intermediacy of publications “pomembnost prispevkov za razvoj znanstvene tematike” Lovro ˇ Ludo Waltman Subelj Leiden University University of Ljubljana Centre for Science and Faculty of Computer and Technology Studies Information Science Vincent Traag Nees Jan van Eck Leiden University Leiden University Centre for Science and Centre for Science and Technology Studies Technology Studies AI seminar ’19
summer research visits CWTS in Leiden, Vincent, Ludo & Nees Tjaˇ sa, Nevi & Maˇ zo, biking, boating & skating etc. 1/18
introduction & motivation algorithmic historiography for evolution of field ( Garfield, 1964– ) relying on citations between scientific publications from WoS & Scopus t p p p p p p p p v p p u p p p p s existing approaches include main paths ( Hummon & Doreian, 1989 ) ( longest/shortest paths ) many irrelevant /miss relevant publications ( intermediacy ) important publications should only be well-connected 2/18
intermediacy measure ( input ) selected source & target publications s & t ( method ) each citation is relevant/active with probability p ( measure ) importance of publication u called intermediacy φ u φ u = Pr ( X u st ) = Pr ( X su ) Pr ( X ut ) t p p p p p p p p v p p u p p p p s X st exists path from s to t & X u st exists path through u 3/18
intermediacy for p → 0 for p → 0 intermediacy φ governed by ℓ ( proof ) for p → 0 if ℓ u < ℓ v then φ u > φ v t p p p p p p p p v p p u p p p p φ u > φ v φ u < φ v s for p ! 0 for p ! 1 ℓ u is length of shortest paths from s to t through u 4/18
intermediacy for p → 1 for p → 1 intermediacy φ governed by σ ( proof ) for p → 1 if σ u < σ v then φ u < φ v t p p p p p p p p v p p u p p p p φ u > φ v φ u < φ v s for p ! 0 for p ! 1 σ u is number of edge-disjoint paths from s to t through u 5/18
intuition for p for what p is direct citation equivalent to k indirect citations Pr ( X uv ) = p = 1 − (1 − p 2 ) k B 1 v 0.8 edge probability p v p p p 0.6 . . . p w 1 w 2 w k 0.4 p p p u 0.2 u Pr( X uv ) = p 0 1 2 3 4 5 6 7 8 Pr( X uv ) = 1 − (1 − p 2 ) k indirect paths k k is number of indirect paths from u to v 6/18
p phase transition for what p source-target path Pr ( X st ) > 0 & intermediacy ∃ u : φ u > 0 p ≥ n / 2 m = 1 / k source-target path probability Pr( X st ) source-target path probability Pr( X st ) 1 1 0.8 1/ k = 0.0899 0.8 0.6 0.6 0.4 0.4 0.2 0.2 1/ k = 0.1147 0 0 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 edge probability p edge probability p k is average number of citations / references 7/18
properties of intermediacy path addition & contraction increase intermediacy ( proof ) t t t 0.12 p 0.12 p 0.12 p p p p 0.34 0.23 w 0.17 p p w p w p p 0.23 0.17 p v p v p p p p p 0.34 p p p p r p p p p p p u u p 0.17 0.23 p p 0.12 0.12 0.12 p p p s s s original graph path addition path contraction path from source to target becomes “easier” ( intuition ) 8/18
alternatives to intermediacy alternatives are main paths & expected paths ( state of the art ) t t t 2 1.04 0.67 p p 2 p v v v p 1 0.72 1 0.72 p p p p 1 1 w w w p p 1 1 p p u p u 1 u p p p 0.67 2 2 1.04 s s s intermediacy main path analysis expected path count alternatives violate path contraction property ( example ) 9/18
exact algorithm decomposition algorithm by edge contraction & removal ( Ball, 1979 ) Pr ( X st | G ) = p Pr ( X st | G / ( s , u )) + (1 − p ) Pr ( X st | G − ( s , u )) A t t t p p p p p p p p p = p + p p p (1 − p ) p p p u u p s p p p s s graph G contraction G / ( s , u ) removal G − ( s , u ) runs in exponential time since NP-hard even in DAG ( Johnson, 1984 ) 10/18
approximate algorithm simple Monte Carlo simulation algorithm by edge sampling N st | G ) = 1 φ u = Pr ( X u � I ( X u st | H k ) N k =1 B H 1 H 2 H 3 t t t t t 0.41 p � ! p 0.61 w w w w w p ! 1 + + + . . . = p v v v v v N p u u u u u p p 0.54 s s s s s intermediacy φ graph G N samples runs in quasi linear time using probabilistic DFS over say 10 6 samples 11/18
