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Scholar H-Index Calculator (the Calculator from now on) is an addon for Firefox which enhances Google Scholar results pages by showing a number of bibliometric data computed using the data appearing on video as input.

Once installed, the Calculator works transparently when querying [[scholar.google.com|Google Scholar]]: as soon as you make a query, result pages are enriched with a number of useful data (e.g. the h-index computed on the basis of displayed data), and new functions are available.   
Scholar H-Index Calculator (the Calculator from now on) is an addon for Firefox and Google Chrome which enhances Google Scholar results pages by showing a number of bibliometric data computed using the data appearing on video as input. Once installed, the Calculator works transparently when querying [[http://scholar.google.com|Google Scholar]]: as soon as you make a query, result pages are enriched with a number of useful data (e.g. the h-index computed on the basis of displayed data), and new functions are available.
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Project Coordinator  Project Coordinator
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You can contact us at shi_AT_mat.unical.it (replace _AT_ with a '@' to obtain our mail address). 

Are you a research or industrial investor interested in financing the development of the Calculator? Do you need directions or have comments on the Calculator? You can contact us at {{{shi_AT_mat.unical.it}}} (replace _AT_ with a '{{{@}}}' to obtain our mail address).
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 * Beta 3.0 (Coming soon).
 * [[http://www.mat.unical.it/ianni/storage/scholar3.xpi|3.1 Release ]] for Firefox.
 * [[https://chrome.google.com/webstore/detail/scholar-h-index-calculato/cdpobfbhbdlpbloccjokjgekjnmifbng|Version 3.1]] for Google Chrome.
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----
== Documentation and examples ==

=== Custom formula editing ===

As of Calculator 3.0, there is the possibility for users to add their own bibliometric formulas and display their outcome next to default indices.
There are two types of custom formulas: [[#normalizations|Normalizations]] and [[#indices|Indices]].

----
== Documentation ==
=== Usage notes ===
Just point your browser to scholar.google.com and make a query! Once installed, the addon displays on top of Google Scholar result pages, the corresponding h-index, g-index, e-index and other measures of impact for the submitted query.

=== Disclaimer ===
{{{#!wiki caution
'''The computed values are obtained from Google Scholar output (and from the Web) ''as it is'', and might include self-citations, inaccuracies, informal and ghost citations. The author does not take any responsibility for the accuracy of indices values nor for the blind, non-manually-cleaned and inaccurate usage of this tool in official comparisons between authors and/or between journals'''.
}}}
You might be here because you are convinced that "high h-index = good scientist". '''Wrong'''. Have a look at [[http://www.mi.sanu.ac.rs/weekly/Dosen2.pdf|this]]. If, on the other hand, you '''wrongly''' think that bibliometric analyses bring no information at all, read, e.g., [[http://arxiv.org/abs/1106.0114v1|this]].

=== Advanced Interface ===
Since version 2.0 a new advanced interface mode can be enabled by clicking on the corresponding link located '''below''' the query textfield. Note that the addon advanced interface is not the same as the pre-existing ''Advanced Scholar Search'' link located at the '''right''' of the query textfield. When the Addon Advanced interface is enabled, a set of controls is visible per each paper. It is possible in turn:

 1. '''to select or deselect a single paper''': deselected papers do not contribute in the computation of impact indices.
 1. '''to manually increase or decrease the number of self citations'''. Self citations are stripped from the total citation count of a given paper.
 1. '''to manually increase or decrease the number of authors for a given paper''': this is useful when the number of authors reported by Google Scholar is not accurate and manual fixing is required (typical when the number of authors exceeds 4-5). Note: semi-automatic author fixing is possible since version 2.1 (see Section below).
 1. '''to load and save data''': users can save their data analysis by simply saving the page at hand after completing their analysis.

=== Tips and description of impact indices ===
To have accurate results, set your Google Scholar preferences on the number of results to 100. In agreement with Google Scholar terms of service (which prohibits automatic querying), it is processed just the displayed result page. As of Version 3.0 (and the current 2.96 beta), the Calculator can parse papers beyond the 100th by clicking on the two links on the sign {{{Do you want to add '''more''' or '''all''' data?}}}. '''More''' will trigger the addition of the next result page on the current page (and indices will be re-computed accordingly). When clicking on '''all''', all the result pages, up to the 1000th paper (this is an intrinsic Google Scholar constraint) will be added and indices computed accordingly. In both cases you will see the added papers on the bottom of the page. If you aim at computing your own indices values accurately, I strongly suggest to use both the addon Advanced interface and the ''Advanced Scholar Search'' form already provided by Google Scholar. In the Advanced Scholar Search page, fill the ''Return articles written by..'' field with the name at hand in quotes (e.g. {{{"Giovambattista Ianni"}}}). Also, in this same form, you might want to restrict search to the supposed field of experience. It is then possible to use the new Addon Advanced Interface (it can be activated looking below the query textfield) for performing fine-grained analysis (toggling papers on and off, etc.)

