287 research outputs found
Beyond Real-world Benchmark Datasets: An Empirical Study of Node Classification with GNNs
Graph Neural Networks (GNNs) have achieved great success on a node
classification task. Despite the broad interest in developing and evaluating
GNNs, they have been assessed with limited benchmark datasets. As a result, the
existing evaluation of GNNs lacks fine-grained analysis from various
characteristics of graphs. Motivated by this, we conduct extensive experiments
with a synthetic graph generator that can generate graphs having controlled
characteristics for fine-grained analysis. Our empirical studies clarify the
strengths and weaknesses of GNNs from four major characteristics of real-world
graphs with class labels of nodes, i.e., 1) class size distributions (balanced
vs. imbalanced), 2) edge connection proportions between classes (homophilic vs.
heterophilic), 3) attribute values (biased vs. random), and 4) graph sizes
(small vs. large). In addition, to foster future research on GNNs, we publicly
release our codebase that allows users to evaluate various GNNs with various
graphs. We hope this work offers interesting insights for future research.Comment: Accepted to NeurIPS 2022 Datasets and Benchmarks Track. 21 pages, 15
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Contextual Centrality: Going Beyond Network Structures
Centrality is a fundamental network property which ranks nodes by their
structural importance. However, structural importance may not suffice to
predict successful diffusions in a wide range of applications, such as
word-of-mouth marketing and political campaigns. In particular, nodes with high
structural importance may contribute negatively to the objective of the
diffusion. To address this problem, we propose contextual centrality, which
integrates structural positions, the diffusion process, and, most importantly,
nodal contributions to the objective of the diffusion. We perform an empirical
analysis of the adoption of microfinance in Indian villages and weather
insurance in Chinese villages. Results show that contextual centrality of the
first-informed individuals has higher predictive power towards the eventual
adoption outcomes than other standard centrality measures. Interestingly, when
the product of diffusion rate and the largest eigenvalue is
larger than one and diffusion period is long, contextual centrality linearly
scales with eigenvector centrality. This approximation reveals that contextual
centrality identifies scenarios where a higher diffusion rate of individuals
may negatively influence the cascade payoff. Further simulations on the
synthetic and real-world networks show that contextual centrality has the
advantage of selecting an individual whose local neighborhood generates a high
cascade payoff when . Under this condition, stronger homophily
leads to higher cascade payoff. Our results suggest that contextual centrality
captures more complicated dynamics on networks and has significant implications
for applications, such as information diffusion, viral marketing, and political
campaigns
On Addressing the Limitations of Graph Neural Networks
This report gives a summary of two problems about graph convolutional
networks (GCNs): over-smoothing and heterophily challenges, and outlines future
directions to explore.Comment: arXiv admin note: substantial text overlap with arXiv:2109.05641,
arXiv:2210.0760
Equivariant Hypergraph Diffusion Neural Operators
Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs
provide a promising way to model higher-order relations in data and further
solve relevant prediction tasks built upon such higher-order relations.
However, higher-order relations in practice contain complex patterns and are
often highly irregular. So, it is often challenging to design an HNN that
suffices to express those relations while keeping computational efficiency.
Inspired by hypergraph diffusion algorithms, this work proposes a new HNN
architecture named ED-HNN, which provably represents any continuous equivariant
hypergraph diffusion operators that can model a wide range of higher-order
relations. ED-HNN can be implemented efficiently by combining star expansions
of hypergraphs with standard message passing neural networks. ED-HNN further
shows great superiority in processing heterophilic hypergraphs and constructing
deep models. We evaluate ED-HNN for node classification on nine real-world
hypergraph datasets. ED-HNN uniformly outperforms the best baselines over these
nine datasets and achieves more than 2\% in prediction accuracy over
four datasets therein.Comment: Code: https://github.com/Graph-COM/ED-HN
GPNet: Simplifying Graph Neural Networks via Multi-channel Geometric Polynomials
Graph Neural Networks (GNNs) are a promising deep learning approach for
circumventing many real-world problems on graph-structured data. However, these
models usually have at least one of four fundamental limitations:
over-smoothing, over-fitting, difficult to train, and strong homophily
assumption. For example, Simple Graph Convolution (SGC) is known to suffer from
the first and fourth limitations. To tackle these limitations, we identify a
set of key designs including (D1) dilated convolution, (D2) multi-channel
learning, (D3) self-attention score, and (D4) sign factor to boost learning
from different types (i.e. homophily and heterophily) and scales (i.e. small,
medium, and large) of networks, and combine them into a graph neural network,
GPNet, a simple and efficient one-layer model. We theoretically analyze the
model and show that it can approximate various graph filters by adjusting the
self-attention score and sign factor. Experiments show that GPNet consistently
outperforms baselines in terms of average rank, average accuracy, complexity,
and parameters on semi-supervised and full-supervised tasks, and achieves
competitive performance compared to state-of-the-art model with inductive
learning task.Comment: 15 pages, 15 figure
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