<i>D</i><sup>2</sup>-GCN: a graph convolutional network with dynamic disentanglement for node classification

doi:10.1007/s11704-023-3339-7

Front. Comput. Sci.

2025, Vol. 19

Issue (1) : 191305 https://doi.org/10.1007/s11704-023-3339-7

Artificial Intelligence

D²-GCN: a graph convolutional network with dynamic disentanglement for node classification

Shangwei WU, Yingtong XIONG, Hui LIANG, Chuliang WENG(

)

School of Data Science and Engineering, East China Normal University, Shanghai 200062, China

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Abstract

Classic Graph Convolutional Networks (GCNs) often learn node representation holistically, which ignores the distinct impacts from different neighbors when aggregating their features to update a node’s representation. Disentangled GCNs have been proposed to divide each node’s representation into several feature units. However, current disentangling methods do not try to figure out how many inherent factors the model should assign to help extract the best representation of each node. This paper then proposes D²-GCN to provide dynamic disentanglement in GCNs and present the most appropriate factorization of each node’s mixed features. The convergence of the proposed method is proved both theoretically and experimentally. Experiments on real-world datasets show that D²-GCN outperforms the baseline models concerning node classification results in both single- and multi-label tasks.

Keywords graph convolutional networks dynamic disentanglement label entropy node classification

Corresponding Author(s): Chuliang WENG

Just Accepted Date: 01 December 2023 Issue Date: 03 April 2024

Cite this article:

Shangwei WU,Yingtong XIONG,Hui LIANG, et al. D²-GCN: a graph convolutional network with dynamic disentanglement for node classification[J]. Front. Comput. Sci., 2025, 19(1): 191305.

URL:

https://academic.hep.com.cn/fcs/EN/10.1007/s11704-023-3339-7
https://academic.hep.com.cn/fcs/EN/Y2025/V19/I1/191305

Fig.1 Effects of different

K

in DisenGCN on Cora. In each subgraph, the

x

-axis represents the number of training epochs, the

y

-axis represents training/test accuracies or training/test losses. (a) Training accuracies; (b) test accuracies; (c) training losses; (d) test losses

Fig.2 Changes in the kinds of predicted labels of three typical nodes’ neighbors across training epochs with different

K

in DisenGCN on the Cora dataset. (a) The test with

v α

; (b) the test with

v β

; (c) the test with

v γ

Fig.3 Counts of nodes with different numbers of predicted neighbor classes (i.e.,

n v i

) at different training stages on the Cora dataset

Fig.4 Changes of

K^v a l

K ˉ v a l

, and

K ~ v a l

during training with different

K

in DisenGCN on the Cora dataset. (a) Changes of

K^v a l

; (b) changes of

K ˉ v a l

; (c) changes of

K ~ v a l

Fig.5 Changes of

n v i

w.r.t. two typical nodes across layers with different

K

in DisenGCN on the Cora dataset. (a) The test with

v α

; (b) the test with

v β

Fig.6 Architecture of

D 2

-GCN with two-level disentanglement during training, i.e., the epoch level and the layer level

Fig.7 Change of

K L v a l

during training with different

K

in DisenGCN. The dataset used here is Cora

Tab.1 Dataset information. The last column implies whether the graphs in the task contain single or multiple labels

Dataset	$S$	Weight decay	Learning rate	Dropout rate	$L$	$λ$	$Δ K$
Cora	6	0.001	0.061	0.41	6	5	2
Citeseer	6	0.086	0.090	0.26	5	5	2
PubMed	6	0.045	0.014	0.22	4	4	1
PPI	6	0.00059	0.0057	0.45	2	6	3
POS	6	0.00048	0.0780	0.45	2	4	3
BlogCatalog	6	0.00036	0.0079	0.40	4	4	4
Flickr	6	0.00025	0.0530	0.36	3	5	2

