LipReLU

This repository is the code for paper "Enhancing Node-Level Adversarial Defenses by Lipschitz Regularization of Graph Neural Networks" in Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD'23). In addition, because of the page limit, some extra experimental results are provided here.

code implement

In the following, we give some major experimental codes and explain their function，our code is based on pytorch and pyg, the methods of adversarial attack and defense is provided by deeprobust libraries, a library including common attack and defense methods, the link is https://github.com/DSE-MSU/DeepRobust

our experimental codes can be found in path: "LipReLU/examples/graph/", there are some major codes for our experiment

• test_gcn_jaccard.py: The implement of Jaccard and LipReLU defense methods against metaattack
• test_gcn_svd: The implement of SVD and LipReLU defense methods against metaattack
• test_dice_attack: The implement of dice attack
• test_dice_gcn: The implement of various defense methods including LipReLU, against DICE attack on gcn
• test_dice_gat: The implement of various defense methods including LipReLU, against DICE attack on gat
• test_topology_attack: The implement of topology attack
• test_topology_gcn: The implement of various defense methods including LipReLU, against Topology attack on gcn
• test_topology_gat: The implement of various defense methods including LipReLU, against Topology attack on gat

You can use the hyperparameter lip_relu to determine whether use LipReLU methods or not, if lip_relu=True, LipReLU works, if lip_relu=False, LipReLU doesn't work. This can be seen in different defense methods, you can set it True to combine it with different defense methods.

supplementary experiments

Comparison of LipReLU and other baseline methods

Baselines on gcn

Topology baseline

Dataset	ptb%	0	5	10	15	20	25
Cora	GCN	83.12±0.41	81.22±0.25	78.29±0.56	74.95±0.23	68.33±0.46	67.09±0.35
	Jaccard	82.03±0.43	81.82±0.21	77.77±0.24	75.35±0.15	71.81±0.33	72.78±0.29
	SVD	77.89±0.21	77.23±0.30	76.91±0.42	73.52±0.25	70.10±0.37	66.57±0.25
	RGCN	83.53±0.24	80.68±0.65	76.58±0.33	74.76±0.12	67.57±0.55	67.07±0.45
	GNNGuard	77.41±0.23	77.01±0.23	74.45±0.67	74.25±0.22	72.69±0.44	72.43±0.66
	LipReLU	84.54±0.62	82.97±0.85	79.76±0.32	78.75±0.42	71.76±0.34	72.27±0.72
Citeseer	GCN	72.49±0.64	71.96±0.47	71.07±0.44	69.11±0.12	68.36±0.85	64.09±0.40
	Jaccard	72.33±0.93	71.94±0.31	71.45±0.46	70.49±0.24	70.28±0.22	69.99±0.19
	SVD	69.81±0.64	68.68±0.27	68.62±0.25	67.28±0.11	67.41±0.30	64.17±0.53
	RGCN	74.25±0.44	72.43±0.77	71.72±0.45	70.89±0.22	70.42±0.31	68.44±0.27
	GNNGuard	71.27±0.30	69.25±0.08	67.36±0.36	67.71±0.11	67.42±0.32	67.59±0.82
	LipReLU	76.07±0.32	75.47±0.12	75.04±0.72	74.27±0.22	73.84±0.62	70.81±0.23
Wisconsin	GCN	53.72±0.41	52.14±0.65	47.11±0.35	46.01±0.51	45.45±0.67	44.90±0.39
	Jaccard	53.17±0.39	52.34±0.38	49.58±0.67	49.04±0.49	47.93±0.37	47.66±0.77
	SVD	61.71±0.39	59.29±0.43	58.13±0.39	58.40±1.40	57.58±1.03	56.20±0.67
	RGCN	49.31±0.08	48.76±0.44	48.21±0.29	47.66±0.34	47.38±0.38	47.11±0.66
	GNNGuard	48.96±0.55	47.93±0.47	47.33±0.14	46.52±0.62	45.95±0.86	44.63±0.42
	LipReLU	56.47±0.39	55.09±0.28	54.27±0.37	54.27±0.59	52.34±0.47	52.61±0.10

