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In this paper, we study the problem of unsupervised graph representation learning by harnessing the control properties of dynamical networks defined on graphs. Our approach introduces a novel framework for contrastive learning, a widely prevalent technique for unsupervised representation learning. A crucial step in contrastive learning is the creation of ‘augmented’ graphs from the input graphs. Though different from the original graphs, these augmented graphs retain the original graph’s structural characteristics. Here, we propose a unique method for generating these augmented graphs by leveraging the control properties of networks. The core concept revolves around perturbing the original graph to create a new one while preserving the controllability properties specific to networks and graphs. Compared to the existing methods, we demonstrate that this innovative approach enhances the effectiveness of contrastive learning frameworks, leading to superior results regarding the accuracy of the classification tasks. The key innovation lies in our ability to decode the network structure using these control properties, opening new avenues for unsupervised graph representation learning.
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Control-based Conditions for Graph Distinguishability
The graph distinguishability problem investigates whether a graph can be uniquely identified by the spectrum of its adjacency matrix, specifically determining if two graphs with the same spectrum are isomorphic. This issue is central to spectral graph theory and has significant implications for graph machine learning. In this paper, we explore the intricate connections between graph distinguishability and graph controllability–an essential concept in the control of networked systems. Focusing on oriented graphs and their skew-adjacency matrices, we establish controllability-based conditions that ensure their distinguishability. Notably, our conditions are less restrictive than existing methods, enabling a broader class of graphs to satisfy the distinguishability criteria. We illustrate the effectiveness of our results with several examples. Our findings highlight the applications of network control methods in tackling this crucial problem in algebraic graph theory, with implications for machine learning and network design.
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- PAR ID:
- 10626554
- Publisher / Repository:
- Society for Industrial and Applied Mathematics
- Date Published:
- ISBN:
- 978-1-61197-874-2
- Page Range / eLocation ID:
- 31 to 38
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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In this paper, we study the problem of unsupervised graph representation learning by harnessing the control properties of dynamical networks defined on graphs. Our approach introduces a novel framework for contrastive learning, a widely prevalent technique for unsupervised representation learning. A crucial step in contrastive learning is the creation of ‘augmented’ graphs from the input graphs. Though different from the original graphs, these augmented graphs retain the original graph’s structural characteristics. Here, we propose a unique method for generating these augmented graphs by leveraging the control properties of networks. The core concept revolves around perturbing the original graph to create a new one while preserving the controllability properties specific to networks and graphs. Compared to the existing methods, we demonstrate that this innovative approach enhances the effectiveness of contrastive learning frameworks, leading to superior results regarding the accuracy of the classification tasks. The key innovation lies in our ability to decode the network structure using these control properties, opening new avenues for unsupervised graph representation learning.more » « less
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Book Chapter:
- https://doi.org/10.1137/1.9781611978742.5
