Citation: Bae, J.-H.; Yu, G.-H.; Lee,
J.-H.; Vu, D.T.; Anh, L.H.; Kim, H.-G.;
Kim, J.-Y. Superpixel Image
Classification with Graph
Convolutional Neural Networks
Based on Learnable Positional
Embedding. Appl. Sci. 2022, 12, 9176.
https://doi.org/10.3390/app12189176
Academic Editors: Katia
Lida Kermanidis, Phivos Mylonas
and Manolis Maragoudakis
Received: 5 August 2022
Accepted: 9 September 2022
Published: 13 September 2022
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Article
Superpixel Image Classification with Graph Convolutional
Neural Networks Based on Learnable Positional Embedding
Ji-Hun Bae
1
, Gwang-Hyun Yu
1
, Ju-Hwan Lee
1
, Dang Thanh Vu
1
, Le Hoang Anh
1
, Hyoung-Gook Kim
2,
*
and Jin-Young Kim
1,
*
1
Department of ICT Convergence System Engineering, Chonnam National University, 77 Yongbong-ro,
Buk-gu, Gwangju 61186, Korea
2
Department of Electronic Convergence Engineering, Kwangwoon University, 20 Gwangun-ro, Nowon-gu,
Seoul 01897, Korea
* Correspondence: hkim@kw.ac.kr (H.-G.K.); beyondi@jnu.ac.kr (J.-Y.K.)
Abstract:
Graph convolutional neural networks (GCNNs) have been successfully applied to a wide
range of problems, including low-dimensional Euclidean structural domains representing images,
videos, and speech and high-dimensional non-Euclidean domains, such as social networks and
chemical molecular structures. However, in computer vision, the existing GCNNs are not provided
with positional information to distinguish between graphs of new structures; therefore, the per-
formance of the image classification domain represented by arbitrary graphs is significantly poor.
In this work, we introduce how to initialize the positional information through a random walk
algorithm and continuously learn the additional position-embedded information of various graph
structures represented over the superpixel images we choose for efficiency. We call this method the
graph convolutional network with learnable positional embedding applied on images (IMGCN-LPE).
We apply IMGCN-LPE to three graph convolutional models (the Chebyshev graph convolutional
network, graph convolutional network, and graph attention network) to validate performance on
various benchmark image datasets. As a result, although not as impressive as convolutional neural
networks, the proposed method outperforms various other conventional convolutional methods and
demonstrates its effectiveness among the same tasks in the field of GCNNs.
Keywords:
graph convolutional neural network (GCNN); superpixel image classification; learnable
positional embedding
1. Introduction
Convolutional neural networks (CNNs) have exhibited the best performance in many
machine learning tasks, especially image processing [
1
–
3
]. However, the CNN structure
has a rectangular-based grid data type, and the same input dimensions must be provided.
Therefore, the application of CNNs to irregular atypical data (e.g., social networks and
molecular structures) and 3D modeling, often encountered in real life, is limited. There
are some studies that adapt CNNs on irregular domains but it therefore includes the
design of classical convolutional layers as a particular case, in which the underlying
graph is a grid [
4
]. Various problems that attempt to capture complex relationships or
interdependencies between data can be expressed and analyzed more naturally in graphs.
Normally, goal of convolution operation is to summarize input data to a reduced form.
Unfortunately, dot product to compute convolution is sensitive to the order, i.e., dot product
is not permutation-invariant. So, convolution requires permutation-invariant operator that
get the same result from a spatial region even if there is randomly shuffled pixels inside
that region. CNNs can detect and recognize the object of image which translate to left or
right by sharing same filter‘s weights across all locations. However, it is difficult to define
convolution on graphs. The main problem is that there is no well de-fined order of nodes
Appl. Sci. 2022, 12, 9176. https://doi.org/10.3390/app12189176 https://www.mdpi.com/journal/applsci