==== delta-H and delta-G ====
These two values measure the minimum number of citations needed for incrementing the current h-index (g-index, respectively), by 1. In the case of delta-h the value is computed as (h+1)-c[h+1] + sum_(from 1 to h)[max((h+1) - c[i],0)], where c[h] is the number of citations for the paper in position h, and h is the current h-index. delta-G is computed as (g+1)^2 - sum(from 1 to g+1)c[i], for g the current g-index. Note that for increasing h-index by 1, one has to obtain delta-H new citations on those '''particular''' papers which fail to have h+1 citations: all the first h+1 papers must reach at least h+1 citations. Usually, the (h+1)-th paper is the main culprit for the value of delta-H. Gaining a citation on a paper already having h+1 citations does not help in decreasing delta-H; viceversa, for increasing g-index, any new citation on the first g+1 papers matters, no matter how it is distributed.

delta-H and delta-G should be a measure of how difficult would be for the author at hand to increase his/her h and g-index. Note that the range of delta-h and delta-g is relatively small (in the worst scenario, delta-h-max= 2h+1 and delta-g-max=2g+1).

==== Normalized Values ====
Normalized values (the second row of data which is displayed) are computed by normalizing the number of citations found per each paper. From version 2.3 on, there are two types of normalization.

'''Normalization per author''': if paper ''i'' has been cited ''t'' times, and has been written by ''k'' authors, its number of normalized citations is ''t/k''. All the indices values, in the row where data are normalized per author, are computed considering these normalized values. In particular the normalized h-index corresponds to h_{I,Norm} of Publish or Perish. Due to limitations on the Google Scholar output format, Scholar H-Index truncates to 4 (or 5) the author count for papers having more than 4 authors. In such a case, the presented h_{I,Norm} has to be taken has an upper bound estimate of its real value (take care, especially for fields like Biology and Chemistry in which 12+ authors is the usual number). For having a finer-grained value the Addon Advanced Interface allows to semi-automatically fix the number of authors to the accurate value (see above).

'''Normalization per age''': if paper ''i'' has been cited ''t'' times, and has been written in 2001, its number of normalized citations per age is ''t/(CY-2001+1)'', for ''CY'' the current year. The above corresponds to the contemporary h-index of Sidiropoulos et al., with parameters delta=1 and gamma=1. Note that indices (h,g and e) computed on values normalized per age do not coincide with any of the Age Weighted metrics displayed by Publish or Perish, nor with hc-index (which is the contemporary h-index with delta=1 and gamma=4).

Although this metric can be subject of criticism (values will abruptly change each Jan 1st 0:00:01; citations on old papers become exponentially less influential year by year), we found it as having an intuitive simmetry and interpretation, compared with plain indices, and compared with indices normalized per co-authorship.

=== Why my h-index is not what I expect? ===
Computed indices values might differ from those of software tools like Publish or Perish mainly because Publish or Perish is hardwired to query {{{http://scholar.google.com}}} no matter which is your actual locale, while the H-Index Calculator works on the locale of your choice (scholar.google.it, scholar.google.co.uk etc.). Results from your local {{{scholar.google.*}}} might differ. Also note that queries submitted to Google Scholar such as {{{author:"John Doe"}}} return different (and tighter) results than {{{author:John author:Doe}}}, and also different from {{{author:J author:Doe}}}. Also you should take into consideration that selecting the field of expertise and narrowing your search with the filters available in the Scholar Advanced Interface will change indices values.

=== Author lists refinement ===
This function allows to (semi)-automatically compute accurate normalized indices, overcoming the underestimate of 4 authors in case of multi-authored papers with 4+ co-authors. If Scholar Preferences are set to display Bibtex data URLs, the advanced interface displays a new control named ''Refine this author list'' per each paper. Given paper P, acting on its corresponding ''Refine this author list'' button will fill the P entry with its full list of authors, and displays the full name of the journal/conference of P (if data is available). Indices are automatically updated accordingly.

It is also available a button named ''Refine all bibliographic entries'', which will automatically perform the abovementioned refinement per each displayed paper. ''Be warned that refining all papers implies heavy traffic from your browser to the Google Scholar portal, and might make Scholar detect you as an automated software, subsequently asking for a captcha.''

