Wikipedia Mathematics

Improving Prediction of Daily Visits of Wikipedia Mathematics Topics using Graph Neural Networks

Number of Daily Visits of Wikipedia Mathematics Topics using Graph-based Convolutional Neural Network as a Robust Machine Learning Model

Abstract

Spatiotemporal signal processing is one of the complex and hot topics especially in web mining like web traffics analysis. The web pages and their links are a graph and their visits or content can be a signal. The PyTorch Geometric Temporal is introduced for spatiotemporal signal mining. This study analyze Wikipedia mathematics pages using PyTorch Geometric Temporal library to improve their visits prediction during the time using grid search for parameter adjustment. The results show 1.15% relative improvement for GConvGRU algorithm versus basic related work which published the library.

Keywords— Web Mining; Traffic Prediction; Graph Convolutional Network (GCN).

Benchmark

#	lags	train ratio	k	linear digit	node features	filters	lr	epoch	time	error
1	14	50%	2	1	14	32	0.01	50	911s	0.8143236637115479
2	14	50%	3	1	14	32	0.01	50	1444s	0.8163800835609436
3	14	50%	4	1	14	32	0.01	50	1947s	0.7932114601135254
4	28	50%	1	1	28	32	0.01	50	441s	0.8761430382728577
5	42	50%	1	1	42	32	0.01	50	443s	0.8508368134498596
6	56	50%	1	1	56	32	0.01	50	461s	0.856105387210846
7	70	50%	1	1	70	32	0.01	50	505s	0.8762531280517578
8	84	50%	1	1	84	32	0.01	50	529s	0.9409999847412109
9	98	50%	1	1	98	32	0.01	50	547s	0.9203919768333435
10	14	50%	2	1	14	32	0.02	50	936s	0.8355252742767334
11	14	50%	3	1	14	32	0.02	50	1839s	0.8604558110237122
12	14	50%	4	1	14	32	0.02	50	2346s	0.8616055846214294
13	14	50%	5	1	14	32	0.02	50	2559s	0.8867608308792114
14	14	50%	10	1	14	32	0.02	50	5376s	0.8464503288269043
15	56	50%	2	1	56	32	0.01	50	1296s	0.8364545106887817
16	70	50%	2	1	70	32	0.01	50	1358s	0.8788001537322998
17	84	50%	2	1	84	32	0.01	50	1185s	0.9005643129348755
18	98	50%	2	1	98	32	0.01	50	1216s	0.8543722629547119
19	42	50%	2	1	42	32	0.01	50	1114s	0.8399303555488586
20	28	50%	2	1	28	32	0.01	50	1050s	0.8465337753295898
21	14	50%	1	1	14	50	0.02	50	464s	0.8963724374771118
22	16	70%	1	1	16	16	0.01	50	608s	1.401132583618164
23	32	70%	1	1	32	16	0.01	50	607s	1.634675145149231
24	16	70%	1	1	16	16	0.01	50	591s	1.3993479013442993
25	64	70%	1	1	64	16	0.01	50	629s	1.669908046722412
26	128	70%	1	1	128	16	0.01	50	659s	1.0828124284744263
27	256	70%	1	1	256	16	0.01	50	668s	0.8271479606628418
28	32	70%	1	1	32	16	0.01	50	606s	1.685264229774475
39	32	70%	2	1	32	16	0.01	50	1326s	1.3383041620254517
30	32	70%	3	1	32	16	0.01	50	2049s	1.3266639709472656
31	2	70%	1	1	2	16	0.01	50	612s	1.2748934030532837
32	4	70%	1	1	4	16	0.01	50	623s	1.3384982347488403
33	8	70%	1	1	8	16	0.01	50	580s	1.364047884941101
34	16	70%	1	1	16	16	0.01	50	582s	1.3909107446670532
35	16	70%	1	1	16	2	0.01	50	565s	1.2858407497406006
36	16	70%	1	1	16	4	0.01	50	601s	1.3470855951309204
37	16	70%	1	1	16	8	0.01	50	608s	1.3956334590911865
38	16	70%	1	1	16	16	0.01	50	624s	1.3498746156692505
39	16	70%	1	1	16	32	0.01	50	639s	1.3010109663009644
40	16	70%	1	1	16	32	0.02	50	629s	1.7191174030303955
41	16	70%	1	1	16	32	0.03	50	648s	1.809025764465332
42	16	70%	1	1	16	16	0.01	50	623s	1.4078537225723267
43	14	30%	1	1	14	32	0.01	50	268s	1.0906275510787964
44	14	40%	1	1	14	32	0.01	50	362s	0.8774722814559937
45	14	60%	1	1	14	32	0.01	50	532s	0.8744056224822998
46	14	70%	1	1	14	32	0.01	50	632s	1.314452052116394
47	14	90%	1	1	14	32	0.01	50	783s	0.66766756772995
48	16	30%	1	1	16	16	0.01	50	271s	1.089638352394104
49	16	40%	1	1	16	16	0.01	50	345s	0.8601189255714417
50	16	50%	1	1	16	16	0.01	50	419s	0.8372963070869446
51	16	60%	1	1	16	16	0.01	50	517s	0.8800567984580994
52	16	70%	1	1	16	16	0.01	50	600s	1.3647654056549072
53	16	80%	1	1	16	16	0.01	50	677s	0.8518020510673523
54	16	90%	1	1	16	16	0.01	50	781s	0.6800107955932617
55	16	70%	1	1	16	64	0.01	50	671s	1.4077645540237427
56	64	70%	1	1	64	2	0.01	50	643s	1.4670355319976807
57	64	70%	1	1	64	4	0.01	50	620s	1.1776090860366821
58	64	70%	1	1	64	8	0.01	50	601s	1.4935400485992432
59	64	70%	1	1	64	16	0.01	50	597s	1.6202009916305542
60	64	70%	1	1	64	32	0.01	50	619s	1.52037513256073
61	64	70%	1	1	64	64	0.01	50	653s	1.5570083856582642
62	64	70%	1	1	64	128	0.01	50	697s	1.526889443397522
63	256	90%	3	1	256	2	0.01	50	4868s	0.6845269799232483
64	256	90%	3	1	256	2	0.005	50	4505s	0.6575148701667786
65	256	90%	3	1	256	2	0.0025	50	4059s	0.6614260077476501
66	256	90%	3	1	256	4	0.01	50	4500s	0.7011445164680481
67	256	90%	2	1	256	2	0.005	50	2333s	0.6535002589225769
68	256	90%	2	1	256	4	0.01	50	2359s	0.6499081254005432
69	256	90%	2	1	256	4	0.0025	50	2519s	0.7072554230690002
70	256	90%	2	1	256	4	0.005	50	2576s	0.6859683990478516
71	16	70%	1	1	16	16	0.01	50	285s	1.3943161964416504
72	16	70%	1	1	16	16	0.01	50	582s	1.3705955743789673
73	16	70%	1	1	16	16	0.01	100	1160s	1.3797444105148315
74	16	70%	1	1	16	16	0.01	150	1741s	1.4409031867980957
75	16	70%	1	1	16	16	0.01	200	2284s	1.4262229204177856

Authors

• Seyyed Ali Mohammadiyeh

  • Department of Pure Mathematics, Faculty of Mathematical Sciences

  • University of Kashan, Kashan, Iran

  • alim [at] kashanu.ac.ir

• Dr. Behzad Soleimani Neysiani

  • Technical Soldier, Department of Research and Development

  • Ava Aria Information Company, Demis Holding, Isfahan, Iran,

  • b.soleimani [at] demisco.com