DICE baseline

Dataset	ptb%	0	5	10	15	20	25
Cora	GCN	83.25±0.51	81.69±0.27	78.45±0.36	77.40±0.52	76.00±0.47	73.79±0.56
	Jaccard	82.03±0.43	82.50±0.23	80.10±0.20	78.91±0.25	77.67±0.26	76.48±0.30
	SVD	78.12±0.61	75.57±0.18	75.19±0.42	73.12±0.45	71.40±0.32	68.34±0.06
	RGCN	83.68±0.22	82.70±0.04	80.31±0.14	78.72±0.45	77.06±0.52	76.01±0.33
	GNNGuard	78.52±0.34	77.92±0.10	76.31±0.57	75.80±0.42	75.65±0.54	72.43±0.33
	LipReLU	84.53±0.08	82.78±0.06	81.14±0.04	79.04±0.05	78.05±0.06	76.34±0.12
Citeseer	GCN	72.04±0.10	70.95±0.40	69.79±0.24	68.46±0.37	67.28±0.23	65.74±0.31
	Jaccard	73.34±0.64	72.37±0.54	71.21±0.44	69.53±0.28	69.94±0.51	69.45±0.23
	SVD	70.93±0.61	69.73±0.64	67.61±0.63	66.77±0.21	66.26±0.73	66.19±0.50
	RGCN	74.35±0.08	72.06±0.24	70.16±0.22	68.70±0.41	67.08±0.39	66.39±0.39
	GNNGuard	71.15±0.14	71.12±0.51	70.20±0.23	70.02±0.27	68.60±0.66	68.31±0.59
	LipReLU	76.07±0.05	75.04±0.12	73.93±0.05	73.54±0.15	72.31±0.17	70.46±0.17
Wisconsin	GCN	53.45±1.03	51.24±0.68	48.49±1.03	47.11±0.67	46.28±0.68	44.26±0.69
	Jaccard	53.30±0.58	53.17±0.39	51.52±1.37	51.52±1.17	50.96±1.40	49.86±1.06
	SVD	61.71±0.39	60.88±0.39	60.61±0.78	59.78±0.69	58.68±1.35	56.19±0.67
	RGCN	49.86±0.04	48.49±0.21	48.76±0.66	48.21±0.09	47.93±0.45	47.38±0.87
	GNNGuard	49.59±0.19	48.76±0.76	48.26±0.14	47.62±0.11	46.61±0.23	46.28±0.47
	LipReLU	55.92±0.39	56.75±0.39	57.30±0.39	56.20±1.17	55.65±0.78	54.27±0.39

Metaatack baseline

Dataset	ptb%	0	5	10	15	20	25
Cora	GCN	83.38±0.26	76.44±0.24	69.30±0.37	61.59±0.82	53.79±0.29	49.04±0.30
	Jaccard	82.06±0.18	79.45±0.08	77.33±0.23	74.72±0.22	74.51±0.31	72.21±0.18
	SVD	77.53±0.30	76.63±0.21	72.06±0.06	69.01±0.21	63.06±0.31	58.63±0.41
	RGCN	83.32±0.29	75.59±0.24	71.94±0.88	68.29±0.08	56.86±0.03	52.63±0.21
	GNNGuard	77.31±0.56	75.75±0.24	74.45±0.67	74.14±0.26	73.89±0.46	75.07±0.13
	LipReLU	84.59±0.18	76.76±0.04	69.85±0.05	62.00±0.08	54.23±0.04	49.22±0.02
Citeseer	GCN	72.00±0.43	70.38±0.20	67.89±0.21	64.05±0.20	57.03±0.50	54.19±0.76
	Jaccard	72.23±0.23	71.31±0.19	70.74±0.25	70.38±0.22	70.28±0.11	70.12±0.17
	SVD	69.72±0.30	70.20±0.54	69.37±0.38	68.90±0.37	68.72±0.48	65.54±0.29
	RGCN	72.57±0.44	70.99±0.12	68.82±0.28	68.99±1.02	68.72±0.68	65.54±0.32
	GNNGuard	70.62±0.22	71.21±0.35	70.32±0.09	68.19±0.17	68.84±0.83	65.70±0.54
	LipReLU	76.24±0.14	75.47±0.59	71.13±0.07	69.59±0.07	58.27±0.09	59.68±0.06
Wisconsin	GCN	53.45±1.03	51.51±0.73	49.59±0.67	48.76±0.67	45.45±0.68	42.98±0.45
	Jaccard	53.17±0.29	53.44±0.78	52.61±1.03	51.61±0.45	48.20±0.39	47.93±0.67
	SVD	60.88±1.03	59.50±0.67	59.50±1.17	59.23±0.78	58.12±0.78	57.30±1.41
	RGCN	49.11±0.08	49.04±0.24	47.66±0.45	49.31±0.21	50.14±0.56	51.24±0.49
	GNNGuard	51.58±0.33	52.47±0.40	52.07±0.44	50.41±0.02	49.59±0.33	47.05±0.87
	LipReLU	57.30±0.39	56.47±1.03	56.47±0.38	56.75±0.39	55.92±0.39	55.10±0.39