=== Version 3.0: complete (aggressive) author list refinement ===
Google Scholar displays only some authors for a given paper P, and this affects the Calculator estimates on the number of authors. Since version 2.1, the Calculator can complete the list of all authors for P: this feature is called '''Author Refinement''' and uses BibTeX data (provided by Scholar). It works only if Scholar Preferences are set to display BibTeX data for the selected paper. Note that BibTeX data may be incomplete: in this case, BibTex author lists are terminated with the string ''"others"'' meaning that the list is incomplete.

Since the 3.0 Release, the Calculator implements a new system that ''aggressively'' completes the list of the authors. We can explain generally how the system acts: it downloads the Web page corresponding to the paper (whose link is provided by Scholar), reasons inductively on it and extracts the remaining authors initially not present. To use the new aggressive refinement system, just click on the button labeled {{{Refine This Author List}}} near each record on Scholar, as in previous versions.

We are currently measuring the precision and recall of the system, with accurate experiments. We can preliminarily say that the system works with a 100% rate precision in most cases. However, aggressive refinement ''is strongly based on the Web page referenced''. This means that if the page does not actually lists the authors for a paper, it is corrupted, it is in PDF format (not supported yet), or it is temporarily unreachable on the Internet, the aggressive refinement system, of course, will not be able to extract accurate data and will report an error message.

=== Version 3.0: Custom formula editing ===
As of Calculator 3.0, there is the possibility for users to add their own bibliometric formulas and display their outcome next to default indices. There are two types of custom formulas: [[#normalizations|Normalizations]] and [[#indices|Indices]].
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In the Calculator information box, each row shows bibliometric indices depending on a given ''Normalization''. Each normalization weighs citations of each paper depending on a given criterion. Three

<<Anchor(indices)>>
In the Calculator information box, each row shows bibliometric indices depending on a given ''Normalization''. Each normalization weighs citations of each paper depending on a given criterion. Three are the default normalizations:

 * 'none' : no normalization. The normalized citations of a paper correspond to those displayed (after subtracting self citations). Same as the custom formula {{{citations-selfCitations}}}.
 * 'by authors': the citations of each paper are normalized by the (estimated) number of authors. Same as the custom formula {{{(citations-selfCitations)/authors}}}. For instance a paper with 100 citations and 4 authors, will score a number of normalized citations of 25. The number of authors cannot be always estimated correctly unless the refinement function is used. You might want to read the [[#refinement|Author Refinement]] section about how the Calculator estimates the number of authors per each paper.
 * 'by age': if paper {{{i}}} has been cited {{{t}}} times, and has been written in {{{2001}}}, its number of normalized citations per age is {{{t/(CY-2001+1)}}}, for CY the current year. Same as the custom formula {{{(citations-selfCitations)/(thisYear-year+1)}}}. As an example, a paper scoring 100 citations and written in 2003, would score 10 normalized citations in 2012.

You can add your own normalization formulas by clicking on the button 'New normalization' on the bottom of the Information box. Two editable textfields will appear. Enter the normalization name in the leftmost field and your custom formulas in the rightmost. Click anywhere else when ready, and if your formula is correct, you should see a new row in which all the available indices are computed according to your new normalization notion. Enjoy!

<<Anchor(customformulas)>>

===== Custom Normalization Formulas Language =====
You should be aware that normalization formulas are applied on per paper basis: your normalization formulas are intended to work in the context of a single paper. For a paper {{{i}}} a custom normalization formula {{{f(i)}}} returns a number of citations, depending on how {{{f}}} behaves. A normalization formula can access the following attributes of the paper {{{i}}}:

 * {{{citations}}} : the number of citations for {{{i}}} (as this value appears on video).
 * {{{year}}}: the year of publication of {{{i}}} (as it appears on video. Conventionally set to '-100,000,000,000,000' if not present).
 * {{{authors}}}: the number of authors of {{{i}}}. This is estimated according on how the author list appears on video, and can be manually edited by clicking on the Authors field or acting on the 'Auth+' and 'Auth-' buttons for the paper 'i'. See the [[#refinement|Author Refinement]] section.
 * {{{selfCitations}}}: the number of self citations of {{{i}}}, as they appear in the 'Self Citations' editable text field. Defaults to 0.
 * {{{cleanCitations}}}: a shortcut for {{{(citations-selfCitations)}}}.
 * {{{age}}} : a shortcut for {{{(thisYear-year+1)}}}.
 * {{{thisYear}}} : current year, as of your PC's wall clock.

Allowed symbols:

 * {{{+}}}, {{{-}}}, {{{/}}}, {{{*}}}, {{{^}}}, {{{(}}}, {{{)}}}, with intuitive meaning ({{{^}}} is exponentiation). The square root of {{{x}}} can be easily obtained as {{{x^0.5}}}.

