Benchmarks

This page contains benchmarks of all models implemented in GraphVite, including their time and performance. All experiments are conducted on a server with 24 CPU threads and 4 V100 GPUs.

Node Embedding

We experiment node embedding models on 3 datasets, ranging from million-scale to half billion-scale. The following table shows the size of each dataset, as well as the time and resource required by LINE model.

Dataset	|V|	|E|	Training Time	GPU memory cost
Youtube	1.1M	4.9M	1.17 mins	4 * 801 MiB
Flickr	1.7M	23M	3.54 mins	4 * 943 MiB
Friendster-small	7.9M	447M	1.84 hrs	4 * 2.42 GiB

The learned node embeddings are evaluated on the standard task of multi-label node classifcation. We report micro-F1 and macro-F1 of each model, with regard to different percentages of training data.

Youtube	%Labeled Data	1%	2%	3%	4%	5%	6%	7%	8%	9%	10%
Micro-F1	DeepWalk	37.41	40.48	42.12	43.63	44.47	44.83	45.41	45.77	46.11	46.39
	LINE	38.36	40.61	42.17	43.70	44.44	44.97	45.47	45.73	46.12	46.25
	node2vec	37.91	40.59	42.37	43.56	44.32	44.94	45.40	45.77	46.07	46.41
Macro-F1	DeepWalk	30.77	33.67	34.91	36.44	37.02	37.27	37.74	38.17	38.35	38.51
	LINE	30.90	33.69	34.88	36.40	36.75	37.44	37.89	38.07	38.30	38.40
	node2vec	30.70	33.69	34.84	36.17	36.45	37.42	37.68	38.05	38.32	38.62

See also

Configuration files: deepwalk_youtube.yaml line_youtube.yaml node2vec_youtube.yaml

For larger datasets, node2vec fails with out-of-memory error, as it requires more than 200 GiB memory to build alias tables for the 2nd order random walks.

Flickr	%Labeled Data	10%	20%	30%	40%	50%	60%	70%	80%	90%
Micro-F1	DeepWalk	62.98	63.44	63.72	63.71	63.79	63.69	63.80	63.93	63.92
	LINE	63.05	63.45	63.69	63.73	63.79	63.82	64.00	63.69	63.79
	node2vec	Out of Memory
Macro-F1	DeepWalk	61.72	62.12	62.36	62.38	62.42	62.36	62.44	62.58	62.55
	LINE	61.77	62.14	62.35	62.39	62.46	62.45	62.64	62.28	62.45
	node2vec	Out of Memory

See also

Configuration files: deepwalk_flickr.yaml line_flickr.yaml

Friendster-small	%Labeled Data	1%	2%	3%	4%	5%	6%	7%	8%	9 %	10%
Micro-F1	DeepWalk	76.93	83.96	86.41	86.91	87.94	88.49	88.84	88.96	88.90	89.18
	LINE	76.53	83.50	85.70	87.29	87.97	88.17	88.69	88.87	88.76	89.20
	node2vec	Out of Memory
Macro-F1	DeepWalk	71.54	81.34	84.57	85.75	86.77	87.48	87.93	88.02	88.25	88.42
	LINE	70.46	80.88	84.07	85.99	86.76	87.39	87.86	87.91	87.72	88.56
	node2vec	Out of Memory

See also

Configuration files: deepwalk_friendster-small.yaml line_friendster-small.yaml

Knowledge Graph Embedding

For knowledge graph embedding, we benchmark TransE, DistMult, ComplEx and RotatE on 5 standard datasets. The training time, evaluation time and resource of RotatE on these datasets are given in the following table.

