Reconstruction of Graph Signals on Complex Manifolds with Kernel Methods

• URL: http://arxiv.org/abs/2505.15202v1
• Date: Wed, 21 May 2025 07:27:38 GMT
• Title: Reconstruction of Graph Signals on Complex Manifolds with Kernel Methods
• Authors: Yu Zhang, Linyu Peng, Bing-Zhao Li,
• Abstract summary: Graph signal processing (GSP) has emerged to facilitate the analysis, processing, and sampling of such signals.<n>This paper introduces a novel framework for reconstructing graph signals using kernel methods on complex manifold.<n>Results on synthetic and real-world datasets demonstrate the effectiveness of this framework.
• Score: 6.923559193433016
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Graph signals are widely used to describe vertex attributes or features in graph-structured data, with applications spanning the internet, social media, transportation, sensor networks, and biomedicine. Graph signal processing (GSP) has emerged to facilitate the analysis, processing, and sampling of such signals. While kernel methods have been extensively studied for estimating graph signals from samples provided on a subset of vertices, their application to complex-valued graph signals remains largely unexplored. This paper introduces a novel framework for reconstructing graph signals using kernel methods on complex manifolds. By embedding graph vertices into a higher-dimensional complex ambient space that approximates a lower-dimensional manifold, the framework extends the reproducing kernel Hilbert space to complex manifolds. It leverages Hermitian metrics and geometric measures to characterize kernels and graph signals. Additionally, several traditional kernels and graph topology-driven kernels are proposed for reconstructing complex graph signals. Finally, experimental results on synthetic and real-world datasets demonstrate the effectiveness of this framework in accurately reconstructing complex graph signals, outperforming conventional kernel-based approaches. This work lays a foundational basis for integrating complex geometry and kernel methods in GSP.

Related papers

• Bespoke multiresolution analysis of graph signals [0.0]
  We present a novel framework for discrete multiresolution analysis of graph signals.<n>The main analytical tool is the samplet transform, originally defined in the Euclidean framework as a discrete wavelet-like construction.<n>For efficient numerical implementation, we combine heavy edge clustering, to partition the graph into meaningful patches.
  arXiv  Detail & Related papers  (2025-07-25T11:43:19Z)
• Learning graphs and simplicial complexes from data [26.926502862698168]
  We present a novel method to infer the underlying graph topology from available data. We also identify three-node interactions, referred to in the literature as second-order simplicial complexes (SCs) Experimental results on synthetic and real-world data showcase a superior performance for our approach compared to existing methods.
  arXiv  Detail & Related papers  (2023-12-16T22:02:20Z)
• Improving embedding of graphs with missing data by soft manifolds [51.425411400683565]
  The reliability of graph embeddings depends on how much the geometry of the continuous space matches the graph structure. We introduce a new class of manifold, named soft manifold, that can solve this situation. Using soft manifold for graph embedding, we can provide continuous spaces to pursue any task in data analysis over complex datasets.
  arXiv  Detail & Related papers  (2023-11-29T12:48:33Z)
• Kernel-based Joint Multiple Graph Learning and Clustering of Graph Signals [2.4305626489408465]
  We introduce Kernel-based joint Multiple GL and clustering of graph signals applications. Experiments demonstrate that KMGL significantly enhances the robustness of GL clustering, particularly in scenarios with high noise levels. These findings underscore the potential of KMGL for improving the performance of Graph Signal Processing methods in diverse real-world applications.
  arXiv  Detail & Related papers  (2023-10-29T13:41:12Z)
• Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphs [131.53471236405628]
  We present three methods that exploit the induced graphon representation of graphs and graph signals on partitions of [0, 1]2 in the graphon space. We prove that those low dimensional representations constitute a convergent sequence of graphs and graph signals. We observe that graphon pooling performs significantly better than other approaches proposed in the literature when dimensionality reduction ratios between layers are large.
  arXiv  Detail & Related papers  (2022-12-15T22:11:34Z)
• Convolutional Learning on Multigraphs [153.20329791008095]
  We develop convolutional information processing on multigraphs and introduce convolutional multigraph neural networks (MGNNs) To capture the complex dynamics of information diffusion within and across each of the multigraph's classes of edges, we formalize a convolutional signal processing model. We develop a multigraph learning architecture, including a sampling procedure to reduce computational complexity. The introduced architecture is applied towards optimal wireless resource allocation and a hate speech localization task, offering improved performance over traditional graph neural networks.
  arXiv  Detail & Related papers  (2022-09-23T00:33:04Z)
• Dist2Cycle: A Simplicial Neural Network for Homology Localization [66.15805004725809]
  Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations. We propose a graph convolutional model for learning functions parametrized by the $k$-homological features of simplicial complexes.
  arXiv  Detail & Related papers  (2021-10-28T14:59:41Z)
• 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)
• Sparse Partial Least Squares for Coarse Noisy Graph Alignment [10.172041234280865]
  Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. We propose a novel regularized partial least squares method which both incorporates the observed graph structures and imposes sparsity in order to reflect the underlying block community structure.
  arXiv  Detail & Related papers  (2021-04-06T21:52:15Z)
• Graph Pooling with Node Proximity for Hierarchical Representation Learning [80.62181998314547]
  We propose a novel graph pooling strategy that leverages node proximity to improve the hierarchical representation learning of graph data with their multi-hop topology. Results show that the proposed graph pooling strategy is able to achieve state-of-the-art performance on a collection of public graph classification benchmark datasets.
  arXiv  Detail & Related papers  (2020-06-19T13:09:44Z)

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.