==== Some further examples ====:

 * [[http://arxiv.org/abs/1106.0114v1|Carbone]]'s normalization: {{{citations/(authors^0.5)}}}.
 * [[http://arxiv.org/abs/cs.DL/0607066|hc-index]](delta,gamma) : {{{gamma*citations/age^delta}}} (replace gamma and delta with your favourite values)
 * Combined age and author weighting: {{{citations/age/authors}}}

Custom formulas are visible only when the Advanced interface is enabled. <<Anchor(indices)>>
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<<Anchor(related)>>
Indices correspond to '''columns''' in the Calculator information box. They correspond to a bibliometric index computed on the basis of a given set of papers. Besides the [[#defaultindices|default indices]] you can add your own.

===== Custom index formulas Language =====
You should be aware that indices formulas are applied on the current sorted list of papers (usually the list of entries displayed on video, sorted by the normalization at hand). The current list of papers can be changed either by ''a)'' making a new query, or ''b)'' telling the Calculator that you want to add more data to the current set, by clicking over the appropriate links presented by the Calculator.
For a sorted set of papers {{{S}}} a custom index formula {{{f(S)}}} returns an index value, depending on how {{{f}}} behaves. An index formula can access the attributes of all the papers of the corpus. ''Per each row in the information box, the corresponding normalization function is applied beforehand, and papers on video are preliminarily sorted according to their number of normalized citations'': then, {{{f}}} is computed per each row, according to the corresponding normalization and the obtained sorting. The language available for custom index formulas is much richer than the normalization language. Constructs available are listed next.

In the following, assume a sorted list of papers {{{S}}}, and a normalization function {{{n(i)}}}, for {{{i}}} denoting the {{{i}}}-th paper of S are given.

Special arrays:

 * {{{citations[x]}}} : the number of normalized citations for the {{{x}}}-th paper in S (i.e. {{{n(x)}}}). Note that sorting of documents might be different per each normalization row: i.e. the formula {{{citations[0]}}} applied on the first row might refer to a different paper in the second row. Think, e.g., at a paper with 2000 citations which is the most cited for an author. If the paper has a similar number of authors (e.g. more than 1000, like [[http://www.sciencedirect.com/science/article/pii/0370269383911772|here]]), it is very likely the same paper will not be the top-most in the 'normalization per author' row.
 * {{{year[x]}}}: the year of publication of the {{{x}}}-th paper in S.
 * {{{age[x]}}}: a shortcut for {{{(thisYear-year[x]+1)}}}
 * {{{authors[x]}}}: the number of authors of the {{{x}}}-th paper in S.
 * {{{selfCitations[x]}}}: the number of self citations of the {{{x}}}-th paper in S (not normalized).
 * {{{plainCitations[x]}}}: the number of citations for the {{{x}}}-th paper in S, without any normalization applied.

{{{x}}} can be any allowed formula.

Special symbols:

 * {{{N}}} : the number of papers in S.
 * {{{h}}}, {{{g}}}, {{{e}}}, {{{deltaH}}}, {{{deltaG}}} : the value of the respective indices, obtained according to the citation normalization at hand.
 * {{{thisYear}}} : current year, as of your PC's wall clock.

Functions:

'''Aggregate''' functions are available: these come in two possible forms:

{{{
funcName(start,end,variable,expression)
}}}
or

{{{
funcName(start,end,variable,booleanExpression,expression)
}}}
Where {{{start}}} and {{{end}}} are expressions denoting respectively the numeric range which {{{variable}}} will sweep on; {{{variable}}} is an identifier of choice, which is allowed to appear in {{{expression}}}. A {{{booleanExpression}}} is in the form {{{expr relOp expr}}} where {{{relOp}}} can be one among {{{<}}},{{{>}}},{{{>=}}},{{{<=}}},{{{==}}},{{{!=}}}.

Currently available aggregate functions are {{{min}}}, {{{max}}}, {{{sum}}} and {{{prod}}}. In order to exemplify how aggregates work, assume to have a set of 5 papers with respectively 10, 6, 4, 2 and 1 citations. Then

{{{
    min(1,N,i,citations[i]) = 1
    max(1,N,i,citations[i]) = 10
    sum(1,N,i,citations[i]) = 23
}}}
Boolean expressions can be used to select which papers should be filtered out in the aggregate function. For instance, the Google My Citations i10-index (the number of publications with at least 10 citations) is

{{{
   sum(1,N,i,citations[i] >= 10,1)
}}}
As in normalization formulas, allowed expression comprehend {{{+}}}, {{{-}}}, {{{/}}}, {{{*}}}, {{{^}}}, {{{(}}}, {{{)}}}, with intuitive meaning.

