Multilevel Graph Clustering with Density-Based Quality Measures

More documents

Recommendations

Info

$Eine Einführung in LaTeX-Beamer - studiy - Brandenburgische ...$

B <strong>Clustering</strong> ResultsRWreach-sgrd 1 RWreach-sgrd 3 RWreach-sgrd 5 WD-sgrdprison alon 0.61288 0.61464 0.61898 0.62077polBooks 0.52724 0.52724 0.52694 0.52724adjnoun 0.30122 0.29690 0.27580 0.31078jazz 0.44468 0.44487 0.44424 0.44468sandi main 0.82779 0.82779 0.82779 0.82773celegansneural 0.50295 0.49997 0.49783 0.50295USAir97 0.36824 0.36603 0.36094 0.36824celegans metabolic 0.45105 0.44075 0.43418 0.45070circuit s838 0.81377 0.81520 0.81447 0.81551polBlogs main 0.43242 0.43233 0.43225 0.43237Yeast main 0.62524 0.62475 0.62710 0.62179Epa main 0.67258 0.66818 0.66667 0.66843USpowerGrid 0.93768 0.93921 0.93937 0.93795Lederberg main 0.70331 0.70382 0.70362 0.70339PairsP 0.65233 0.65434 0.65346 0.65067astro-ph main 0.76328 0.76365 0.76440 0.76261DIC28 main 0.85106 0.85285 0.85152 0.84747Table B.4: <strong>Clustering</strong> Results from the Refinement Phasenone SGR-density CGR KLChain8 0.3571429 (2) 0.3571429 (2) 0.3571429 (2) 0.3775510 (3)Star9 -0.0078125 (2) 0.0000000 (1) 0.0000000 (1) 0.0000000 (1)K55 0.3000000 (2) 0.3000000 (2) 0.3000000 (2) 0.3000000 (2)Student government 0.1299822 (3) 0.1817371 (2) 0.1817371 (2) 0.1817371 (2)Tree15 0.5051020 (5) 0.5051020 (5) 0.5051020 (5) 0.5127551 (4)ModMath main 0.4201827 (4) 0.4290513 (4) 0.4290513 (4) 0.4488041 (4)SouthernWomen 0.3153011 (2) 0.3197197 (3) 0.3197197 (3) 0.3360056 (3)Hi-tech main 0.2932112 (4) 0.3164654 (3) 0.3164422 (4) 0.3167893 (3)karate 0.4086949 (4) 0.4197896 (4) 0.4197896 (4) 0.4197896 (4)football 0.3560299 (4) 0.3602930 (5) 0.3602930 (5) 0.3603160 (5)mexican power 0.3281102 (4) 0.3477610 (5) 0.3477610 (5) 0.3595222 (4)Grid66 0.5131944 (4) 0.5500000 (4) 0.5500000 (4) 0.5412500 (5)morse 0.2238226 (5) 0.2260019 (5) 0.2260019 (5) 0.2276623 (4)Sawmill 0.5500780 (4) 0.5500780 (4) 0.5500780 (4) 0.5500780 (4)Food 0.3989169 (4) 0.4022119 (4) 0.4022119 (4) 0.4022119 (4)dolphins 0.5178593 (4) 0.5258692 (5) 0.5258692 (5) 0.5258692 (5)WorldImport1999 0.2746734 (3) 0.2750381 (3) 0.2750381 (3) 0.2750381 (3)prison alon 0.6158375 (9) 0.6207735 (9) 0.6207735 (9) 0.6207735 (9)lesmis 0.5662983 (6) 0.5666880 (6) 0.5666880 (6) 0.5666880 (6)world trade 0.3416073 (3) 0.3458804 (3) 0.3458804 (3) 0.3458804 (3)polBooks 0.5036225 (4) 0.5272366 (5) 0.5272366 (5) 0.5256066 (6)adjnoun 0.2842824 (7) 0.3107820 (6) 0.3107820 (6) 0.3107820 (6)afootball 0.5768034 (7) 0.5878718 (7) 0.5878718 (7) 0.5941993 (7)baywet 0.3616026 (4) 0.3630110 (4) 0.3630111 (4) 0.3630111 (4)jazz 0.3915476 (4) 0.4446760 (4) 0.4446760 (4) 0.4448713 (4)A99m main 0.6994806 (12) 0.7093229 (12) 0.7093229 (12) 0.7139006 (11)SmallW main 0.4444636 (3) 0.4489310 (3) 0.4489310 (3) 0.4494608 (3)A01 main 0.5760183 (10) 0.6163954 (11) 0.6195992 (11) 0.6321622 (12)sandi main 0.8208257 (15) 0.8277276 (15) 0.8277276 (15) 0.8277276 (15)celegansneural 0.4740477 (5) 0.5029479 (5) 0.5029479 (5) 0.5029479 (5)USAir97 0.3435344 (6) 0.3682440 (6) 0.3682440 (6) 0.3682440 (6)8Clusters 0.2844054 (8) 0.2940509 (8) 0.2940509 (8) 0.2940509 (8)WorldCities main 0.1162580 (5) 0.1772768 (4) 0.1773516 (4) 0.1789302 (4)celegans metabolic 0.4006559 (9) 0.4507027 (9) 0.4507027 (9) 0.4509054 (9)circuit s838 0.7904052 (15) 0.8155133 (15) 0.8155118 (15) 0.8155133 (15)Roget main 0.5371181 (14) 0.5800064 (14) 0.5801273 (14) 0.5868690 (16)CSphd main 0.9248402 (33) 0.9255843 (33) 0.9255843 (33) 0.9255843 (33)email 0.5293695 (11) 0.5771250 (12) 0.5771250 (12) 0.5776780 (11)polBlogs main 0.4144859 (3) 0.4323714 (13) 0.4323714 (13) 0.4324173 (13)NDyeast main 0.8135195 (34) 0.8209006 (32) 0.8211389 (33) 0.8225031 (31)Yeast main 0.5718771 (23) 0.6217924 (23) 0.6202976 (22) 0.6232274 (22)SciMet main 0.5485112 (14) 0.6206436 (18) 0.6210574 (18) 0.6224638 (16)102
none SGR-density CGR KLODLIS main 0.4607628 (12) 0.5134514 (12) 0.5128609 (12) 0.5137963 (12)DutchElite main 0.8389162 (49) 0.8493005 (48) 0.8482894 (48) 0.8492394 (47)geom main 0.7250140 (36) 0.7470261 (43) 0.7470261 (43) 0.7472464 (42)Epa main 0.6270148 (28) 0.6684264 (27) 0.6685486 (26) 0.6709372 (27)eva main 0.9333784 (53) 0.9357163 (52) 0.9357164 (52) 0.9360090 (50)USpowerGrid 0.9328997 (41) 0.9379491 (39) 0.9382380 (39) 0.9381809 (39)hep-th main 0.8425086 (58) 0.8551498 (59) 0.8548411 (57) 0.8552368 (57)Erdos02 0.6848450 (31) 0.7159228 (38) 0.7159229 (38) 0.7161150 (39)Lederberg main 0.6508633 (20) 0.7033853 (22) 0.7033853 (22) 0.7033671 (22)PairsP 0.6145969 (35) 0.6506679 (35) 0.6510081 (33) 0.6520954 (31)PGPgiantcompo 0.8631499 (66) 0.8832731 (94) 0.8832732 (94) 0.8839220 (102)astro-ph main 0.7300281 (49) 0.7623166 (58) 0.7621238 (58) 0.7631902 (58)eatRS 0.4466266 (26) 0.4999899 (25) 0.4998523 (26) 0.5005763 (22)DIC28 main 0.8015399 (58) 0.8474654 (105) 0.8475762 (102) 0.8478136 (104)hep-th-new main 0.5798309 (18) 0.6663347 (31) 0.6663266 (31) 0.6667373 (30)cond-mat-2003 main 0.7891245 (70) 0.8135988 (76) 0.8134295 (75) 0.8137741 (77)average 0.52305183903 0.54608087341 0.54609771377 0.54810369879Table B.5: Runtime Measurements. All times are in seconds.vertices edges none SGR-density CGR KLChain8 8 7 0.28800 0.32700 0.29000 0.35100K55 10 25 0.42300 0.40100 0.37800 0.43800Hi-tech main 33 91 0.90900 0.93300 0.87800 1.12900lesmis 77 254 1.16100 1.20900 1.15600 1.28100A99m main 233 325 1.39100 1.52100 1.43500 2.49300SmallW main 233 994 1.83700 1.96800 1.89600 3.08400A01 main 249 635 1.55100 1.76400 1.71000 3.35600celegansneural 297 2148 2.02100 2.21100 2.18600 5.16600Roget main 994 3641 2.75000 3.20600 3.85200 24.25000CSphd main 1025 1043 1.66000 2.04300 1.96100 22.72700NDyeast main 1458 1993 2.03800 2.80200 3.32300 37.48900SciMet main 2678 10369 4.75600 6.44700 14.37800 84.12400ODLIS main 2898 16381 6.35300 8.02400 13.80900 79.36200Epa main 4253 8897 4.54300 7.70500 30.41500 201.82000hep-th main 5835 13815 5.27600 11.26100 27.64100 423.34600Erdos02 6927 11850 6.04900 11.31000 34.10100 359.59600Lederberg main 8212 41436 14.61700 20.20700 83.13300 392.03800PairsP 10617 63786 22.13300 33.34600 127.07900 769.91300PGPgiantcompo 10680 24316 9.00400 22.69000 55.56700 1255.66100astro-ph main 14845 119652 29.20600 52.03700 365.39200 1917.59600eatRS 23219 305501 192.21500 236.66900 2115.29200 4003.69600DIC28 main 24831 71014 24.79100 76.99900 816.51200 4755.91700hep-th-new main 27400 352059 143.37100 186.87100 1608.20900 4553.72100cond-mat-2003 main 27519 116181 33.39300 76.34600 1019.13700 4158.93400103
