Basing on the scoring rule approach, there was designed a citation metrics, allowing for not only the number of author’s articles published and their citations but also the impact factors of journals in which the articles were published as well as the impact factors of journals with articles citing the autho

Golikov, N. A.

Isaev, I. F.

Moskovkin, V. M.

Serkina, O. V.

DSpace at Belgorod State University

Research Journal of Applied Sciences 9 (12): 1167-1170, 2014ISSN: 1815-932X© Medwell Journals, 2014Corresponding Author: Vladimir M. Moskovkin, Belgorod State University, Pobedy St. 85, 308015 Belgorod, Russia1167Construction IF-Scoring Rule Within The Framework ofNew Generation of Metric CitationsVladimir M. Moskovkin, Nikolay A. Golikov, Ilya F. Isaev and Olesya V. Serkina1    2    1     1¹Belgorod State University, Pobedy St. 85, 308015 Belgorod, RussiaIndependent Researcher, Kharkov, Ukraine2Abstract: On the basis of a scoring rule approach, a citation metrics has been developed in this study whichtakes into account not only the number of articles published by an author and their citations but also the impactfactors of journals in which the articles were published and impact factors of journals with articles citing theresearcher in question. We have developed a special algorithm and a program on the basis of the Pythonlanguage to identify the titles of Scopus-journals (so that they could be searched for with the help of GoogleScholar) in which an author's articles are published and to determine their IF using SCIMAGO platform. Thealgorithm and program has been tested on two Google Scholar profiles of the most cited scientists (physicists)of Belgorod State University (Russia) Ruslan Kaibyshev and Andrey Belyakov.Key words: Belgorod State University, bibliometric rankings, citation metrics, Google scholar, h-index, impactfactor, python language, scopus-journals, SCIMAGO platform, IF-scoring ruleINTRODUCTION The imperfection of h-index at a fundamental level isStarting with the classical research of Hirsch (2005),there came a boom of modifying h-index and creatingsimilar indicators. As shown by Waltman and van Eck(2012), both in 2010 and 2011 almost one out of fourpublication in Scientometrics and Journals of Informetricscited above mentioned Hirsch’s work. In the scientificliterature, one can find a set of indices (m, g, e, w, q , hg,2etc.) used for the assessment of research productivity interms of the number of publications and citations. Asfurther noted by Waltman and van Eck (2012), a large partof the literature building on Hirsch’s work is concernedwith introducing variants, extensions and generalizationsof the h-index. Thus, by Bornmann et al. (2011) we find alist of no <37 variants of the h-index.The essence of all research of this kind was welldescribed by Marchant (2009): “many researchers,analyzing previously existing indices, find that they havesome drawbacks and then propose an adapted version ofthe incriminated index or a brand new one, supposedlybetter than the older one. Unfortunately, the reasoning ofthe proponents of such new indices is often ad hoc: theypropose a new index not suffering the same drawbacks asthe older one that they analyzed but nothing guaranteesthat the new index does not have many otherweaknesses”.demonstrated in the work of  Waltman and van Eck (2012).This index turns out to violate the following threeproperties:C If two scientists achieve the same relativeperformance improvement, their ranking relative toeach other should remain unchangedC If two scientists achieve the same absoluteperformance improvement, their ranking relative toeach other should remain unchangedC If the scientist X  is ranked higher than scientist Y1      1and scientist X  is ranked higher than scientist Y ,2      2then a research group consisting of scientists X  and1X  should be ranked higher than a research group2consisting of scientists Y  and Y1  2MATERIALS AND METHODSGiven the inconsistency problem of the h-index andmany other indicators, one may wonder what kind ofalternative indicators can be used that does not have asimilar problem (Waltman and van Eck, 2012). Thisproblem was solved by Marchant (2009), throughintroducing the scoring rules (score-based or summation-based rankings (indices)).