Graph Signal Inference by Learning Narrowband Spectral Kernels

• URL: http://arxiv.org/abs/2502.13686v1
• Date: Wed, 19 Feb 2025 12:54:39 GMT
• Title: Graph Signal Inference by Learning Narrowband Spectral Kernels
• Authors: Osman Furkan Kar, Gülce Turhan, Elif Vural,
• Abstract summary: We propose a novel graph signal model where the signal spectrum is represented through the combination of narrowband kernels in the graph frequency domain. We show that the proposed method offers quite satisfactory signal accuracy in comparison with a variety of reference approaches in the literature.
• Score: 1.740992908651449
• License:
• Abstract: While a common assumption in graph signal analysis is the smoothness of the signals or the band-limitedness of their spectrum, in many instances the spectrum of real graph data may be concentrated at multiple regions of the spectrum, possibly including mid-to-high-frequency components. In this work, we propose a novel graph signal model where the signal spectrum is represented through the combination of narrowband kernels in the graph frequency domain. We then present an algorithm that jointly learns the model by optimizing the kernel parameters and the signal representation coefficients from a collection of graph signals. Our problem formulation has the flexibility of permitting the incorporation of signals possibly acquired on different graphs into the learning algorithm. We then theoretically study the signal reconstruction performance of the proposed method, by also elaborating on when joint learning on multiple graphs is preferable to learning an individual model on each graph. Experimental results on several graph data sets shows that the proposed method offers quite satisfactory signal interpolation accuracy in comparison with a variety of reference approaches in the literature.

Related papers

• Graph-Dictionary Signal Model for Sparse Representations of Multivariate Data [49.77103348208835]
  We define a novel Graph-Dictionary signal model, where a finite set of graphs characterizes relationships in data distribution through a weighted sum of their Laplacians. We propose a framework to infer the graph dictionary representation from observed data, along with a bilinear generalization of the primal-dual splitting algorithm to solve the learning problem. We exploit graph-dictionary representations in a motor imagery decoding task on brain activity data, where we classify imagined motion better than standard methods.
  arXiv  Detail & Related papers  (2024-11-08T17:40:43Z)
• Graph Laplacian Learning with Exponential Family Noise [8.594140167290098]
  We propose a versatile graph inference framework for learning from graph signals corrupted by exponential family noise. Our framework generalizes previous methods from continuous smooth graph signals to various data types.
  arXiv  Detail & Related papers  (2023-06-14T02:09:52Z)
• Spectral Augmentations for Graph Contrastive Learning [50.149996923976836]
  Contrastive learning has emerged as a premier method for learning representations with or without supervision. Recent studies have shown its utility in graph representation learning for pre-training. We propose a set of well-motivated graph transformation operations to provide a bank of candidates when constructing augmentations for a graph contrastive objective.
  arXiv  Detail & Related papers  (2023-02-06T16:26:29Z)
• 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)
• Learning Product Graphs from Spectral Templates [3.04585143845864]
  Graph Learning (GL) is at the core of inference and analysis of connections in data mining and machine learning (ML) We propose learning product (high dimensional) graphs from product spectral templates with significantly reduced complexity. In contrast to the rare current approaches, our approach can learn all types of product graphs without knowing the type of graph products.
  arXiv  Detail & Related papers  (2022-11-05T12:28:11Z)
• 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)
• FiGLearn: Filter and Graph Learning using Optimal Transport [49.428169585114496]
  We introduce a novel graph signal processing framework for learning the graph and its generating filter from signal observations. We show how this framework can be used to infer missing values if only very little information is available.
  arXiv  Detail & Related papers  (2020-10-29T10:00:42Z)
• A Hierarchical Graph Signal Processing Approach to Inference from Spatiotemporal Signals [14.416786768268233]
  Motivated by the emerging area of graph signal processing (GSP), we introduce a novel method to draw inference from signals. In this paper we leverage techniques to develop a hierarchical feature extraction approach. We test our approach on the intracranial EEG (iEEG) data set of the K aggle seizure detection contest.
  arXiv  Detail & Related papers  (2020-10-25T17:08:13Z)
• Joint Inference of Multiple Graphs from Matrix Polynomials [34.98220454543502]
  Inferring graph structure from observations on the nodes is an important and popular network science task. We study the problem of jointly inferring multiple graphs from the observation of signals at their nodes. We propose a convex optimization method along with sufficient conditions that guarantee the recovery of the true graphs.
  arXiv  Detail & Related papers  (2020-10-16T02:45:15Z)
• Gaussian Processes on Graphs via Spectral Kernel Learning [9.260186030255081]
  We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. We demonstrate the interpretability of the model in synthetic experiments from which we show the various ground truth spectral filters can be accurately recovered.
  arXiv  Detail & Related papers  (2020-06-12T17:51:22Z)
• Sampling Signals on Graphs: From Theory to Applications [119.19108613761915]
  We review current progress on sampling over graphs focusing on theory and potential applications. Although most methodologies used in graph signal sampling are designed to parallel those used in sampling for standard signals, sampling theory for graph signals significantly differs from the theory of Shannon--Nyquist and shift-invariant sampling.
  arXiv  Detail & Related papers  (2020-03-09T07:49:40Z)

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.