arXiv subjects

Fanchen Bu

Publications and source records attributed to Fanchen Bu.

27 records · Page 2Linked to original sources

arXiv2023

Robust Graph Clustering via Meta Weighting for Noisy Graphs

How can we find meaningful clusters in a graph robustly against noise edges? Graph clustering (i.e., dividing nodes into groups of similar ones) is a fundamental problem in graph analysis with applications in various fields. Recent studies have demonstrated that graph neural network (GNN) based approaches yield promising results for graph clustering. However, we observe that their performance degenerates significantly on graphs with noise edges, which are prevalent in practice. In this work, we propose MetaGC for robust GNN-based graph clustering. MetaGC employs a decomposable clustering loss function, which can be rephrased as a sum of losses over node pairs. We add a learnable weight to each node pair, and MetaGC adaptively adjusts the weights of node pairs using meta-weighting so that the weights of meaningful node pairs increase and the weights of less-meaningful ones (e.g., noise edges) decrease. We show empirically that MetaGC learns weights as intended and consequently outperforms the state-of-the-art GNN-based competitors, even when they are equipped with separate denoising schemes, on five real-world graphs under varying levels of noise. Our code and datasets are available at https://github.com/HyeonsooJo/MetaGC.

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arXiv2023

How Transitive Are Real-World Group Interactions? -- Measurement and Reproduction

Many real-world interactions (e.g., researcher collaborations and email communication) occur among multiple entities. These group interactions are naturally modeled as hypergraphs. In graphs, transitivity is helpful to understand the connections between node pairs sharing a neighbor, and it has extensive applications in various domains. Hypergraphs, an extension of graphs, are designed to represent group relations. However, to the best of our knowledge, there has been no examination regarding the transitivity of real-world group interactions. In this work, we investigate the transitivity of group interactions in real-world hypergraphs. We first suggest intuitive axioms as necessary characteristics of hypergraph transitivity measures. Then, we propose a principled hypergraph transitivity measure HyperTrans, which satisfies all the proposed axioms, with a fast computation algorithm Fast-HyperTrans. After that, we analyze the transitivity patterns in real-world hypergraphs distinguished from those in random hypergraphs. Lastly, we propose a scalable hypergraph generator THera. It reproduces the observed transitivity patterns by leveraging community structures, which are pervasive in real-world hypergraphs. Our code and datasets are available at https://github.com/kswoo97/hypertrans.

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arXiv2023

On Improving the Cohesiveness of Graphs by Merging Nodes: Formulation, Analysis, and Algorithms

Graphs are a powerful mathematical model, and they are used to represent real-world structures in various fields. In many applications, real-world structures with high connectivity and robustness are preferable. For enhancing the connectivity and robustness of graphs, two operations, adding edges and anchoring nodes, have been extensively studied. However, merging nodes, which is a realistic operation in many scenarios (e.g., bus station reorganization, multiple team formation), has been overlooked. In this work, we study the problem of improving graph cohesiveness by merging nodes. First, we formulate the problem mathematically using the size of the $k$-truss, for a given $k$, as the objective. Then, we prove the NP-hardness and non-modularity of the problem. After that, we develop BATMAN, a fast and effective algorithm for choosing sets of nodes to be merged, based on our theoretical findings and empirical observations. Lastly, we demonstrate the superiority of BATMAN over several baselines, in terms of speed and effectiveness, through extensive experiments on fourteen real-world graphs.

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arXiv2023

Towards Deep Attention in Graph Neural Networks: Problems and Remedies

Graph neural networks (GNNs) learn the representation of graph-structured data, and their expressiveness can be further enhanced by inferring node relations for propagation. Attention-based GNNs infer neighbor importance to manipulate the weight of its propagation. Despite their popularity, the discussion on deep graph attention and its unique challenges has been limited. In this work, we investigate some problematic phenomena related to deep graph attention, including vulnerability to over-smoothed features and smooth cumulative attention. Through theoretical and empirical analyses, we show that various attention-based GNNs suffer from these problems. Motivated by our findings, we propose AEROGNN, a novel GNN architecture designed for deep graph attention. AERO-GNN provably mitigates the proposed problems of deep graph attention, which is further empirically demonstrated with (a) its adaptive and less smooth attention functions and (b) higher performance at deep layers (up to 64). On 9 out of 12 node classification benchmarks, AERO-GNN outperforms the baseline GNNs, highlighting the advantages of deep graph attention. Our code is available at https://github.com/syleeheal/AERO-GNN.