Baselines on gat

Topology baseline

Dataset	ptb%	0	5	10	15	20	25
Cora	GAT	84.09±0.40	81.96±0.35	77.99±0.13	70.14±0.17	64.00±0.45	59.01±0.14
	LipNorm	84.59±0.20	83.85±0.44	82.14±0.19	74.06±0.09	66.75±0.54	62.27±0.27
	GNNGuard	84.26±0.14	82.55±0.56	80.28±0.76	74.25±0.32	66.97±0.28	58.60±0.41
	LipReLU	85.38±0.13	83.88±0.14	81.76±0.06	74.02±0.16	67.94±0.46	59.96±0.14
Citeseer	GAT	74.13±0.65	73.22±0.25	71.50±0.27	70.34±0.49	68.32±0.36	62.13±0.10
	LipNorm	73.57±0.32	72.74±0.47	72.27±0.15	71.68±0.34	69.19±0.55	65.52±0.49
	GNNGuard	74.47±0.33	73.05±0.16	70.68±0.50	69.31±0.34	71.45±0.45	64.99±0.29
	LipReLU	77.58±1.17	75.36±0.51	73.76±0.09	73.42±0.07	72.02±0.35	65.82±0.27
Wisconsin	GAT	51.79±1.03	50.41±0.67	48.76±0.68	47.11±0.69	44.90±0.78	43.25±0.78
	LipNorm	50.98±0.33	50.76±0.45	48.95±0.19	47.36±0.13	47.10±0.34	45.60±0.21
	GNNGuard	52.17±0.13	50.96±0.09	51.24±0.11	50.45±0.33	49.56±0.21	48.96±0.64
	LipReLU	52.62±0.94	52.43±0.38	50.14±0.28	52.07±0.67	51.24±0.68	50.97±0.56

DICE baseline

Dataset	ptb%	0	5	10	15	20	25
Cora	GAT	84.69±0.25	82.17±0.12	80.52±0.67	79.20±0.25	76.71±0.39	74.20±0.24
	LipNorm	83.60±0.33	82.29±0.39	81.18±0.44	79.62±0.13	78.01±0.12	75.90±0.54
	GNNGuard	83.80±0.78	82.90±0.45	80.89±0.31	80.94±0.23	77.11±0.12	74.07±0.48
	LipReLU	85.48±0.06	84.51±0.08	82.77±0.12	80.85±0.16	78.95±0.29	76.37±0.09
Citeseer	GAT	72.69±0.38	71.25±0.18	70.16±0.37	68.13±0.63	66.82±0.39	65.11±0.30
	LipNorm	73.51±0.29	71.56±0.31	70.61±0.12	70.14±0.45	68.83±0.37	67.23±0.79
	GNNGuard	72.93±0.09	71.86±0.23	69.11±0.21	68.54±0.14	66.11±0.55	64.99±0.62
	LipReLU	74.74±0.14	74.33±0.07	73.32±0.27	70.69±0.07	71.13±0.07	67.34±0.12
Wisconsin	GAT	51.79±1.03	48.76±0.68	47.38±1.03	45.73±0.39	44.63±0.67	41.60±0.95
	LipNorm	49.58±0.51	48.75±0.27	47.96±0.14	47.92±0.59	47.10±0.56	46.28±0.66
	GNNGuard	52.07±0.98	49.53±0.45	47.67±0.49	47.62±0.30	46.54±0.32	46.28±0.77
	LipReLU	52.34±0.38	52.62±0.38	52.07±1.03	51.79±0.39	50.96±0.78	50.41±0.17