Page 1:
Brandenburgische Technische Univers
Page 5 and 6:
ContentsList of FiguresList of Tabl
Page 7:
List of Figures1.1 Graph of the Mex
Page 11 and 12:
1 IntroductionSince the rise of com
Page 13 and 14:
1.2 Objectives and Outline1.2 Objec
Page 15 and 16:
2 Graph ClusteringThis chapter intr
Page 17 and 18:
2.2 The Modularity Measure of Newma
Page 19 and 20:
2.3 Density-Based Clustering Qualit
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
2.4 Fundamental Clustering Strategi
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
3 The Multi-Level Refinement Algori
Page 37 and 38:
3.1 The Multi-Level Schemeas starti
Page 39 and 40:
3.2 Graph CoarseningData: graph,sel
Page 41 and 42:
3.2 Graph Coarseningnearly no edges
Page 43 and 44:
3.3 Merge SelectorsExtent Name Desc
Page 45 and 46:
3.3 Merge Selectorsdifferent size.
Page 47 and 48:
3.3 Merge SelectorsThe probability
Page 49 and 50:
3.3 Merge SelectorsAs selection qua
Page 51 and 52:
3.3 Merge Selectorsvectors the eige
Page 53 and 54:
3.4 Cluster Refinementleave the loc
Page 55 and 56:
3.4 Cluster Refinementmoving v from
Page 57 and 58:
3.4 Cluster RefinementAlgorithm Sea
Page 59 and 60:
3.4 Cluster RefinementData: graph,c
Page 61 and 62: 3.4 Cluster RefinementModularity0.2
Page 63 and 64: 3.5 Further Implementation NotesInd
Page 65 and 66: 3.5 Further Implementation NotesBOO
Page 67: 3.5 Further Implementation Notesfor
Page 70 and 71: 4 Evaluationparameter component des
Page 72 and 73: 4 Evaluationsignificance scale also
Page 74 and 75: 4 EvaluationModularity by Match Fra
Page 76 and 77: 4 Evaluation5% 10% 30% 50% 100%G-no
Page 78 and 79: 4 Evaluationmean modularity0.50 0.5
Page 80 and 81: 4 Evaluation1 2 3 4RWreach-none 1 0
Page 82 and 83: 4 EvaluationG-none M-none G-sgrd M-
Page 84 and 85: 4 Evaluationmean modularity time DI
Page 86 and 87: 4 EvaluationRuntime vs. Graph SizeR
Page 88 and 89: 4 EvaluationComparison of Modularit
Page 90 and 91: 4 Evaluation(a) karate(b) dolphinsF
Page 92 and 93: 4 Evaluation(a) jazz(b) celegans me
Page 94 and 95: 4 Evaluationadministrators, and gra
Page 97 and 98: 5 Results and Future WorkThe object
Page 99 and 100: 5.3 Directions for Future Workstrat
Page 101: 5.3 Directions for Future Workties
Page 104 and 105: BIBLIOGRAPHY[14] B.L. Chamberlain.
Page 106 and 107: BIBLIOGRAPHY[42] H. Jeong, B. Tombo
Page 108 and 109: BIBLIOGRAPHY[71] A. J. Soper and C.
Page 110 and 111: A The Benchmark Graph Collectionsub
Page 114: B Clustering Resultswalktrap leadin
show all

Multilevel Graph Clustering with Density-Based Quality Measures

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?