Abstract
Along with the classical applications like graph partitioning, graph visualization, etc., graph coarsening has been recently applied in graph convolutional neural network (GCNN) architectures to perform the pooling operation in the graph domain. In this paper, we propose a novel two-stage graph coarsening method rooted on the graph signal processing with its application in the GCNN architecture. In the first stage of coarsening, the graph wavelet transform (GWT) based features are used to obtain a coarsened graph which preserves the topological characteristics of the original graph. In the second stage, the coarsening problem is formulated as an optimization problem where the reduced Laplacian operator at each level is obtained as a restriction of the original Laplacian operator to a specified subspace that also maximizes the topological similarity. The performance of the proposed coarsening algorithm is quantified in the general coarsening context using different graph coarsening quality measures. Its effectiveness as a pooling operator in GCNN is validated by applying it for the graph coarsening operation in the GCNN architecture. This modified GCNN architecture is then used as a graph signal classifier for the early detection of Alzheimer's disease. The results show that the proposed coarsening method outperforms state-of-the-art methods, both in the general coarsening context and as a pooling operator in the GCNN architecture.
Highlights
A new area of research called graph signal processing (GSP) has emerged in the field of signal processing which deals with the data residing on irregular structure e.g. biological networks [1], sensor networks [2] etc
BASIC PRELIMINARIES AND RELATED WORK we review some basic theory and concepts about the graph wavelet transform, graph coarsening and the graph convolutional neural network (GCNN) which form the basis of the proposed GWT-based graph coarsening method and its application in GCNN
This modified GCNN architecture is used for the classification purpose in three standard datasets and for the early detection of Alzheimer’s disease (AD) using resting-state fMRI (rs-fMRI) data
Summary
A new area of research called graph signal processing (GSP) has emerged in the field of signal processing which deals with the data residing on irregular structure e.g. biological networks [1], sensor networks [2] etc. Graph coarsening has found its application in the field of machine learning and artificial neural network where the graph coarsening is used to perform the pooling operation in the graph convolutional neural network (GCNN) [12], [13]. We propose a novel two-stage multilevel graph coarsening algorithm, in which we attempt to overcome the above drawbacks using the concepts of graph signal processing and validate the proposed algorithm in the context of GCNN. In order to improve the overall performance of the GCNN architectures, we applied our proposed graph coarsening algorithm in the pooling layer of the GCNN and the resulting classification accuracy was compared with that of the existing GCNN classifiers. The existing GCNN architecture is modified by applying the proposed graph coarsening method to perform the pooling operation and its utility is illustrated in different graph signal classification applications.
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