Diffusion Maps for Signal Filtering in Graph Learning

• URL: http://arxiv.org/abs/2312.14758v1
• Date: Fri, 22 Dec 2023 15:17:44 GMT
• Title: Diffusion Maps for Signal Filtering in Graph Learning
• Authors: Todd Hildebrant
• Abstract summary: The paper showcases the effectiveness of this approach through examples involving synthetically generated and real-world temperature sensor data. The results provide new approaches for the analysis and understanding of complex, non-Euclidean data structures.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the Markov Variation minimization problem. The paper showcases the effectiveness of this approach through examples involving synthetically generated and real-world temperature sensor data. These examples also compare the diffusion map graph signal model with other commonly used graph signal operators. The results provide new approaches for the analysis and understanding of complex, non-Euclidean data structures.

Related papers

• SaGess: Sampling Graph Denoising Diffusion Model for Scalable Graph Generation [7.66297856898883]
  SaGess is able to generate large real-world networks by augmenting a diffusion model (DiGress) with a generalized divide-and-conquer framework. SaGess outperforms most of the one-shot state-of-the-art graph generating methods by a significant factor.
  arXiv  Detail & Related papers  (2023-06-29T10:02:39Z)
• 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)
• DiGress: Discrete Denoising diffusion for graph generation [79.13904438217592]
  DiGress is a discrete denoising diffusion model for generating graphs with categorical node and edge attributes. It achieves state-of-the-art performance on molecular and non-molecular datasets, with up to 3x validity improvement. It is also the first model to scale to the large GuacaMol dataset containing 1.3M drug-like molecules.
  arXiv  Detail & Related papers  (2022-09-29T12:55:03Z)
• Graph Condensation via Receptive Field Distribution Matching [61.71711656856704]
  This paper focuses on creating a small graph to represent the original graph, so that GNNs trained on the size-reduced graph can make accurate predictions. We view the original graph as a distribution of receptive fields and aim to synthesize a small graph whose receptive fields share a similar distribution.
  arXiv  Detail & Related papers  (2022-06-28T02:10:05Z)
• Capturing Graphs with Hypo-Elliptic Diffusions [7.704064306361941]
  We show that the distribution of random walks evolves according to a diffusion equation defined using the graph Laplacian. This results in a novel tensor-valued graph operator, which we call the hypo-elliptic graph Laplacian. We show that this method competes with graph transformers on datasets requiring long-range reasoning but scales only linearly in the number of edges.
  arXiv  Detail & Related papers  (2022-05-27T16:47:34Z)
• Stratified Graph Spectra [0.0]
  This paper seeks a generalized transformation decoding the magnitudes of eigencomponents from vector-valued signals. Several attempts are explored, and it is found that performing the transformation at hierarchical levels of adjacency help profile the spectral characteristics of signals more insightfully.
  arXiv  Detail & Related papers  (2022-01-10T23:35:13Z)
• 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 User Guide to Low-Pass Graph Signal Processing and its Applications [31.90359683602266]
  We show how to leverage properties of low-pass graph filters to learn the graph topology or identify its community structure. We illustrate how to represent graph data through sampling, recover missing measurements, and de-noise graph data.
  arXiv  Detail & Related papers  (2020-08-04T03:27:17Z)
• 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.