detection accuracy by up to 8.5% while being more scalable than the top alternatives. We also present case studies illustrating key features of our model.

Zexi Huang, Arlei Silva, Ambuj Singh

From the 2016 U.S. presidential election to the 2021 Capitol riots to the spread of misinformation related to COVID-19, many have blamed social media for today's deeply divided society. Recent advances in machine learning for signed networks hold the promise to guide small interventions with the goal of reducing polarization in social media. However, existing models are especially ineffective in predicting conflicts (or negative links) among users. This is due to a strong correlation between link signs and the network structure, where negative links between polarized communities are too sparse to be predicted even by state-of-the-art approaches. To address this problem, we first design a partition-agnostic polarization measure for signed graphs based on the signed random-walk and show that many real-world graphs are highly polarized. Then, we propose POLE (POLarized Embedding for signed networks), a signed embedding method for polarized graphs that captures both topological and signed similarities jointly via signed autocovariance. Through extensive experiments, we show that POLE significantly outperforms state-of-the-art methods in signed link prediction, particularly for negative links with gains of up to one order of magnitude.

Wei Ye, Omid Askarisichani, Alex Jones et al.

Graph-structured data arise in many scenarios. A fundamental problem is to quantify the similarities of graphs for tasks such as classification. R-convolution graph kernels are positive-semidefinite functions that decompose graphs into substructures and compare them. One problem in the effective implementation of this idea is that the substructures are not independent, which leads to high-dimensional feature space. In addition, graph kernels cannot capture the high-order complex interactions between vertices. To mitigate these two problems, we propose a framework called DeepMap to learn deep representations for graph feature maps. The learned deep representation for a graph is a dense and low-dimensional vector that captures complex high-order interactions in a vertex neighborhood. DeepMap extends Convolutional Neural Networks (CNNs) to arbitrary graphs by generating aligned vertex sequences and building the receptive field for each vertex. We empirically validate DeepMap on various graph classification benchmarks and demonstrate that it achieves state-of-the-art performance.

Wei Ye, Dominik Mautz, Christian Boehm et al.

Graph clustering has been studied extensively on both plain graphs and attributed graphs. However, all these methods need to partition the whole graph to find cluster structures. Sometimes, based on domain knowledge, people may have information about a specific target region in the graph and only want to find a single cluster concentrated on this local region. Such a task is called local clustering. In contrast to global clustering, local clustering aims to find only one cluster that is concentrating on the given seed vertex (and also on the designated attributes for attributed graphs). Currently, very few methods can deal with this kind of task. To this end, we propose two quality measures for a local cluster: Graph Unimodality (GU) and Attribute Unimodality (AU). The former measures the homogeneity of the graph structure while the latter measures the homogeneity of the subspace that is composed of the designated attributes. We call their linear combination as Compactness. Further, we propose LOCLU to optimize the Compactness score. The local cluster detected by LOCLU concentrates on the region of interest, provides efficient information flow in the graph and exhibits a unimodal data distribution in the subspace of the designated attributes.

Wei Ye, Zhen Wang, Rachel Redberg et al.

Graph-structured data arise ubiquitously in many application domains. A fundamental problem is to quantify their similarities. Graph kernels are often used for this purpose, which decompose graphs into substructures and compare these substructures. However, most of the existing graph kernels do not have the property of scale-adaptivity, i.e., they cannot compare graphs at multiple levels of granularities. Many real-world graphs such as molecules exhibit structure at varying levels of granularities. To tackle this problem, we propose a new graph kernel called Tree++ in this paper. At the heart of Tree++ is a graph kernel called the path-pattern graph kernel. The path-pattern graph kernel first builds a truncated BFS tree rooted at each vertex and then uses paths from the root to every vertex in the truncated BFS tree as features to represent graphs. The path-pattern graph kernel can only capture graph similarity at fine granularities. In order to capture graph similarity at coarse granularities, we incorporate a new concept called super path into it. The super path contains truncated BFS trees rooted at the vertices in a path. Our evaluation on a variety of real-world graphs demonstrates that Tree++ achieves the best classification accuracy compared with previous graph kernels.

Sahil Manchanda, Akash Mittal, Anuj Dhawan et al.

There has been an increased interest in discovering heuristics for combinatorial problems on graphs through machine learning. While existing techniques have primarily focused on obtaining high-quality solutions, scalability to billion-sized graphs has not been adequately addressed. In addition, the impact of budget-constraint, which is necessary for many practical scenarios, remains to be studied. In this paper, we propose a framework called GCOMB to bridge these gaps. GCOMB trains a Graph Convolutional Network (GCN) using a novel probabilistic greedy mechanism to predict the quality of a node. To further facilitate the combinatorial nature of the problem, GCOMB utilizes a Q-learning framework, which is made efficient through importance sampling. We perform extensive experiments on real graphs to benchmark the efficiency and efficacy of GCOMB. Our results establish that GCOMB is 100 times faster and marginally better in quality than state-of-the-art algorithms for learning combinatorial algorithms. Additionally, a case-study on the practical combinatorial problem of Influence Maximization (IM) shows GCOMB is 150 times faster than the specialized IM algorithm IMM with similar quality.

Xuan-Hong Dang, Arlei Silva, Ambuj Singh et al.

Detecting a small number of outliers from a set of data observations is always challenging. This problem is more difficult in the setting of multiple network samples, where computing the anomalous degree of a network sample is generally not sufficient. In fact, explaining why the network is exceptional, expressed in the form of subnetwork, is also equally important. In this paper, we develop a novel algorithm to address these two key problems. We treat each network sample as a potential outlier and identify subnetworks that mostly discriminate it from nearby regular samples. The algorithm is developed in the framework of network regression combined with the constraints on both network topology and L1-norm shrinkage to perform subnetwork discovery. Our method thus goes beyond subspace/subgraph discovery and we show that it converges to a global optimum. Evaluation on various real-world network datasets demonstrates that our algorithm not only outperforms baselines in both network and high dimensional setting, but also discovers highly relevant and interpretable local subnetworks, further enhancing our understanding of anomalous networks.

Victor Amelkin, Ambuj Singh, Petko Bogdanov

Analysis of opinion dynamics in social networks plays an important role in today's life. For applications such as predicting users' political preference, it is particularly important to be able to analyze the dynamics of competing opinions. While observing the evolution of polar opinions of a social network's users over time, can we tell when the network "behaved" abnormally? Furthermore, can we predict how the opinions of the users will change in the future? Do opinions evolve according to existing network opinion dynamics models? To answer such questions, it is not sufficient to study individual user behavior, since opinions can spread far beyond users' egonets. We need a method to analyze opinion dynamics of all network users simultaneously and capture the effect of individuals' behavior on the global evolution pattern of the social network. In this work, we introduce Social Network Distance (SND) - a distance measure that quantifies the "cost" of evolution of one snapshot of a social network into another snapshot under various models of polar opinion propagation. SND has a rich semantics of a transportation problem, yet, is computable in time linear in the number of users, which makes SND applicable to the analysis of large-scale online social networks. In our experiments with synthetic and real-world Twitter data, we demonstrate the utility of our distance measure for anomalous event detection. It achieves a true positive rate of 0.83, twice as high as that of alternatives. When employed for opinion prediction in Twitter, our method's accuracy is 75.63%, which is 7.5% higher than that of the next best method. Source Code: https://cs.ucsb.edu/~victor/pub/ucsb/dbl/snd/