==== Some examples ====

 * The h-index itself: {{{ max(1,N,x, sum(1,x,i,citations[i]>=x,1) ) }}}
 * The g-index: {{{max(1,N,x,sum(1,x,i,citations[i])>=x*x,x)}}}
 * Equivalent impact of the Top-10 articles: {{{sum(1,10,i,citations[i])^0.5}}}
 * e-index : {{{sum(1,h,i,citations[i])-h^2}}}
 * AR-index: {{{sum(1,h,i,citations[i])^0.5}}} (corresponds to the AR index when citations are normalized by age).
 * Sum of citations in the last five years: {{{sum(1,N,i,age[i] <= 5,citations[i])}}}
 * H-Index points per year of scientific production: {{{h/max(1,N,i,year[i]>1900,age[i])}}}, where the condition {{{year[i]>1900}}} avoids selecting papers of unknown date of publication. This is one of the [[http://attiministeriali.miur.it/anno-2012/giugno/dm-07062012.aspx|criteria]] which was tentatively prescribed by the Italian Research Ministry for selecting Associate and Full professors.
 * Citations per year since first publications {{{sum(1,N,i,citations[i])/max(1,N,i,year[i]>1900,age[i])}}}

=== Indices used in the 2012 Italian "Abilitazione Scientifica Nazionale" ===

These can be programmed in the following way:

 * '''Total number of citations normalized by the academic age of the author''': add as ''index'' formula
{{{
sum(1,N,i,citations[i])/max(1,N,i,year[i]>1900,age[i])
}}}
Here {{{sum(1,N,i,citations[i])}}} is the total number of citations reported, while {{{max(1,N,i,year[i]>1900,age[i])}}} estimates the academic age of an author as the age of the oldest paper appearing in the current set of papers.
 * '''The h-c index''': add as ''normalization'' formula {{{4*citations/age}}}. The column displaying the h-index will have a new row. The content of this new row will report the h-c index in the h-index column (as well as, in other rows, the h-index with several other normalizations).
 * '''Number of journal papers in the last 10 years of activity''', possibly normalized if the academic age is less than 10: this cannot currently be obtained, due to technical constraints on how Scholar presents data about whether a paper is published in a journal or not.

<<Anchor(releasenotes)>>

----
=== Support for CiteseerX ===
Automatic index calculation when visiting CiteseerX has been discontinued since version 2.0.

== Release Notes and history ==
May-Jun 2012. 3.0 Release with many new features:

 * Possibility to add custom normalization and indices formulas see the [[#customformulas|Custom Formulas]] section
 * 'Refine author list' and 'Refine all bibliographic entries' functions now much more accurate (can correctly extract lists of thousands of authors in almost all cases)
 * Can now compute h-index values greater than 100
 * Support for the new Scholar Modern look
 * Many bug fixes and internal code optimization

 * Jan 13th, 2012. 2.3.5 Adapted to Google Scholar page layout changes. Other minor bug fixing.
 * May 31th, 2011. 2.3 Improved layout. Added indices normalized per age.
 * Apr 26th, 2011. 2.2 Authors names are now clickable and point to the corresponding query on Scholar.
 * Feb 24th, 2011. 2.1 New advanced refinement button per paper. Other minor improvements and bug fixing.
 * Oct 23th, 2010. 2.0 Introduction of the advanced fine-tuning interface. Minor bug fixing and accuracy improvement in border cases.
 * Nov 26th, 2009. 1.4 and 1.4.1 Added radio buttons for selecting the query type on the fly. Improved author parsing.
 * Nov 21th, 2009. 1.3.3 Added on hover tooltips.
 * Nov 19th, 2009. 1.3.2 Improved appearance. Added link to the same query with 100 results if h-index and g-index fail to compute properly.
 * Nov 17th, 2009. 1.3 Introduced normalized indices and support for CiteSeerX (discontinued as of 2.0 version).
 * Oct 26th, 2009. 1.2.3 Introduced checks for overflow of h,g,e,deltah,deltag values.
 * Oct 21th, 2009. 1.2.1 A minor fix on delta-H computation.
 * Oct 20th, 2009. 1.2. Introduced delta-H and delta-G. Minor fixes.
 * Oct 16th, 2009. 1.1.1. Fix bug on e-index computation.
 * Oct 11th, 2009. 1.1. Fix bug related to Google Scholar not strictly respecting citation descending order. Fix some citation values evaluated as NaN.
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Scholar H-Index Calculator - Home page


About Scholar H-Index Calculator

Scholar H-Index Calculator (the Calculator from now on) is an addon for Firefox and Google Chrome which enhances Google Scholar results pages by showing a number of bibliometric data computed using the data appearing on video as input. Once installed, the Calculator works transparently when querying Google Scholar: as soon as you make a query, result pages are enriched with a number of useful data (e.g. the h-index computed on the basis of displayed data), and new functions are available.


