Modified Impact Factors

New versions of JCR IF are proposed for comparing them with JCR IF. They focus on the journal self-citation and the number of citing sources. The proposed versions are grouped into: 1) IFs penalized by self-citations, 3) IF encouraged by the number of citing sources and 3) IFs combining the penalized IFs and encouraged IF. This study evaluates the impact of journal self-citations and distribution of citations among sources on JCR IF. The study indicates that selfcitationshave little impact on the values of IF and the IF rankings, whether or not journal self-citations areincluded. The proposed indicators have been evaluated for the 30 journals in Computer Science field indexed in JCR 2013. The Spearman’s ρ correlation between the JCR IF and IFs penalized by self-citations is in the range of 0.76-0.96 and the Kendall’s τ correlation is in the range of 0.57-0.86. The study also indicates that compared to the IFs penalized by self-citations, the IF encouraged (EIF) by the number of citing sources correlated moderate with the JCR IF, the Spearman’s ρ correlation is 0.73 and the Kendall’s τ correlation is 0.59. Experiment results showed that the JCR IF moderately correlated with the combined IFs, Spearman’s ρ correlation is in the range of 0.69-0.72 and Kendall’s τ correlation is in the range of 0.55-0.58. We also showed that penalization strategy of self-citation can influence on the result. For example, IF linearly penalized (LPIF) by self-citations highly correlated with the JCR IF (Spearman’s ρ correlation is 0.99 and Kendall’s τ correlation is 0.93), and IF non-linearly penalized (nLPIF) by self-citations moderately correlated with the JCR IF (Spearman’s ρ correlation is 0.76 and Kendall’s τ correlation is 0.57). Finally, we concluded that IFs with and without penalization lowly correlated with the number of articles and the number of citing sources.


INTRODUCTION
The quality of a scientific journal is generally measured in impact factors provided by ISI Web of Knowledge Journal Citation Reports (JCR).Impact Factor is the most important indicator to determine the influence of a journal.This indicator represents the average number of citations to a journal over a specific period of time, usually two years. 1,2 where IF y J is the impact factor of journal J in a year y; y J N is the number of journals citing the articles of journal J in the year y; is the total number of articles published in journal J in the two previous years y -1 and y -2; is the number of citations received by journal J in the year y from journal I.
In Eq.( 1), the numerator is the number of citations in year y to any items published in the journal in previous 2 years; and the denominator is the number of articles published in the same 2 years. 3spite popularity of impact factor there are many adverse effects of ranking the journals by IF. 4 Pointed out several limitations regarding the use of impact factors, e.g.manipulations by authors and editors, disambiguation with peer-review process, distinction between the qualities of journal articles, etc. Ways forboosting the prestige of a journal, in other words, "tricks" of engineering and IF manipulating on purpose of increasing the nominator or decreasing the denominator of Eq.( 1) were pointed out. 5 In calculation of impact factor or not considered either not widely studied following factors: -Number of citingsources -10 citations from different journals must be preferred to 10 citations from one journal, because large-scale distribution of citations proves widely adoption of given journal among different researchers; -Fractions of self-citations -in certain cases, authors are forced to cite articles from the same journal.Although some of self-citations may be legitimate, they can distort the scientific literature and opinion of science policymakers. 6,7Found that high self-citing rate of journal may strongly affect the impact factor.
In this paper, penalized impact factors, considering weight fractions of self-citations, encouraged impact factor, considering distribution scale of citing sources and combinationof both penalized and encouraged impact factors are proposed.