Metaattack baseline

Dataset	ptb%	0	5	10	15	20	25
Cora	GAT	83.63±0.22	78.80±0.08	74.02±0.45	70.89±0.41	57.26±0.41	50.50±0.21
	LipNorm	84.75±0.15	80.38±0.17	76.09±0.43	70.82±0.09	57.59±0.55	53.16±0.27
	GNNGuard	82.50±0.04	78.87±0.09	76.36±0.28	72.28±0.49	59.96±0.51	54.68±0.21
	LipReLU	85.51±0.81	80.40±0.31	75.42±0.20	71.80±0.06	58.30±0.21	52.89±0.15
Citeseer	GAT	73.64±0.27	72.13±0.62	69.55±0.39	65.62±0.34	60.98±0.25	60.92±0.34
	LipNorm	73.28±0.48	72.39±0.23	71.50±0.44	69.54±0.22	61.07±0.13	61.90±0.12
	GNNGuard	73.22±0.14	72.99±0.25	71.21±0.21	69.25±0.45	60.90±0.12	59.66±0.65
	LipReLU	75.12±0.10	74.15±0.15	72.10±0.05	68.95±0.24	62.40±0.17	63.35±0.22
Wisconsin	GAT	51.51±1.03	49.59±0.67	48.21±0.78	47.11±0.67	44.63±0.67	42.15±1.16
	LipNorm	50.41±0.19	51.23±0.22	51.21±0.19	49.55±0.29	48.76±0.11	47.95±0.31
	GNNGuard	49.12±0.12	48.86± 0.44	47.93±0.46	47.65± 0.57	46.28±1.00	45.45±0.90
	LipReLU	52.54±0.39	52.90±1.16	52.62±0.77	52.62±0.38	52.07±0.67	50.96±0.42

The run time of the experiments in paper

The run time of GCN under Topology attack

Dataset	ptb%	0	5	10	15	20	25
Cora	GCN	1.80±0.08	1.70±0.08	1.56±0.08	1.70±0.08	1.73±0.08	1.66±0.09
	GCN+LipReLU	30.37±0.21	29.33±0.34	28.80±0.16	30.17±0.39	28.67±0.39	30.67±0.45
	Jaccard	364.13±2.21	362.03±1.32	368.03±3.57	371.57±0.59	371.30±3.68	370.06±0.68
	Jaccard+LipReLU	380.17±0.60	379.63±3.44	385.33±5.56	381.00±6.01	388.50±0.70	387.93±1.22
	SVD	2.67±0.17	2.65±0.12	2.60±0.16	2.60±0.82	2.57±0.47	2.67±0.94
	SVD+LipReLU	31.50±0.46	30.83±0.46	30.77±0.45	30.80±0.43	31.30±0.67	34.73±3.51
Citeseer	GCN	1.50±0.08	1.50±0.09	1.40±0.08	1.40±0.08	1.53±0.07	1.60±0.09
	GCN+LipReLU	26.00± 0.10	28.23± 0.04	26.40± 0.23	26.33± 0.31	25.70± 0.05	25.80± 0.09
	Jaccard	315.50±0.34	317.69±0.56	315.73±0.45	316.77±1.09	317.70±1.02	320.77±2.11
	Jaccard+LipReLU	332.76±1.45	333.45±0.76	331.89±1.21	334.56±1.45	332.78±2.22	331.43±1.67
	SVD	2.73±0.34	2.60±0.12	2.63±0.04	2.83±0.02	2.76±0.09	2.67±0.08
	SVD+LipReLU	27.13±0.67	27.53±0.44	27.30±0.55	26.83±0.23	26.80±0.34	27.10±1.01
Wisconsin	GCN	1.50±0.08	1.53±0.12	1.57±0.08	1.50±0.09	1.50±0.21	1.57±0.08
	GCN+LipReLU	5.90±0.04	5.10±0.08	5.56±0.05	5.90±0.04	6.00±0.08	6.10±0.05
	Jaccard	41.43±0.54	42.12±0.32	44.12±0.42	41.63±0.45	42.57±0.55	44.45±0.43
	Jaccard+LipReLU	45.56±0.77	46.89±0.45	45.12±0.45	45.74±0.34	44.91±0.83	46.12±0.16
	SVD	5.34±0.32	5.12±0.44	4.98±0.17	5.67±0.34	5.43±0.08	5.67±0.31
	SVD+LipReLU	9.30±0.08	9.57±0.04	9.32±0.21	9.12±0.12	9.70±0.08	10.83±0.20