The Team

Project Coordinator

Developers Team

  • Francesco Cauteruccio (Aggressive refining engine), Susanna Cozza (General code maintainance), Stefano Germano (Custom formulas parser), Maria Carmela Santoro (General code refactoring, Additional results browsing code).

Are you a research or industrial investor interested in financing the development of the Calculator? Do you need directions or have comments on the Calculator? You can contact us at shi_AT_mat.unical.it (replace _AT_ with a '@' to obtain our mail address).


Download


Documentation

Usage notes

Just point your browser to scholar.google.com and make a query! Once installed, the addon displays on top of Google Scholar result pages, the corresponding h-index, g-index, e-index and other measures of impact for the submitted query.

Disclaimer

The computed values are obtained from Google Scholar output (and from the Web) as it is, and might include self-citations, inaccuracies, informal and ghost citations. The author does not take any responsibility for the accuracy of indices values nor for the blind, non-manually-cleaned and inaccurate usage of this tool in official comparisons between authors and/or between journals.

You might be here because you are convinced that "high h-index = good scientist". Wrong. Have a look at this. If, on the other hand, you wrongly think that bibliometric analyses bring no information at all, read, e.g., this.

Advanced Interface

Since version 2.0 a new advanced interface mode can be enabled by clicking on the corresponding link located below the query textfield. Note that the addon advanced interface is not the same as the pre-existing Advanced Scholar Search link located at the right of the query textfield. When the Addon Advanced interface is enabled, a set of controls is visible per each paper. It is possible in turn:

  1. to select or deselect a single paper: deselected papers do not contribute in the computation of impact indices.

  2. to manually increase or decrease the number of self citations. Self citations are stripped from the total citation count of a given paper.

  3. to manually increase or decrease the number of authors for a given paper: this is useful when the number of authors reported by Google Scholar is not accurate and manual fixing is required (typical when the number of authors exceeds 4-5). Note: semi-automatic author fixing is possible since version 2.1 (see Section below).

  4. to load and save data: users can save their data analysis by simply saving the page at hand after completing their analysis.

Tips and description of impact indices

To have accurate results, set your Google Scholar preferences on the number of results to 100. In agreement with Google Scholar terms of service (which prohibits automatic querying), it is processed just the displayed result page. As of Version 3.0 (and the current 2.96 beta), the Calculator can parse papers beyond the 100th by clicking on the two links on the sign Do you want to add '''more''' or '''all''' data?. More will trigger the addition of the next result page on the current page (and indices will be re-computed accordingly). When clicking on all, all the result pages, up to the 1000th paper (this is an intrinsic Google Scholar constraint) will be added and indices computed accordingly. In both cases you will see the added papers on the bottom of the page. If you aim at computing your own indices values accurately, I strongly suggest to use both the addon Advanced interface and the Advanced Scholar Search form already provided by Google Scholar. In the Advanced Scholar Search page, fill the Return articles written by.. field with the name at hand in quotes (e.g. "Giovambattista Ianni"). Also, in this same form, you might want to restrict search to the supposed field of experience. It is then possible to use the new Addon Advanced Interface (it can be activated looking below the query textfield) for performing fine-grained analysis (toggling papers on and off, etc.)

delta-H and delta-G

These two values measure the minimum number of citations needed for incrementing the current h-index (g-index, respectively), by 1. In the case of delta-h the value is computed as (h+1)-c[h+1] + sum_(from 1 to h)[max((h+1) - c[i],0)], where c[h] is the number of citations for the paper in position h, and h is the current h-index. delta-G is computed as (g+1)^2 - sum(from 1 to g+1)c[i], for g the current g-index. Note that for increasing h-index by 1, one has to obtain delta-H new citations on those particular papers which fail to have h+1 citations: all the first h+1 papers must reach at least h+1 citations. Usually, the (h+1)-th paper is the main culprit for the value of delta-H. Gaining a citation on a paper already having h+1 citations does not help in decreasing delta-H; viceversa, for increasing g-index, any new citation on the first g+1 papers matters, no matter how it is distributed.

delta-H and delta-G should be a measure of how difficult would be for the author at hand to increase his/her h and g-index. Note that the range of delta-h and delta-g is relatively small (in the worst scenario, delta-h-max= 2h+1 and delta-g-max=2g+1).