Tab.2 Hyperparameter settings

Model	Dataset
Model	Cora	Citeseer	PubMed
MLP [38]	55.1±0.25	46.5±0.33	71.4±0.46
ManiReg [39]	59.5±0.18	60.1±0.24	70.7±0.31
SemiEmb [40]	59.0±0.23	59.6±0.21	71.1±0.28
LP [41]	68.0±0.13	45.3±0.22	63.0±0.26
DeepWalk [35]	67.2±0.11	43.2±0.32	65.3±0.36
ICA [42]	75.1±0.23	69.1±0.26	73.9±0.31
Planetoid [43]	75.7±0.22	64.7±0.19	77.2±0.30
ChebNet [44]	81.2±0.12	69.8±0.23	74.4±0.25
GCN [1]	81.5±0.17	70.3±0.23	79.0±0.42
MoNet [45]	81.7±0.24	71.4±0.27	78.8±0.35
GAT [34]	83.0±0.15	72.5±0.18	79.0±0.22
MixHop [46]	82.3±0.23	72.1±0.18	81.0±0.26
DisenGCN [18]	83.2±0.20	71.5±0.25	79.9±0.19
IPGDN [19]	83.9±0.15	72.8±0.19	80.7±0.21
$D 2$ -GCN	85.4±0.11	73.5±0.12	81.8±0.14

Tab.3 Test accuracy results in single-label node classification on Cora, Citeseer, and PubMed (unit: percentage)

	Model	Dataset
	Model	PPI	POS	BlogCatalog	Flickr
Macro-F1	DeepWalk	17.8±0.19	11.9±0.21	23.1±0.24	15.3±0.26
	LINE	17.3±0.25	11.8±0.18	22.8±0.27	19.7±0.15
	node2vec	17.9±0.19	12.9±0.25	23.6±0.31	22.4±0.27
	GCN	17.7±0.16	20.1±0.20	24.4±0.28	27.2±0.18
	GAT	19.2±0.13	16.1±0.22	26.8±0.25	30.6±0.23
	DisenGCN	21.4±0.17	26.5±0.21	28.9±0.15	34.2±0.14
	$D 2$ -GCN	22.3±0.11	27.8±0.14	29.6±0.12	35.7±0.17
Micro-F1	DeepWalk	20.7±0.20	49.3±0.22	38.8±0.26	30.6±0.17
	LINE	21.1±0.23	49.0±0.16	38.5±0.24	34.2±0.19
	node2vec	20.6±0.17	49.9±0.22	39.0±0.28	38.4±0.31
	GCN	20.7±0.18	50.9±0.18	35.9±0.25	44.3±0.12
	GAT	22.3±0.14	50.7±0.16	39.7±0.22	46.5±0.23
	DisenGCN	25.7±0.18	54.1±0.21	41.8±0.16	49.2±0.16
	$D 2$ -GCN	26.6±0.15	55.4±0.11	42.7±0.14	50.9±0.15

Tab.4 Test Macro-F1 and Micro-F1 scores in multi-label node classification on PPI, POS, and BlogCatalog (unit: percentage)

Fig.8 Loss curves in DisenGCN and

D 2

-GCN on Cora, Citeseer, and PubMed. Here ‘trn’ or ‘tst’ means the loss on the training/test set. (a) On Cora; (b) on Citeseer; (c) on PubMed

Fig.9

K ~ v a l

and

K ~ d y n a

in DisenGCN and

D 2

-GCN on Cora, Citeseer, and PubMed. Here

K ~ d y n a

means the

K

altered by our model during training. (a) On Cora; (b) on Citeseer; (c) on PubMed

Fig.10

K L v a l

in DisenGCN and

D 2

-GCN on Cora, Citeseer, and PubMed. (a) On Cora; (b) on Citeseer; (c) on PubMed

Model	Dataset
Model	Cora	Citeseer	PubMed	PPI	POS	BlogCatalog	Flickr
DisenGCN $H P O$	81.42	79.07	445.29	2547.29	2735.17	8724.36	35672.13
$D 2$ -GCN	23.04	18.21	237.24	470.03	626.39	1337.25	3917.56

Tab.5 Comparison of total time cost between DisenGCN

H P O

and

D 2

-GCN (unit: second)