MATERIALS AND METHODS
Using citations for evaluation of the performance of scientific journals was initiated 1 and he established the first citation indexes (Science Citation Index) and the company, the Institute for Scientific Information (ISI). 8ng time JCR IF was the predominant metric for evaluation of the journals despite considerable criticism.
Recently have been proposed new indicators including the Eigen factor, the h-index, SJR and SNIP.It is important to understand how these indicators differ from each other, and the degree of their validity. 8,9The Eigen factor explicitly excludes journal self-citations unlike most other indicators. 10eviews the literature on citation impact indicators.There have also been several reviews of the use of indicators in research evaluation. 11Since IF only measures the average number of citations per article in a certain time window, it can be argued that it does not reflect the real value of a periodical.The book 2 defines five dimensions, which build a framework for a multidimensional method of journal evaluation.
Unweighted citations also have been noted as main disadvantage of IF, so in IF calculation all citations are counted with equal weight, regardless the prestige of the citing journal. 12mpact factor takes into account only the quantity of the citations but not their quality.Different modifications of IF, weighted by cited journals' IF were proposed, 13,14,15,16 constructed mathematical model of generalized weighted impact factor. 17An approach presented in 18 takes into consideration the fact, who quoted the papers analyzed: (2) The only difference is that instead of counting the numbers of citation c j of a given article j, this formula sums the weighted citations ω j : ( where c j is the number of independent quotations of the article j; W i is the weighting factor of the ith author quoting the article j.
In 14 proposed a new way of calculating a journal impact factor, called the CHAL impact factor, an abbreviation for "cited half-life" IF.They proposed the following definition of a journal impact factor. 14,19 where MIF y J denotes the median IF of journal J in the year y; denotes the cumulative number of articles published by journal J during the period [y -y m , y]; y m is the median cited age; y J C is the total number of citations received by journal J in the year y which is calculated as follows: (5) Self-citation of a journal may affect its impact factor.Journal self-citations, defined as a citation received from an article published in the same journal.Journal self-citations are an important subject in scientometrics studies which can be are classified into the self-citing rate and the self-cited rate.The self-citing rate relates a journal self-citation to the total number of references it gives.The self-cited rate relates journal self-citations to the number of times it is cited by all journals, including itself. 20,21,22Investigated the effect of the self-citation rate of a journal on its IF of pediatric journals indexed in the JCR. 23Spearman's ranked correlation showed that IF was significantly and inversely correlated with self-citation rate.
Classified the research studies that have been conducted in the investigation of journal self-citations into four categories 20 : 1) The first category explored the basic characteristics of journal self-citation; 2) The second category studied the self-citing and self-cited rates of journals of an individual country; 3) The third category investigated journal self-citation rates for a certain subject; 4) The fourth category investigated the journal self-citation rates and the manipulation of their impact factors.The mathematical expressions of the relation between journal self-citation rate and its impact factor were established in 24 analyzed the possibility that journal editors manipulate the journal impact factors by raising the self-cited rate.Stated that coerced journal self-citation is unethical and if unchecked it will continue to falsify the value of IF. 25 Analyzed journals selected from list of JCR from 1998 to 2007, with large increases or decreases in their IFs from a given year to the following. 26About 54% of the increases and 42% of the decreases in the journal IFs were associated with changes in the journal self-citations.Was found that, in some journals rate of self-citation is a dominant influence in the total level of citation.In these cases, self-citation has the potential to distort the real influence of the journal in given subject. 27Demanding of authors by journal editors to cite articles from recent years of the journal had been detected as strategy of IF manipulation. 28,29,30oticed that publishing large amounts of editorial material with many self-citations by academic journals is one of the ways for increasing impact factor. 31Analyzed that publishing relatively many review articles by self-citations and limiting the number of included articles is also one of the ways to increase IF of journals. 32sed on data of the JCR of ISI in the subject category "Ecology", 33 found that journals with higher impacts have lower self-citation rates.He also detected that with increasing journal impact the self-citation rates decrease.To avoid further deliberate increases in self-citation rates, Krauss suggested take journal-specific self-citation rates into account for journal rankings.He proposed adjusted impact factorwhichexcludes journal self-citations in calculating impact factor: where sC denotes the number of self-citations of journal J in the year y.
In 34 have been analyzed problems associated with the use of journal impact factors and has been remarked that journal self-citation is one of the problems associated with the use of journal impact factors.Cases of coercive self-citation by peer reviewers have been analyzed in. 35e absolute value of any particular index is arguably meaningless unless compared with other indices.It is clear different metrics result in divergent rankings.So to provide more objective ranking of journals 36 developed a κ-resampled composite rank incorporating five indices: IF, Immediacy Index, SNIP, SJR and Google 5-year h-index.
One of the most important values for determining the journal impact is distribution of citations among citing sources.Offered fractionally citation counts normalized in terms of the citing sources. 37Fractional counting of citations defined the significance of differences among small and large sets of citing sources.The audience factor was proposed 38 as a variant of a fractional citation-counting scheme.Audience factor is a weighted impact factor, addressing field-discrepancies by citing-side normalization, in contrast both with post-facto field-normalization and influence measures. 39For solutions of the problem related by citation frequencies between different sciences has been offered Scopus's Source Normalized Impact per Paper (SNIP). 40In ranking scientific journals by SNIP following characteristics of journals considered as the main aspects: its properly defined subject field, the frequency at which authors cite other papers in their reference lists, the rapidity of maturing of citation impact, and the extent to which a database used for the assessment covers the field's literature.

Proposed Versions of Impact Factor
In this section, we propose new versions of IF which have beentaken into consideration the journal self-citations and distribution of citations among citing sources.

Penalized Impact Factors
Distortion cases of IF by journal self-citations have been noticed above.For more adequate ranking of scientific journals we proposed the following versions ofimpact factor penalized by self-citations which decrease by increasing self-citations.
In this study, to penalize self-citations we set the following relation between α and β, β = 2a.From the equality α + β = 1 we obtain that 1 3 α = and 2 .3 β = From Eqs.( 6) and ( 7) we obtain the following relation between LPIF and AIF: From Eqs.(1), ( 5) and ( 6) we obtain the following relation between JCR IF and AIF: Impact factor non-linearly penalized (nLPIF) by self-citations.This version of IF is defined as follows: Pure Impact Factor (PrIF).The PrIF in calculating the impact factor not only excludes the journal self-citations it also excludes the uncited articles: PrIF , where 1 y j cA − and 2 y j cA − are the number of articles published in journal J in the years y -1 and y -2, respectively, that have been cited at least once in the year y.

Encouraged Impact Factor
Impact factorencouraged by the number of citing sourcestakes into considerationan influence sphere of the journal: Where N y − is the number of journals registered in JCR in the year y.