Normalized Values

Normalized values (the second row of data which is displayed) are computed by normalizing the number of citations found per each paper. From version 2.3 on, there are two types of normalization.

Normalization per author: if paper i has been cited t times, and has been written by k authors, its number of normalized citations is t/k. All the indices values, in the row where data are normalized per author, are computed considering these normalized values. In particular the normalized h-index corresponds to h_{I,Norm} of Publish or Perish. Due to limitations on the Google Scholar output format, Scholar H-Index truncates to 4 (or 5) the author count for papers having more than 4 authors. In such a case, the presented h_{I,Norm} has to be taken has an upper bound estimate of its real value (take care, especially for fields like Biology and Chemistry in which 12+ authors is the usual number). For having a finer-grained value the Addon Advanced Interface allows to semi-automatically fix the number of authors to the accurate value (see above).

Normalization per age: if paper i has been cited t times, and has been written in 2001, its number of normalized citations per age is t/(CY-2001+1), for CY the current year. The above corresponds to the contemporary h-index of Sidiropoulos et al., with parameters delta=1 and gamma=1. Note that indices (h,g and e) computed on values normalized per age do not coincide with any of the Age Weighted metrics displayed by Publish or Perish, nor with hc-index (which is the contemporary h-index with delta=1 and gamma=4).

Although this metric can be subject of criticism (values will abruptly change each Jan 1st 0:00:01; citations on old papers become exponentially less influential year by year), we found it as having an intuitive simmetry and interpretation, compared with plain indices, and compared with indices normalized per co-authorship.

Why my h-index is not what I expect?

Computed indices values might differ from those of software tools like Publish or Perish mainly because Publish or Perish is hardwired to query http://scholar.google.com no matter which is your actual locale, while the H-Index Calculator works on the locale of your choice (scholar.google.it, scholar.google.co.uk etc.). Results from your local scholar.google.* might differ. Also note that queries submitted to Google Scholar such as author:"John Doe" return different (and tighter) results than author:John author:Doe, and also different from author:J author:Doe. Also you should take into consideration that selecting the field of expertise and narrowing your search with the filters available in the Scholar Advanced Interface will change indices values.

Author lists refinement

This function allows to (semi)-automatically compute accurate normalized indices, overcoming the underestimate of 4 authors in case of multi-authored papers with 4+ co-authors. If Scholar Preferences are set to display Bibtex data URLs, the advanced interface displays a new control named Refine this author list per each paper. Given paper P, acting on its corresponding Refine this author list button will fill the P entry with its full list of authors, and displays the full name of the journal/conference of P (if data is available). Indices are automatically updated accordingly.

It is also available a button named Refine all bibliographic entries, which will automatically perform the abovementioned refinement per each displayed paper. Be warned that refining all papers implies heavy traffic from your browser to the Google Scholar portal, and might make Scholar detect you as an automated software, subsequently asking for a captcha.

Version 3.0: complete (aggressive) author list refinement

Google Scholar displays only some authors for a given paper P, and this affects the Calculator estimates on the number of authors. Since version 2.1, the Calculator can complete the list of all authors for P: this feature is called Author Refinement and uses BibTeX data (provided by Scholar). It works only if Scholar Preferences are set to display BibTeX data for the selected paper. Note that BibTeX data may be incomplete: in this case, BibTex author lists are terminated with the string "others" meaning that the list is incomplete.

Since the 3.0 Release, the Calculator implements a new system that aggressively completes the list of the authors. We can explain generally how the system acts: it downloads the Web page corresponding to the paper (whose link is provided by Scholar), reasons inductively on it and extracts the remaining authors initially not present. To use the new aggressive refinement system, just click on the button labeled Refine This Author List near each record on Scholar, as in previous versions.

We are currently measuring the precision and recall of the system, with accurate experiments. We can preliminarily say that the system works with a 100% rate precision in most cases. However, aggressive refinement is strongly based on the Web page referenced. This means that if the page does not actually lists the authors for a paper, it is corrupted, it is in PDF format (not supported yet), or it is temporarily unreachable on the Internet, the aggressive refinement system, of course, will not be able to extract accurate data and will report an error message.

Version 3.0: Custom formula editing

As of Calculator 3.0, there is the possibility for users to add their own bibliometric formulas and display their outcome next to default indices. There are two types of custom formulas: Normalizations and Indices.

