JST CREST: Graph CREST 2
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1 JST CREST , 18 1
2 JST CREST: Graph CREST 2
3 3
4 4
5 Deep South A. Davis (1941) 14 Events 18 Women 5
6 Deep South [DGG41], [HOM50], [P&C72], [BGR74], [BBA75], [BCH78], [DOR79], [BCH91], [FRE92], [E&B93], [FR193], [FR293], FW193, [FW293], [BE97], [S&F99], [ROB00], [OSB00], [NEW01],... 6
7 Karate Club W. W. Zachary, An information flow model for conflict and fission in small groups, J. Anthropological Research 33, (1977)
8 Twitter Follower/Followee 8
9 Follows & Replies-to on Twitter: forward2012 in tweets (sep. 9-10, 2012) 9
10 Gephi NodeXL MS Excel gephi.org 10
11 Gephi NodeXL MS Excel gephi.org Visual analytics Exploratory data analysis 11
12 12
13 G = (V, E) V: E:
14 12 6 0: 1, 2, 3, 4, 5, 6, 7, 8,... 1: 0, 2, 3, 7,... 2: 0,1, 3, 7, 8, 9,... 3: 0, 1, 2, 7, : 0, 6, : 0, 6,... 6: 0, 4, 5,... 14
15 0: 1, 2, 3, 4, 5, 6, 7, 8,... 1: 0, 2, 3, 7,... 2: 0,1, 3, 7, 8, 9,... 3: 0, 1, 2, 7,... 4: 0, 6,... 5: 0, 6,...? : 0, 4, 5,
16 16
17 17
18 18
19 : [Eades 1984], [FR 1991] : [KK 1989], [DH 1996] Distance scaling: [TKS 1980] (MDS): [BP 2007] 19
20 Eades (1984) G = (V, E) V e = (v 1, v 2 ) in V V. if e in E: else: repeat M: v in V: P. Eades: A heuristic for graph drawing. Congressus Numerantium (42),
21 Eades (1984) G = (V, E) V e = (v 1, v 2 ) in V V. if e in E: c 1 log(d/l) else: -c 2 /d 2 repeat M: v in V: 21
22 Fruchterman & Reingold (1991) G = (V, E) V e = (v 1, v 2 ) in V V. if e in E: d 2 /k else: -k 2 /d repeat M: v in V: T. M. Fruchterman & E. M. Reingold: Graph drawing by force-directed placement. Software Pract. Expre. (21),
23 Kamada & Kawai (1989) vs X Energy = ( p i p j l ij ) 2 (v 1,v 2 )2E Compute (p1, p 2,...) that minimize Energy Newton-Raphson T. Kamada & S. Kawai: An algorithm for drawing general undirected graphs. Inform Process Lett. (31),
24 Torgerson-Kruskal-Seery (1980) (MDS) MDS(D) (p1, p 2,...): p i P pi = q i: p i 2 q i J. B. Kruscal & J. B. Seery: Designing network diagrams. in proc. conf. Social graphics,
25 Hosobe (2012): (Eades, Kamada-Kawai, Fruchterman-Reingold) L- BFGS (a) L-BFGS/KK (b) L-BFGS/HC (c) L-BFGS/Eades (d) L-BFGS/FR H. Hosobe: Numerical optimization-based graph drawing revisited, PacificVis, 2012, IEEE. 25
26 26
27 KK, MDS: O( V 2 ) : O( V 3 ) << 27
28 28
29 29
30 6 <
31 Barnes-Hut : N graph layouts either in 2D or 3D. Implicit surfaces are u visually simplified representation of vertex clusters, and edge bundles are formed for the simplification of edges. ally, dedicated transition techniques are provided for co adaptive and adjustable views of graphs that range from stract to very detailed representations. Keywords: Graph visualization, level-of-detail, cluster implicit surfaces, edge bundles. Index Terms: I.3.6 [Methodology and Techniques]: I Techniques; H.5.2 [Information Interfaces and Presentat Interfaces; J. Barnes & P. Hut: A hierarchical O(N log N) force-calculation algorithm, Nature (324), O(N 2 ) O(N log N) Loack s LinLog: A. Noack: An energy model for visual graph clustering, in proc. GD03, Clustered Graph & LoD M. Balzer & O. Deussen: Level-of-Detail visualization of clustered graph layout, in proc. APVIS ( ) (Social Cosmo Browser) 31
32 Singed (D3.js/Google Chrome) Signed: Singed 32
33 Signedネットワークの素朴な可視化 33
34 構造をもったネットワークの可視化 34
35 Social Cosmo Browser K. Wakita & T. Tsurumi: Finding community structure in mega-scale social networking service, in proc. IADIS WWW/Internet, MDS 3D LoD : 28(2),
36 Social Cosmo Browser 36
37 Social Cosmo Browser (4min. for 88 LoD 622 3,350 ) MDS 3 (TKS ) 37
38 AGI3D: UI H. Hosobe: An extended high-dimensional method for interactive graph drawing, in proc. APVIS : 2012-HCI-164(6),
39 Graph IBM 39
40 UI: LoD & 40 Social Cosmo Browser High Performance Gephi
41 Social Cosmo Browser AGI3D /GPGPU DB 41
42 Desktop Social Cosmo Browser 42
43 : UI HPC UI 43
2. Eades 1) Kamada-Kawai 7) Fruchterman 2) 6) ACE 8) HDE 9) Kruskal MDS 13) 11) Kruskal AGI Active Graph Interface 3) Kruskal 5) Kruskal 4) 3. Kruskal
1 2 3 A projection-based method for interactive 3D visualization of complex graphs Masanori Takami, 1 Hiroshi Hosobe 2 and Ken Wakita 3 Proposed is a new interaction technique to manipulate graph layouts
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ÕÒÖÎ ÆÉ ÐÖÔÒ Ñ ˆ e Ê j ÉÏÏÔÐÏÒuu ËÊ o y * ÎÏ Ó ÏÕ( ) (* É ) An Improvement of Force-directed Hierarchical Graph Layout And Its Application to Web Site Visualization Jun DOI Takayuki ITOH IBM Research,
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