Combined Impact Factors
We introduce the followingindicators combining the both penalized and encouragedIFs: PrE_IF .
When ranking the journals using these indicators, we take into account both the portion of self-citations in all citations and the degree of distribution of the citations among citing sources.

Data collection
For evaluation of the proposed indicators we have selected 30 journals in the Computer Sciencefieldindexed in JCR 2013.Theproposed indicators have been calculated for these journals and compared with their JCR IFs.Table 1 gives a list of the journals analyzed in the study and their bibliometric characteristics, i.e. impact factors, number of citations, self-citations, number of citing sources, number of articles and number of cited articles.

RESULTS
In this section, were calculated impact factors penalized by self-citations, impact factor encouraged by the number of citing sources and combined impact factors of the journals (Table 2).
From the Table 2 we obtain the following ranking lists of journalsgenerated by different indicators (Table 3).

DISCUSSION AND CONCLUSIONS
In order to see how theproposed indicators have influenced to the ranks of journalswe have compiled a table of the ranks difference (Table 4).
In Table 4, the positive numbers indicate that compared to the IF's ranks the journals improved their position in the corresponding indicators, and negative numbers are the opposite.As can be seen in   To make a clear picture, we used correlation coefficient between the indicators.Then, we examined whether Spearman or Pearson correlation coefficient is appropriate for constructing the correlation matrix between the indicators.Since Spearman coefficient (ρ) is independent of the normality of the data distribution and moreover it can handle ties, in this study has been used Spearman ρ coefficient for the construction of the correlation matrix. 41,9The correlation matrix (12×12) was formulated and most indicators were found to be significantly correlated (Spearman ρ > 0.8) with each other at a statistical significance level of 0.05, but there were also a few indicators that showed no strong correlation (ρ < 0.5) with the majority of other indicators.
Table 5 shows that, the Spearman's ρ correlation coefficient between JCRIF and AIF (after removing self-citations) reaches a statistical significance level with a high correlation, ρ = 0.96.Table 5  From the perspective of rankings, as seen in Table 5, the overall rankings of journals based on JCRIF and penalized Ifs values produce Spearman's ρ that reaches a statistical significance level as highly correlated: is in the range of 0.76-0.96.Compared to these results, JCR IF is moderately correlated with the EIF and with combined IFs (AE_IF, LPE_IF, nLPE_IF, PrE_IF), is 0.73 and is in the rangeof 0.69-0.72,respectively.
A similar result was also obtained in the calculation of Kendall correlation.The results of calculation were shown in Table 6.
Similar to Spearman's ρ correlation coefficient the Kendall's τ correlation coefficient among the indicators JCR IF, AIF, LPIF and PrIF is also high, in the range of 0.73-0.93.
Here the exception is nLPIF.Compared to the indicators AIF, LPIF and PrIF, correlation between the JCR and Nlpif can be considered as moderate, τ =0.57.
In this study, we also investigated the influence of the parameters α and β on the correlation between JCR IF and LPIF.As can be seen in Figure 1, journal self-citation does not influence on ranking of journals.Correlation between these indicators is high for different values of the parameters α and β.
According to the findings of this study, journals' IF values and rankings with or without self-citations are all highly correlated.It is hereby recommended that, in comparison with journals' IF values or ranking, self-citations do not need to be eliminated.As scholarly communication behaviors vary in different disciplines, this recommendation may be a useful consideration for Computer Science and can serve as a reference for other disciplines.

CONFLICT OF INTEREST
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the article entitled, "Modified Impact Factors".The study was conducted by the authors, no other people involved in conceiving, performing, and writing this study!
also shows that, not only after removing self-citations and also removing noncited articles, the Spearman's ρ correlation coefficient between JCR IF and PrIF reaches a statistical significance level with a high correlation, ρ = 0.87.In the correlation between IFs (JCR IF, AIF, LPIF, nLPIF, and PrIF, i.e. after removing or penalizing self-citations and also removing non-cited articles) andnumber of articlesthere is low correlation, in the range of 0.25-0.33.While the indicators JCR IF, AIF, LPIF, nLPIF, and PrIFare moderately correlated with number of citing sources, in the range of 0.44-0.57.As seen, unlike the penalized IFs (AIF, LPIF, nLPIF and PrIF) the encouraged IF (EIF) and combined IFs (AE_IF, LPE_IF, nLPE_IF, PrE_IF) highly correlated with the number of articles and citing sources, in the range of 0.65-0.72 and 0.90-0.94,respectively.High correlation of these indicators with the number of citing sources is obvious.It follows immediately from the definition(12).Another interesting result is that compared to high correlation (ρ = 0.99) between the JCR IF and LPIF, correlation between the JCR IF and nLPIF is low (ρ = 0.76).It follows that penalization strategy of selfcitation can influence on the result.

Figure 1 :
Figure 1: Spearman's ρ coefficient between JCR and LPIF for different values of α and β

Table 5
, the best (IEEE Transactions on Pattern Analysis and Machine Intelligence) and worst (International Journal of Pattern Recognition and Artificial Intelligence) ranked journals (based on JCR IF ranking) retained their positions in all rankings.Some journals (Genetic Programming and