The run time of GCN under Dice attack

Dataset	ptb%	0	5	10	15	20	25
Cora	GCN	4.03±0.09	4.09±0.08	4.09±0.08	4.07±0.12	4.00±0.08	4.23±0.20
	GCN+LipReLU	398.70±6.49	365.17±2.50	380.30±1.47	379.63±1.13	381.06±0.99	387.37±1.18
	Jaccard	3.70±0.08	3.76±0.04	3.70±0.08	3.80±0.08	3.63±0.12	3.80±0.08
	Jaccard+LipReLU	377.63±1.29	374.56±1.63	362.13±1.19	367.37±0.41	383.67±1.06	370.03±2.85
	SVD	32.60±2.88	35.86±2.88	31.96±1.24	28.83±0.20	31.43±2.52	31.23±0.44
	SVD+LipReLU	41.93±0.16	41.36±0.26	40.90±0.29	41.10±0.58	40.43±0.12	40.70±0.08
Citeseer	GCN	3.97±0.16	3.93±0.12	3.90±0.08	3.80±0.04	3.76±0.04	3.90±0.08
	GCN+LipReLU	323.26±1.32	336.20±0.58	308.43±1.10	335.20±0.80	324.00±1.77	311.77±3.63
	Jaccard	3.80±0.08	3.67±0.04	4.00±0.21	3.70±0.08	3.70±0.24	3.96±0.16
	Jaccard+LipReLU	327.23±0.69	328.23±1.82	320.20±1.84	298.30±0.97	298.30±0.97	312.29±0.89
	SVD	27.23±0.24	26.23±0.26	27.10±0.29	27.40±1.39	26.09±0.29	27.06±1.37
	SVD+LipReLU	36.89±0.24	36.23±0.26	37.10±0.29	37.73±1.39	36.09±0.29	37.06±1.37
Wisconsin	GCN	3.60±0.08	3.73±0.20	3.80±0.08	3.83±0.04	3.70±0.08	3.83±0.04
	GCN+LipReLU	41.57±0.20	41.33±0.16	43.19±0.37	41.57±0.26	42.87±0.23	40.26±0.24
	Jaccard	4.06±0.12	4.33±0.32	4.19±0.14	4.57±0.20	4.87±0.20	4.26±0.12
	Jaccard+LipReLU	46.76±0.20	47.53±0.44	48.39±0.08	47.30±0.08	46.69±0.21	45.80±0.63
	SVD	5.93±0.16	6.56±0.16	6.86±0.12	6.93±0.12	6.80±0.28	6.10±0.08
	SVD+LipReLU	25.30±0.08	23.56±0.16	26.98±1.20	25.78±0.23	23.56±0.77	25.89±0.45

The run time of GCN under metaattack

Dataset	ptb%	0	5	10	15	20	25
Cora	GCN	3.93±0.12	3.67±0.23	3.80±0.08	3.73±0.09	3.86±0.20	3.56±0.16
	GCN+LipReLU	385.67±3.02	381.56±2.09	381.99±0.19	378.67±1.12	375.33±1.47	376.76±2.40
	Jaccard	3.63±0.23	3.53±0.65	3.80±0.08	3.63±0.87	3.73±0.09	3.56±0.12
	Jaccard+LipReLU	386.09±0.78	389.06±2.41	385.86±1.44	35.49±0.57	386.36±0.74	384.03±0.77
	SVD	2.60±0.23	2.53±0.65	2.66±0.08	2.68±0.87	2.69±0.09	2.67±0.12
	SVD+LipReLU	32.40±0.78	32.90±2.41	34.79±1.11	33.06±0.57	35.16±0.74	33.36±0.77
Citeseer	GCN	3.76±0.23	3.83±0.06	3.70±0.12	3.83±0.14	3.60±0.08	3.83±0.21
	GCN+LipReLU	334.83±2.68	314.11±1.02	329.92±1.47	330.06±1.46	336.46±3.76	335.73±1.23
	Jaccard	3.63±0.16	3.80±0.23	3.93±0.76	3.83±0.72	3.86±0.45	3.76±0.32
	Jaccard+LipReLU	325.43±2.30	316.00±3.50	316.20±3.02	311.83±0.66	325.06±1.84	313.75±3.82
	SVD	2.40±0.16	2.26±0.12	2.66±0.12	2.33±0.14	2.63±0.13	2.40±0.12
	SVD+LipReLU	24.23±2.68	27.23±0.32	27.73±0.24	27.36±0.24	27.43±0.23	27.63±0.43
Wisconsin	GCN	1.52±0.34	1.53±0.71	1.70±0.08	1.60±0.08	1.49±0.08	1.60±0.16
	GCN+LipReLU	5.93±0.23	5.90±0.08	6.23±0.12	6.16±0.16	5.93±0.12	6.40±0.24
	Jaccard	41.73±0.45	42.13±0.78	42.86±1.11	41.33±0.89	41.86±0.92	43.23±0.57
	Jaccard+LipReLU	44.10±0.06	46.13±1.01	45.86±0.67	46.36±0.23	46.00±0.66	47.23±0.31
	SVD	5.20±1.55	5.23±1.11	5.03±0.12	5.86±0.45	6.03±0.14	5.86±0.99
	SVD+LipReLU	7.16±0.08	7.00±0.14	7.09±0.22	9.13±0.45	7.09±0.32	8.03±0.08

