Geodesic Distance Between Graphs: A Spectral Metric for Assessing the Stability of Graph Neural Networks

• URL: http://arxiv.org/abs/2406.10500v2
• Date: Sat, 05 Oct 2024 03:38:01 GMT
• Title: Geodesic Distance Between Graphs: A Spectral Metric for Assessing the Stability of Graph Neural Networks
• Authors: Soumen Sikder Shuvo, Ali Aghdaei, Zhuo Feng,
• Abstract summary: We introduce a Graph Geodesic Distance (GGD) metric for assessing the generalization and stability of Graph Neural Networks (GNNs) We show that the proposed GGD metric can effectively quantify dissimilarities between two graphs by encapsulating their differences in key structural (spectral) properties. The proposed GGD metric shows significantly improved performance for stability evaluation of GNNs especially when only partial node features are available.
• Score: 4.110108749051657
• License:
• Abstract: This paper presents a spectral framework for assessing the generalization and stability of Graph Neural Networks (GNNs) by introducing a Graph Geodesic Distance (GGD) metric. For two different graphs with the same number of nodes, our framework leverages a spectral graph matching procedure to find node correspondence so that the geodesic distance between them can be subsequently computed by solving a generalized eigenvalue problem associated with their Laplacian matrices. For graphs with different sizes, a resistance-based spectral graph coarsening scheme is introduced to reduce the size of the bigger graph while preserving the original spectral properties. We show that the proposed GGD metric can effectively quantify dissimilarities between two graphs by encapsulating their differences in key structural (spectral) properties, such as effective resistances between nodes, cuts, the mixing time of random walks, etc. Through extensive experiments comparing with the state-of-the-art metrics, such as the latest Tree-Mover's Distance (TMD) metric, the proposed GGD metric shows significantly improved performance for stability evaluation of GNNs especially when only partial node features are available.

Related papers

• Generalization, Expressivity, and Universality of Graph Neural Networks on Attributed Graphs [33.266521866968304]
  We analyze the universality and generalization of graph neural networks (GNNs) on attributed graphs with node attributes. We prove a universal approximation theorem for GNNs and bounds generalization for GNNs on any data distribution of attributed graphs. Our work extends and unites previous approaches which either derived theory only for graphs with no attributes, derived compact metrics under which GNNs are continuous but without separation power, or derived metrics under which GNNs are continuous and separate points.
  arXiv  Detail & Related papers  (2024-11-08T10:34:24Z)
• Spectral Greedy Coresets for Graph Neural Networks [61.24300262316091]
  The ubiquity of large-scale graphs in node-classification tasks hinders the real-world applications of Graph Neural Networks (GNNs) This paper studies graph coresets for GNNs and avoids the interdependence issue by selecting ego-graphs based on their spectral embeddings. Our spectral greedy graph coreset (SGGC) scales to graphs with millions of nodes, obviates the need for model pre-training, and applies to low-homophily graphs.
  arXiv  Detail & Related papers  (2024-05-27T17:52:12Z)
• Graph GOSPA metric: a metric to measure the discrepancy between graphs of different sizes [3.8823562292981393]
  This paper proposes a metric to measure the dissimilarity between graphs that may have a different number of nodes. The proposed graph GOSPA metric includes costs associated with node attribute errors for properly assigned nodes, missed and false nodes and edge mismatches between graphs.
  arXiv  Detail & Related papers  (2023-11-10T11:40:24Z)
• Stable and Transferable Hyper-Graph Neural Networks [95.07035704188984]
  We introduce an architecture for processing signals supported on hypergraphs via graph neural networks (GNNs) We provide a framework for bounding the stability and transferability error of GNNs across arbitrary graphs via spectral similarity.
  arXiv  Detail & Related papers  (2022-11-11T23:44:20Z)
• A Spectral Analysis of Graph Neural Networks on Dense and Sparse Graphs [13.954735096637298]
  We analyze how sparsity affects the graph spectra, and thus the performance of graph neural networks (GNNs) in node classification on dense and sparse graphs. We show that GNNs can outperform spectral methods on sparse graphs, and illustrate these results with numerical examples on both synthetic and real graphs.
  arXiv  Detail & Related papers  (2022-11-06T22:38:13Z)
• Tree Mover's Distance: Bridging Graph Metrics and Stability of Graph Neural Networks [54.225220638606814]
  We propose a pseudometric for attributed graphs, the Tree Mover's Distance (TMD), and study its relation to generalization. First, we show that TMD captures properties relevant to graph classification; a simple TMD-SVM performs competitively with standard GNNs. Second, we relate TMD to generalization of GNNs under distribution shifts, and show that it correlates well with performance drop under such shifts.
  arXiv  Detail & Related papers  (2022-10-04T21:03:52Z)
• Graph Spectral Embedding using the Geodesic Betweeness Centrality [76.27138343125985]
  We introduce the Graph Sylvester Embedding (GSE), an unsupervised graph representation of local similarity, connectivity, and global structure. GSE uses the solution of the Sylvester equation to capture both network structure and neighborhood proximity in a single representation.
  arXiv  Detail & Related papers  (2022-05-07T04:11:23Z)
• SIGMA: A Structural Inconsistency Reducing Graph Matching Algorithm [21.1095092767297]
  We propose a novel criterion to measure the graph matching accuracy, structural inconsistency (SI) Specifically, SI incorporates the heat diffusion wavelet to accommodate the multi-hop structure of the graphs. We show that SIGMA can be derived by using a mirror descent method to solve the Gromov-Wasserstein distance with a novel K-hop-structure-based matching costs.
  arXiv  Detail & Related papers  (2022-02-06T15:18:37Z)
• Graph Neural Networks with Feature and Structure Aware Random Walk [7.143879014059894]
  We show that in typical heterphilous graphs, the edges may be directed, and whether to treat the edges as is or simply make them undirected greatly affects the performance of the GNN models. We develop a model that adaptively learns the directionality of the graph, and exploits the underlying long-distance correlations between nodes.
  arXiv  Detail & Related papers  (2021-11-19T08:54:21Z)
• Spectral-Spatial Global Graph Reasoning for Hyperspectral Image Classification [50.899576891296235]
  Convolutional neural networks have been widely applied to hyperspectral image classification. Recent methods attempt to address this issue by performing graph convolutions on spatial topologies.
  arXiv  Detail & Related papers  (2021-06-26T06:24:51Z)
• Graphon Pooling in Graph Neural Networks [169.09536309161314]
  Graph neural networks (GNNs) have been used effectively in different applications involving the processing of signals on irregular structures modeled by graphs. We propose a new strategy for pooling and sampling on GNNs using graphons which preserves the spectral properties of the graph.
  arXiv  Detail & Related papers  (2020-03-03T21:04:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.