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arXiv2023

Interplay between Topology and Edge Weights in Real-World Graphs: Concepts, Patterns, and an Algorithm

What are the relations between the edge weights and the topology in real-world graphs? Given only the topology of a graph, how can we assign realistic weights to its edges based on the relations? Several trials have been done for edge-weight prediction where some unknown edge weights are predicted with most edge weights known. There are also existing works on generating both topology and edge weights of weighted graphs. Differently, we are interested in generating edge weights that are realistic in a macroscopic scope, merely from the topology, which is unexplored and challenging. To this end, we explore and exploit the patterns involving edge weights and topology in real-world graphs. Specifically, we divide each graph into layers where each layer consists of the edges with weights at least a threshold. We observe consistent and surprising patterns appearing in multiple layers: the similarity between being adjacent and having high weights, and the nearly-linear growth of the fraction of edges having high weights with the number of common neighbors. We also observe a power-law pattern that connects the layers. Based on the observations, we propose PEAR, an algorithm assigning realistic edge weights to a given topology. The algorithm relies on only two parameters, preserves all the observed patterns, and produces more realistic weights than the baseline methods with more parameters.

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arXiv2023

Hypercore Decomposition for Non-Fragile Hyperedges: Concepts, Algorithms, Observations, and Applications

Hypergraphs are a powerful abstraction for modeling high-order relations, which are ubiquitous in many fields. A hypergraph consists of nodes and hyperedges (i.e., subsets of nodes); and there have been a number of attempts to extend the notion of $k$-cores, which proved useful with numerous applications for pairwise graphs, to hypergraphs. However, the previous extensions are based on an unrealistic assumption that hyperedges are fragile, i.e., a high-order relation becomes obsolete as soon as a single member leaves it. In this work, we propose a new substructure model, called ($k$, $t$)-hypercore, based on the assumption that high-order relations remain as long as at least $t$ fraction of the members remain. Specifically, it is defined as the maximal subhypergraph where (1) every node is contained in at least $k$ hyperedges in it and (2) at least $t$ fraction of the nodes remain in every hyperedge. We first prove that, given $t$ (or $k$), finding the ($k$, $t$)-hypercore for every possible $k$ (or $t$) can be computed in time linear w.r.t the sum of the sizes of hyperedges. Then, we demonstrate that real-world hypergraphs from the same domain share similar ($k$, $t$)-hypercore structures, which capture different perspectives depending on $t$. Lastly, we show the successful applications of our model in identifying influential nodes, dense substructures, and vulnerability in hypergraphs.

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arXiv2023

Characterization of Simplicial Complexes by Counting Simplets Beyond Four Nodes

Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we concentrate on the local patterns in simplicial complexes called simplets, a generalization of graphlets. We formulate the problem of counting simplets of a given size in a given simplicial complex. For this problem, we extend a sampling algorithm based on color coding from graphs to simplicial complexes, with essential technical novelty. We theoretically analyze our proposed algorithm named SC3, showing its correctness, unbiasedness, convergence, and time/space complexity. Through the extensive experiments on sixteen real-world datasets, we show the superiority of SC3 in terms of accuracy, speed, and scalability, compared to the baseline methods. Finally, we use the counts given by SC3 for simplicial complex analysis, especially for characterization, which is further used for simplicial complex clustering, where SC3 shows a strong ability of characterization with domain-based similarity.

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arXiv2022

Feedback Gradient Descent: Efficient and Stable Optimization with Orthogonality for DNNs

The optimization with orthogonality has been shown useful in training deep neural networks (DNNs). To impose orthogonality on DNNs, both computational efficiency and stability are important. However, existing methods utilizing Riemannian optimization or hard constraints can only ensure stability while those using soft constraints can only improve efficiency. In this paper, we propose a novel method, named Feedback Gradient Descent (FGD), to our knowledge, the first work showing high efficiency and stability simultaneously. FGD induces orthogonality based on the simple yet indispensable Euler discretization of a continuous-time dynamical system on the tangent bundle of the Stiefel manifold. In particular, inspired by a numerical integration method on manifolds called Feedback Integrators, we propose to instantiate it on the tangent bundle of the Stiefel manifold for the first time. In the extensive image classification experiments, FGD comprehensively outperforms the existing state-of-the-art methods in terms of accuracy, efficiency, and stability.

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arXiv2020

Double Prioritized State Recycled Experience Replay

Experience replay enables online reinforcement learning agents to store and reuse the previous experiences of interacting with the environment. In the original method, the experiences are sampled and replayed uniformly at random. A prior work called prioritized experience replay was developed where experiences are prioritized, so as to replay experiences seeming to be more important more frequently. In this paper, we develop a method called double-prioritized state-recycled (DPSR) experience replay, prioritizing the experiences in both training stage and storing stage, as well as replacing the experiences in the memory with state recycling to make the best of experiences that seem to have low priorities temporarily. We used this method in Deep Q-Networks (DQN), and achieved a state-of-the-art result, outperforming the original method and prioritized experience replay on many Atari games.

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