Model	Dataset
Model	Cora	Citeseer	PubMed	PPI	POS	BlogCatalog	Flickr
DisenGCN	2066	2186	7852	2166	2316	4488	34928
$D 2$ -GCN	1938	2104	2884	1614	1534	1706	14772

Tab.6 Comparison of memory consumption between DisenGCN and

D 2

-GCN (unit: MB)

Fig.11 Effects of

λ

on Cora. (a) Test accuracy; (b)

K ~ v a l

; (c)

K L v a l

Fig.12 Effects of

Δ K

on Cora. (a) Test accuracy; (b)

K ~ v a l

; (c)

K L v a l

Model	Dataset
Model	Cora	Citeseer	PubMed
$D 2$ -GCN $(E D, F d)$	85.4±0.11	73.5±0.12	81.8±0.14
$D 2$ -GCN $(E D, F Δ d)$	84.8±0.23	72.7±0.18	81.3±0.16
$D 2$ -GCN $(L D, F d)$	82.7±0.15	72.2±0.22	81.0±0.13
$D 2$ -GCN $(L D, F Δ d)$	82.6±0.17	71.8±0.12	80.8±0.21
$D 2$ -GCN $(E D + L D, F d)$	83.3±0.11	73.2±0.24	81.2±0.17
$D 2$ -GCN $(E D + L D, F Δ d)$	83.1±0.14	73.0±0.16	80.9±0.22

Tab.7 Test accuracy results of

D 2

-GCN with different disentangling strategies in single-label tasks (unit: percentage)

	Model	Dataset
	Model	PPI	POS	BlogCatalog	Flickr
Macro-F1	$D 2$ -GCN $(E D, F d)$	21.3±0.16	26.5±0.12	28.4±0.15	34.0±0.17
	$D 2$ -GCN $(E D, F Δ d)$	21.5±0.12	26.8±0.14	28.5±0.11	34.2±0.16
	$D 2$ -GCN $(L D, F d)$	21.6±0.14	27.1±0.17	28.7±0.13	34.7±0.11
	$D 2$ -GCN $(L D, F Δ d)$	21.8±0.11	27.2±0.15	28.8±0.12	34.9±0.13
	$D 2$ -GCN $(E D + L D, F d)$	21.9±0.13	27.4±0.16	29.1±0.12	35.4±0.15
	$D 2$ -GCN $(E D + L D, F Δ d)$	22.3±0.11	27.8±0.14	29.6±0.12	35.7±0.17
Micro-F1	$D 2$ -GCN $(E D, F d)$	25.5±0.13	53.8±0.11	41.5±0.10	49.6±0.14
	$D 2$ -GCN $(E D, F Δ d)$	25.6±0.14	54.0±0.12	41.6±0.11	49.8±0.17
	$D 2$ -GCN $(L D, F d)$	25.8±0.12	54.3±0.13	41.8±0.15	49.9±0.10
	$D 2$ -GCN $(L D, F Δ d)$	25.9±0.09	54.5±0.11	42.1±0.14	50.2±0.16
	$D 2$ -GCN $(E D + L D, F d)$	26.1±0.11	54.7±0.15	42.3±0.13	50.6±0.12
	$D 2$ -GCN $(E D + L D, F Δ d)$	26.6±0.15	55.4±0.11	42.7±0.14	50.9±0.15

Tab.8 Test Macro-F1 and Micro-F1 scores of

D 2

-GCN with different disentangling strategies in multi-label tasks (unit: percentage)

Fig.13 Visualizations of DisenGCN’s node classification performance on the test set in Cora, Citeseer, and PubMed. The rectangles with red borders are used to highlight the ambiguous boundaries among different node classes. (a) DisenGCN on Cora; (b) DisenGCN on Citeseer; (c) DisenGCN on PubMed

Fig.14 Visualizations of

D 2

-GCN’s node classification performance on the test set in Cora, Citeseer, and PubMed. (a)

D 2

-GCN on Cora; (b)

D 2

-GCN on Citeseer; (c)

D 2

-GCN on PubMed

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