The run time of GAT under Topology attack

Dataset	ptb%	0	5	10	15	20	25
Cora	GAT	5.83±0.04	5.76±0.09	5.80±0.04	5.90±0.08	6.13±0.07	5.96±0.05
	GAT+LipReLU	3681.49±84.63	3597.76±100.12	3600.56±13.83	3594.23±47.00	3637.67±75.09	3700.30±27.44
Citeseer	GAT	5.53±0.04	5.76±0.06	5.79±0.05	5.86±0.04	5.73±0.04	5.73±0.08
	GAT+LipReLU	2581.57±53.65	2480.53±23.76	2421.73±78.45	2442.26±33.89	2391.53±99.67	2541.86±43.17
Wisconsin	GAT	5.90±0.08	5.76±0.12	5.96±0.14	5.90±0.43	6.23±0.09	6.20±0.12
	GAT+LipReLU	232.56±14.55	246.76±10.94	244.43±16.78	233.29±22.89	249.03±10.89	229.36±11.34

The run time of GAT under Dice attack

Dataset	ptb%	0	5	10	15	20	25
Cora	GAT	4.83±0.04	5.03±0.04	5.26±0.06	4.93±0.06	5.13±0.06	5.20±0.05
	GAT+LipReLU	3562.93±9.51	3596.50±21.65	3592.36±5.40	3539.79±7.18	3626.23±27.00	3578.16±8.43
Citeseer	GAT	4.87±0.09	4.69±0.43	5.00±0.16	4.96±0.19	5.06±0.12	5.03±0.08
	GAT+LipReLU	2436.90±12.94	2626.83±27.64	2531.02±11.56	2563.93±80.16	2453.60±21.02	2496.89±44.25
Wisconsin	GAT	5.73±0.16	5.76±0.12	5.86±0.09	5.29±0.12	5.00±0.16	5.06±0.18
	GAT+LipReLU	242.43±1.87	235.43±6.27	244.43±10.85	242.47±9.35	257.00±25.36	238.02±10.93

The run time of gat under metaattack

Dataset	ptb%	0	5	10	15	20	25
Cora	GAT	4.90±0.21	5.13±0.24	4.90±0.08	5.29±0.14	5.00±0.08	5.06±0.09
	GAT+LipReLU	3604.20±40.10	3627.70±16.10	3590.76±21.37	3646.50±5.88	3703.67±11.98	3579.80±88.72
Citeseer	GAT	4.73±0.09	4.80±0.06	4.83±0.05	4.93±0.06	5.00±0.08	4.80±0.07
	GAT+LipReLU	2412.40±14.89	2401.13±11.60	2520.36±75.19	2413.23±28.56	2487.80±26.01	2456.50±15.95
Wisconsin	GAT	5.83±0.04	5.86±0.24	6.26±0.12	6.03±0.12	5.93±0.45	5.96±0.67
	GAT+LipReLU	256.47±5.79	255.60±0.71	219.67±2.56	237.20±1.12	279.40±4.54	238.63±4.22