intermediacy � = centrality correlation coefficient between intermediacies φ & citations / references 1 1 p = 0.1 1.00 0.69 0.28 0.16 0.12 0.19 0.20 p = 0.1 1.00 0.42 0.21 0.10 0.04 0.16 0.03 0.9 0.9 0.8 0.8 p = 0.3 0.69 1.00 0.78 0.58 0.44 0.49 0.43 p = 0.3 0.42 1.00 0.80 0.45 0.19 0.19 0.10 0.7 0.7 p = 0.5 0.28 0.78 1.00 0.92 0.77 0.50 0.36 p = 0.5 0.21 0.80 1.00 0.78 0.39 0.18 0.14 0.6 0.6 0.16 0.58 0.92 1.00 0.94 0.43 0.26 0.5 0.10 0.45 0.78 1.00 0.77 0.26 0.23 0.5 p = 0.7 p = 0.7 0.4 0.4 p = 0.9 0.12 0.44 0.77 0.94 1.00 0.35 0.19 p = 0.9 0.04 0.19 0.39 0.77 1.00 0.26 0.24 0.3 0.3 cit. 0.19 0.49 0.50 0.43 0.35 1.00 0.00 cit. 0.16 0.19 0.18 0.26 0.26 1.00 0.01 0.2 0.2 0.1 0.1 ref. 0.20 0.43 0.36 0.26 0.19 0.00 1.00 ref. 0.03 0.10 0.14 0.23 0.24 0.01 1.00 0 0 Pearson correlation Pearson correlation intermediacy φ uncorrelated with standard centrality measures 12/18
modularity example ( target ) Newman & Girvan (2004), Finding and evaluating community. . . , Phys. Rev. E 69 (2), 026113. ( source ) Klavans & Boyack (2017), Which type of citation analysis generates. . . , JASIST 68 (4), 984-998. 1 Waltman & Van Eck (2013), A smart local moving algorithm for large- scale modularity-based community detection, EPJB 86 , 471. Newman (2004) 2 Waltman & Van Eck (2012), A new methodology for constructing a publication-level classification system. . . , JASIST 63 (12), 2378-2392. Newman (2004) 3 Hric et al. (2014), Community detection in networks: Structural com- munities versus ground truth, Phys. Rev. E 90 (6), 062805. Newman (2006) 4 Fortunato (2010), Community detection in graphs, Phys. Rep. 486 (3- Newman (2006) 5), 75-174. Blondel (2008) Rosvall (2008) 5 Newman (2006), Modularity and community structure in networks, PNAS 103 (23), 8577-8582. 6 Ruiz-Castillo & Waltman (2015), Field-normalized citation impact in- dicators using algorithmically. . . , J. Informetr. 9 (1), 102-117. Waltman (2012) Fortunato (2010) 7 Blondel et al. (2008), Fast unfolding of communities in large networks, J. Stat. Mech. , P10008. Waltman (2013) 8 Newman (2006), Finding community structure in networks using the Hric (2014) eigenvectors of matrices, Phys. Rev. E 74 (3), 036104. Ruiz-Castillo (2015) 9 Newman (2004), Fast algorithm for detecting community structure in networks, Phys. Rev. E 69 (6), 066133. 10 Rosvall & Bergstrom (2008), Maps of random walks on complex net- Klavans (2017) works reveal community structure, PNAS 105 (4), 1118-1123. in-house version of Scopus database at CWTS 13/18
peer review example ( target ) Cole & Cole (1967), Scientific output and recognition , Am. Sociol. Rev. 32 (3), 377-390. ( source ) Garcia et al. (2015), The author-editor game , Scientometrics 104 (1), 361-380. 1 Lee et al. (2013), Bias in peer review, JASIST 64 (1), 2-17. Cole (1967) 2 Zuckerman & Merton (1971), Patterns of evaluation in science: Insti- tutionalisation, structure and functions. . . , Minerva 9 (1), 66-100. Crane (1967) 3 Campanario (1998), Peer review for journals as it stands today: Part 1, Sci. Commun. 19 (3), 181-211. Merton (1968) 4 Crane (1967), The gatekeepers of science: Some factors affecting the selection of articles for scientific journals, Am. Sociol. 2 (4), 195-201. Zuckerman (1971) 5 Campanario (1998), Peer review for journals as it stands today: Part Gottfredson (1978) 2, Sci. Commun. 19 (4), 277-306. 6 Gottfredson (1978), Evaluating psychological research reports: Dimen- Campanario (1998) Campanario (1998) sions, reliability, and correlates. . . , Am. Psychol. 33 (10), 920-934. Bornmann (2011) 7 Bornmann (2011), Scientific peer review, Annu. Rev. Inform. Sci. 45 (1), 197-245. Bornmann (2012) 8 Bornmann (2012), The Hawthorne effect in journal peer review, Sci- entometrics 91 (3), 857-862. Lee (2013) 9 Bornmann (2014), Do we still need peer review? An argument for Bornmann (2014) change, JASIST 65 (1), 209-213. 10 Merton (1968), The Matthew effect in science, Science 159 (3810), Garcia (2015) 56-63. snapshot of WoS collected by ( Batagelj et al., 2017 ) 14/18
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