A novel approach to graph distinction through GENEOs and permutants

• URL: http://arxiv.org/abs/2406.08045v1
• Date: Wed, 12 Jun 2024 09:53:14 GMT
• Title: A novel approach to graph distinction through GENEOs and permutants
• Authors: Giovanni Bocchi, Massimo Ferri, Patrizio Frosini,
• Abstract summary: This paper explores the use of GENEOs for distinguishing $r$-regular graphs up to isomorphisms. Our experiments show that GENEOs offer a good compromise between efficiency and computational cost in comparing $r$-regular graphs. GENEOs could be a general-purpose approach to discriminative problems in Machine Learning.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The theory of Group Equivariant Non-Expansive Operators (GENEOs) was initially developed in Topological Data Analysis for the geometric approximation of data observers, including their invariances and symmetries. This paper departs from that line of research and explores the use of GENEOs for distinguishing $r$-regular graphs up to isomorphisms. In doing so, we aim to test the capabilities and flexibility of these operators. Our experiments show that GENEOs offer a good compromise between efficiency and computational cost in comparing $r$-regular graphs, while their actions on data are easily interpretable. This supports the idea that GENEOs could be a general-purpose approach to discriminative problems in Machine Learning when some structural information about data and observers is explicitly given.

Related papers

• On the Validation of Gibbs Algorithms: Training Datasets, Test Datasets and their Aggregation [70.540936204654]
  dependence on training data of the Gibbs algorithm (GA) is analytically characterized. This description enables the development of explicit expressions involving the training errors and test errors of GAs trained with different datasets.
  arXiv  Detail & Related papers  (2023-06-21T16:51:50Z)
• Transfer operators on graphs: Spectral clustering and beyond [1.147633309847809]
  We show that spectral clustering of undirected graphs can be interpreted in terms of eigenfunctions of the Koopman operator. We propose novel clustering algorithms for directed graphs based on generalized transfer operators.
  arXiv  Detail & Related papers  (2023-05-19T15:52:08Z)
• Generalized Permutants and Graph GENEOs [0.0]
  We adapt the theory of group equivariant non-expansive operators (GENEOs) to act on the space of all graphs weighted on vertices or edges. This is done by showing how the general concept of GENEO can be used to transform graphs and to give information about their structure. An experimental section concludes the paper, illustrating the possible use of our operators to extract information from graphs.
  arXiv  Detail & Related papers  (2022-06-29T17:56:37Z)
• Geometry Contrastive Learning on Heterogeneous Graphs [50.58523799455101]
  This paper proposes a novel self-supervised learning method, termed as Geometry Contrastive Learning (GCL) GCL views a heterogeneous graph from Euclidean and hyperbolic perspective simultaneously, aiming to make a strong merger of the ability of modeling rich semantics and complex structures. Extensive experiments on four benchmarks data sets show that the proposed approach outperforms the strong baselines.
  arXiv  Detail & Related papers  (2022-06-25T03:54:53Z)
• Graph Neural Networks Intersect Probabilistic Graphical Models: A Survey [0.0]
  We study the intersection of Graph Neural Networks (GNNs) and Probabilistic Graphical Models (PGMs) GNNs can benefit from learning structured representations in PGMs, generate explainable predictions by PGMs, and how PGMs can infer object relationships. We summarize the benchmark datasets used in recent studies and discuss promising future directions.
  arXiv  Detail & Related papers  (2022-05-24T03:36:25Z)
• Heterogeneous Graph Neural Networks using Self-supervised Reciprocally Contrastive Learning [102.9138736545956]
  Heterogeneous graph neural network (HGNN) is a very popular technique for the modeling and analysis of heterogeneous graphs. We develop for the first time a novel and robust heterogeneous graph contrastive learning approach, namely HGCL, which introduces two views on respective guidance of node attributes and graph topologies. In this new approach, we adopt distinct but most suitable attribute and topology fusion mechanisms in the two views, which are conducive to mining relevant information in attributes and topologies separately.
  arXiv  Detail & Related papers  (2022-04-30T12:57:02Z)
• DoGR: Disaggregated Gaussian Regression for Reproducible Analysis of Heterogeneous Data [4.720638420461489]
  We introduce DoGR, a method that discovers latent confounders by simultaneously partitioning the data into overlapping clusters (disaggregation) and modeling the behavior within them (regression) When applied to real-world data, our method discovers meaningful clusters and their characteristic behaviors, thus giving insight into group differences and their impact on the outcome of interest. By accounting for latent confounders, our framework facilitates exploratory analysis of noisy, heterogeneous data and can be used to learn predictive models that better generalize to new data.
  arXiv  Detail & Related papers  (2021-08-31T01:58:23Z)
• Learning the Implicit Semantic Representation on Graph-Structured Data [57.670106959061634]
  Existing representation learning methods in graph convolutional networks are mainly designed by describing the neighborhood of each node as a perceptual whole. We propose a Semantic Graph Convolutional Networks (SGCN) that explores the implicit semantics by learning latent semantic-paths in graphs.
  arXiv  Detail & Related papers  (2021-01-16T16:18:43Z)
• Embedding Graph Auto-Encoder for Graph Clustering [90.8576971748142]
  Graph auto-encoder (GAE) models are based on semi-supervised graph convolution networks (GCN) We design a specific GAE-based model for graph clustering to be consistent with the theory, namely Embedding Graph Auto-Encoder (EGAE) EGAE consists of one encoder and dual decoders.
  arXiv  Detail & Related papers  (2020-02-20T09:53:28Z)
• Block-Approximated Exponential Random Graphs [77.4792558024487]
  An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. We propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) distributions. Our methods are scalable to sparse graphs consisting of millions of nodes.
  arXiv  Detail & Related papers  (2020-02-14T11:42:16Z)

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.