(n2 n i1i 1I C ,C , ..., C ) f (C )== åif (C) C=i if (C ) C=ni ii 1I(C ) C== åj J x N a NU(f ) f (i, x, a) u(j, x, a)Î Î Î= å å åxIF( j)u(j, x, a)(a+1)=12iii1 2 i n 1 11 12 1j 1c2 21 22 2 j 2ci i1 i2 ij icn n1 n 2 nj ncCni iji 1 j 1U(P , P .., P , .., P ) IF (IF IF ... IF ... IF )IF (IF IF ... IF ... IF )IF (IF IF ... IF ... IF )IF (IF IF ... IF ... IF )IFIF= == + + + + + ++ + + + + ++ + + + + ++ + + + += åånii 1U C== Sni ii 1U IFC== SiCiji 1IF 1=S =nii 1U IF== SRes. J. Applied Sci., 9 (12): 1167-1170, 20141168In the simplest case, to calculate a scoring rule for a In this case, we obtain a simple scoring rule rankingset of publications, one first calculates a score for eachindividual publication in the set. The score of apublication is determined by the number of citations ofthe publication. After calculating a score for eachindividual publication, the scoring rule is obtained bycalculating the sum of the individual publication scores.Somewhat more formally, given a set of N publicationswith C , C , ..., C  citations, a scoring rule is equal to:1  2   n(1)where, f(C) is an increasing function that determines thescore of a publication based on the number of time thepublication has been cited (Waltman and van Eck, 2012).It is proposed to use a slightly increasing convexfunctions like  or f(C) = In(C ) (Lundberg, 2007)i   i+1in the form of f(C ). In the work of Levene et al. (2012) iniEq. 1, a relationship  and a function were also considered.With a proper approximation, T. Marchant puts downthe scoring rule in the following way:(2)where, f(i, x, a) is the number of publications of researcherf in a journal j with exactly x citations and a co-authors(the  number  of  authors  being  a+1).  u(j,  x,  a)  is  thevalue  or  the  score  of  one  publication  in  the   journalj  with  x  citations   and   a   co-authors;   J = {j, k, l, ...}dN:represents  the  set  of  journals  and  N  is  the  set  ofintegers.The triple sum (Eq. 2) represents the total score of theauthor. As noticed by Marchant (2009), many popularbibliometric rankings are scoring rules. For example, if wechoose U equal to a positive constant, we obtain theranking based on the number of publications. If we defineU by u(j, x, a) = x for all j0J, x, a0N, we obtain the ranking,based  on  the  number of citations. If we define u by u =(j, x, a) = IF(j) for all j0J, x, a0N where IF(j) is the impactfactor of the journal j, we obtain a ranking based on thesum of the impact factors, used by Fava and Ottolini(2000).For the purpose of the current research, we considerthe usage of the function u(j, x, a) as shown below as themost suitable:(3)authors according to their number of citations weightedby the number of researchers and the impact factor(Marchant, 2009). In the research, we shall abstract awayfrom the number of researchers a but take into accountadditional impact-factors of journals corresponding tothose articles which have links to the articles of theresearcher in question.We suggested the idea of constructing IF-scoringrule by Moskovkin and Golikov (2013). Now, we are goingto render a conception and a mathematical model ofconstructing IF-scoring rule. A flowchart of IF-scoringrule calculation we suggested is shown in Fig. 1.In  it  (P ,  P ,  ...,  P ,  ...,  P )  stand  for a set of articles1   2     i     npublished by some author; (J , J , ..., J , ..., J ) a set of1  2   i   njournals in which the articles in questions are published;(IF , IF , ..., IF , ..., IF ) a set of impact-factors of the above1  2   i   njournals; (P , P , ..., P , ..., P ) a set of the C number ofi1  i2   ij   ici      iarticles citing P  article; (J , J , ..., J , ..., J ) a set ofi  i1  i2   ij   icijournals corresponding to the set of articles; (P , P , ..., P ,i1  i2   ij..., P ); (IF , IF , ..., IF , ..., IF ) a set of impact-factors ofici  i1  i2   ij   iciciting journals. It is worth noting that some journals fromsets (J , J , ..., J , ..., J ) and (J , J , ..., J , ..., J ) can1  2   i   n   i1  i2   ij   icicoincide.In the simple case, the formula for calculating thescore rule, corresponding to the above algorithm (Fig. 1),can be put down as follows:(4)It means that U(P , P , ..., P , ..., P ) = Q(IF , IF ) is an1  2   i   n   i  ijincreasing   quadratic   function   of   many   variables.   Ithas a characteristic feature common to all scoringrules:U(IF +)IF , IF +)IF ) where )IF >)IF >0 stand fori i  ij ij   i ijsmall increments. Let us have a look at some special casesof the function (Eq. 4):C If IF  = IF  = 1 then i  ijC If If1, If  = 1 then i  ijC If  then All these cases have resulted from the application ofEq. 2 by Marchant (2009).ni ii 1U U IFC== = åiCij ij 1IF C=>åq U/U 1,= >i11 Cn 22i iji 1 j 1U IF IF= =æ ö= ç ÷è øå åi i1 1 1 1C Cn n2 2 2 2i ij i iji 1 j 1 i 1 j 1U IF IF IF IF= = = == =å å åå( )iCni iji 1 j 1U IF IF= == d +åå( )i1Cn 1 22i iji 1 j 1U IF IF= =æ ö= d + ç ÷è øå åi1 1 1Cn2 2 2i iji 1 j 1U IF IF= =æ ö= d +ç ÷è øå åRes. J. Applied Sci., 9 (12): 1167-1170, 20141169Fig. 1: A flowchart of IF-scoring rule calculationTaking:as a normalized function, one can see that when:and when the total  impact  factor of the journals citing thearticles exceeds the number of citations, it will be true that otherwise q<1.In addition to function (Eq. 4), we introduce five morefunctions of many variables:(5)(6)(7)(8)(9)where, * is some positive parameter. For Eq. 5, 6, 8 and 9,we take the square root in accordance with Lundberg(2007) to inhibit the growth of function U.  Parameter  *  inEq. 7-9 is introduced in order to attach value to the citedarticles which were published in journals with a zeroimpact factor (If  = 0).iRESULTS AND DISCUSSIONFor calculation by using Eq. 4-9, we developed aspecial algorithm and a Python-based program to identifytitles of Scopus-journals (so that they could be searchedfor with the help of Google Scholar) in which an author'sarticles are published and to determine their IF usingSCIMAGO platform.The task of calculating IF-scoring rule for a particularauthor is divided into 2 sub-tasks: collection ofinformation necessary for calculating, calculation proper.In the current research, the  subtask  (a)  is  much  moretime-consuming. It is, in turn, divided into 5 stages:C Obtaining a list of journals with their IFC Obtaining a list of author's articles with identifiers(titles) of journals in which the articles werepublishedC Obtaining a list of citing articles for every author'spublication with identifiers (titles) of journals inwhich the articles were publishedOne should note that since the lists of articlesreferred to in points 2 and 3 were generated by scrappingand the following parsing of a search output of GoogleScholar, this resulted in solving the most laboriousproblems of the entire program.C Overcoming Google Scholar’s protection from webcrawlersC Identifying and matching the titles of journals (ortheir fragments), obtained from the search outputwith the titles of journals from point 1The algorithm and program were tested on the basisof two Google Scholar profiles of the most cited scientists(physicists) of Belgorod State University (Russia) RuslanKaibyshev and Andrey Belyakov (Table 1). The gatheringof the initial information for calculating (Eq. 4-9) with thehelp of Google Scholar and SCIMAGO platform was donein August, 2013. If , IF  in Eq. 4-9 were taken fromi  ijSCIMAGO platform as IF = Cites/Doc (2 years).In Table 1, the calculations by Eq. 7 when * = 0conform with the calculations by Eq. 4; the calculationsby  Eq.  8  when  * = 0 conform with the calculations byEq. 5; the calculations by Eq. 9 when * = 0 conform withthe