Dataset	|V|	|E|	|R|	Training / Evaluation Time	GPU memory cost
FB15k	15K	483K	1.3K	28.1 mins / 55.8 s	4 * 788 MiB
FB15k-237	15K	272K	237	15.3 mins / 20.8 s	4 * 758 MiB
WN18	41K	141K	18	16.4 mins / 12.0 s	4 * 776 MiB
WN18RR	41K	87K	11	14.8 mins / 8.98 s	4 * 776 MiB
Wikidata5m	5.0M	21M	828	2.10 hrs / 54.9 mins	4 * 2.96 GiB

To evaluate the knowledge graph embeddings, we test them on the link prediction task. We report the results for each model on the test set, where ranking metrics are computed based on filtered results.

FB15k	MR	MRR	HITS@1	HITS@3	HITS@10
TransE	57	0.614	0.459	0.739	0.849
DistMult	70	0.765	0.698	0.812	0.874
ComplEx	236	0.679	0.596	0.735	0.821
SimplE	87	0.791	0.737	0.828	0.882
RotatE	36	0.767	0.687	0.830	0.891

See also

Configuration files: transe_fb15k.yaml distmult_fb15k.yaml complex_fb15k.yaml simple_fb15k.yaml rotate_fb15k.yaml

FB15k-237	MR	MRR	HITS@1	HITS@3	HITS@10
TransE	172	0.288	0.190	0.324	0.487
DistMult	224	0.295	0.204	0.329	0.478
ComplEx	372	0.271	0.184	0.301	0.447
SimplE	253	0.284	0.196	0.315	0.462
RotatE	201	0.314	0.218	0.348	0.506

See also

Configuration files: transe_fb15k-237.yaml distmult_fb15k-237.yaml complex_fb15k-237.yaml simple_fb15k-237.yaml rotate_fb15k-237.yaml

WN18	MR	MRR	HITS@1	HITS@3	HITS@10
TransE	522	0.545	0.211	0.881	0.933
DistMult	661	0.819	0.717	0.918	0.945
ComplEx	1262	0.877	0.857	0.892	0.909
SimplE	487	0.944	0.941	0.946	0.949
RotatE	303	0.948	0.924	0.950	0.957

See also

Configuration files: transe_wn18.yaml distmult_wn18.yaml complex_wn18.yaml simple_wn18.yaml rotate_wn18.yaml

WN18RR	MR	MRR	HITS@1	HITS@3	HITS@10
TransE	3834	0.219	0.015	0.398	0.523
DistMult	5065	0.449	0.419	0.466	0.504
ComplEx	12602	0.328	0.312	0.339	0.353
SimplE	5569	0.446	0.421	0.458	0.492
RotatE	2359	0.500	0.455	0.518	0.589

See also

Configuration files: transe_wn18rr.yaml distmult_wn18rr.yaml complex_wn18rr.yaml simple_wn18rr.yaml rotate_wn18rr.yaml

Wikidata5m	MR	MRR	HITS@1	HITS@3	HITS@10
TransE	109370	0.253	0.170	0.311	0.392
DistMult	211030	0.253	0.209	0.278	0.334
ComplEx	244540	0.281	0.228	0.310	0.373
SimplE	112754	0.296	0.252	0.317	0.377
RotatE	89459	0.290	0.234	0.322	0.390

See also

Configuration files: transe_wikidata5m.yaml distmult_wikidata5m.yaml complex_wikidata5m.yaml simple_wikidata5m.yaml rotate_wikidata5m.yaml

Graph & High-dimensional Data Visualization

The high-dimensional data visualization is evaluated on two popular image datasets. The training time and resource needed by LargeVis is given in the following table. Note that more than 95% GPU memory cost comes from the construction of KNN Graph, and can be traded off with speed if necessary.

Dataset	Vector	N	dim	Training Time	GPU memory cost
MNIST	Raw pixels	70K	784	13.9 s	2.86 GiB
ImageNet	ResNet50 feature	1.33M	2048	13.6 mins	15.1 GiB

See also

Configuration files: largevis_mnist_2d.yaml largevis_imagenet.yaml

Here is a 3D visualization result of MNIST.

For ImageNet, since it contains 1000 classes, we visualize classes according to their hierarchy in WordNet. The following animation shows how the class of english setter (a kind of dog) is traversed in the hierarchy.