calculations by Eq. 6. In Table 2, we show the values)U(*) = (U(* = 1)-U(* = 0)/U(* = 0))×100% calculated onthe basis of the data from Table 1.Res. J. Applied Sci., 9 (12): 1167-1170, 20141170Table 1: Calculation of IF-scoring rule for two most cited scientists of Belgorod State University (Russia), August 2013Formula number/*-----------------------------------------------------------------------------------------------------------------------------------7 8 9--------------------------------------------- ------------------------------------- -------------------------------------------Author’s Name     0 0.01 0.1 1.0    0 0.01 0.1 1.0     0 0.01 0.1 1.0Rustam Kaibyshev Cited articles: 69 4014.9 4027.1 4137.3 5238.7 232.9 233.6 239.5 286.8 1389.9 1469.0 1639.9 2180.3Citing articles from identified journals: 621Andrey Belyakov 1640.3 1646.5 1702.0 2257.0 173.2 173.6 177.5 210.6 592.6 630.2 711.5 968.7Cited articles: 40Citing articles from identified journals: 292Table 2: Values )U(*), calculated on the basis of data from Table 1 (%)Formula number-------------------------------------------------------Author’s Name   7 8 9Rustam Kaibyshev 30.5 23.1 56.9Andrey Belyakov 37.6 21.6 63.5From  Table  2,  we can see that the calculations byEq. 8 are less sensitive to parameter variation * and thisformula produces by-factor-of-ten smaller abcolute valuesof  function  U  compared  with  those  obtained  throughuse of Eq. 7 and 9. This implies that for furthercalculations we recommend applying Eq. 5 as a particularcase of Eq. 8.CONCLUSIONBasing on the scoring rule approach, there wasdesigned a citation metrics, allowing for not only thenumber of author’s articles published and their citationsbut also the impact factors of journals in which the articleswere published as well as the impact factors of journalswith articles citing the author. To calculate such a metrics,there were suggested six variants of formulas. Forcalculations by using these formulas, a special algorithmand  a  Python-based  program  identifying  titles  ofScopus-journals and determining their impact factors isdeveloped.The algorithm and program were tested on the twoGoogle scholar profiles of the most cited scientists(physicists) of Belgorod State University (Russia). Fromthe above mentioned computational formulas, wesuggested applying the one providing by factor of tensmaller results. 63: 406-415.ACKNOWLEDGEMENTResearch Was Done According to The GovernmentTask of The Ministry of Education and Science of TheRussian Federation for 2014, Project Code-516).REFERENCESBornmann,   L.,   R.  Mutz,  S.E.  Hug  and  H.D.  Daniel,2011. A multilevel meta-analysis of studies reportingcorrelations between the h index and 37 different hindex variants. J. Informetr., 5: 346-359.Fava,  G.A.  and  F.  Ottolini,  2000.   Impact   factorsversus  actual  citations.  Psychother.  Psychosom.,69: 285-286.Hirsch, J.E., 2005. An index to quantify an individual'sscientific research output. Proc. Natl. Acad. Sci.USA., 102: 16569-16572.Levene, M., T. Fenner and J. Bar-Ilan, 2012. A bibliometricindex based on the complete list of cited Publications.Cybermetrics, Vol. 16, No. 1. Lundberg, J., 2007. Lifting the crown-citation z-score. J.Informetr., 1: 145-154.Marchant,  T.,   2009.  Score-based  bibliometric  rankingsof   authors.   J.   Am.   Soc.   Inform.   Sci.   Technol.,60: 1132-1137.Moskovkin, V.M. and N.A. Golikov, 2013. [The newgeneration of citation metrics]. Proceedings of theInternational Conference on Construction of IF-Scoring   Rules,   October   10-12,   2013,   Moscow,pp: 92-93.Waltman,  L.  and  N.J.  van  Eck,  2012. The inconsistencyof  the  h-index.  J.  Am.  Soc.  Inform.  Sci.  Technol.,

Construction IF-scoring rule within the framework of new generation of metric citations

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Construction IF-scoring rule within the framework of new generation of metric citations

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