Normalizations

In the Calculator information box, each row shows bibliometric indices depending on a given Normalization. Each normalization weighs citations of each paper depending on a given criterion. Three are the default normalizations:

  • 'none' : no normalization. The normalized citations of a paper correspond to those displayed (after subtracting self citations). Same as the custom formula citations-selfCitations.

  • 'by authors': the citations of each paper are normalized by the (estimated) number of authors. Same as the custom formula (citations-selfCitations)/authors. For instance a paper with 100 citations and 4 authors, will score a number of normalized citations of 25. The number of authors cannot be always estimated correctly unless the refinement function is used. You might want to read the Author Refinement section about how the Calculator estimates the number of authors per each paper.

  • 'by age': if paper i has been cited t times, and has been written in 2001, its number of normalized citations per age is t/(CY-2001+1), for CY the current year. Same as the custom formula (citations-selfCitations)/(thisYear-year+1). As an example, a paper scoring 100 citations and written in 2003, would score 10 normalized citations in 2012.

You can add your own normalization formulas by clicking on the button 'New normalization' on the bottom of the Information box. Two editable textfields will appear. Enter the normalization name in the leftmost field and your custom formulas in the rightmost. Click anywhere else when ready, and if your formula is correct, you should see a new row in which all the available indices are computed according to your new normalization notion. Enjoy!

Custom Normalization Formulas Language

You should be aware that normalization formulas are applied on per paper basis: your normalization formulas are intended to work in the context of a single paper. For a paper i a custom normalization formula f(i) returns a number of citations, depending on how f behaves. A normalization formula can access the following attributes of the paper i:

  • citations : the number of citations for i (as this value appears on video).

  • year: the year of publication of i (as it appears on video. Conventionally set to '-100,000,000,000,000' if not present).

  • authors: the number of authors of i. This is estimated according on how the author list appears on video, and can be manually edited by clicking on the Authors field or acting on the 'Auth+' and 'Auth-' buttons for the paper 'i'. See the Author Refinement section.

  • selfCitations: the number of self citations of i, as they appear in the 'Self Citations' editable text field. Defaults to 0.

  • cleanCitations: a shortcut for (citations-selfCitations).

  • age : a shortcut for (thisYear-year+1).

  • thisYear : current year, as of your PC's wall clock.

Allowed symbols:

  • +, -, /, *, ^, (, ), with intuitive meaning (^ is exponentiation). The square root of x can be easily obtained as x^0.5.

==== Some further examples ====:

  • Carbone's normalization: citations/(authors^0.5).

  • hc-index(delta,gamma) : gamma*citations/age^delta (replace gamma and delta with your favourite values)

  • Combined age and author weighting: citations/age/authors

Custom formulas are visible only when the Advanced interface is enabled.

Indices

Indices correspond to columns in the Calculator information box. They correspond to a bibliometric index computed on the basis of a given set of papers. Besides the default indices you can add your own.

Custom index formulas Language

You should be aware that indices formulas are applied on the current sorted list of papers (usually the list of entries displayed on video, sorted by the normalization at hand). The current list of papers can be changed either by a) making a new query, or b) telling the Calculator that you want to add more data to the current set, by clicking over the appropriate links presented by the Calculator. For a sorted set of papers S a custom index formula f(S) returns an index value, depending on how f behaves. An index formula can access the attributes of all the papers of the corpus. Per each row in the information box, the corresponding normalization function is applied beforehand, and papers on video are preliminarily sorted according to their number of normalized citations: then, f is computed per each row, according to the corresponding normalization and the obtained sorting. The language available for custom index formulas is much richer than the normalization language. Constructs available are listed next.

In the following, assume a sorted list of papers S, and a normalization function n(i), for i denoting the i-th paper of S are given.

Special arrays:

  • citations[x] : the number of normalized citations for the x-th paper in S (i.e. n(x)). Note that sorting of documents might be different per each normalization row: i.e. the formula citations[0] applied on the first row might refer to a different paper in the second row. Think, e.g., at a paper with 2000 citations which is the most cited for an author. If the paper has a similar number of authors (e.g. more than 1000, like here), it is very likely the same paper will not be the top-most in the 'normalization per author' row.

  • year[x]: the year of publication of the x-th paper in S.

  • age[x]: a shortcut for (thisYear-year[x]+1)

  • authors[x]: the number of authors of the x-th paper in S.

  • selfCitations[x]: the number of self citations of the x-th paper in S (not normalized).

  • plainCitations[x]: the number of citations for the x-th paper in S, without any normalization applied.

x can be any allowed formula.

Special symbols:

  • N : the number of papers in S.

  • h, g, e, deltaH, deltaG : the value of the respective indices, obtained according to the citation normalization at hand.

  • thisYear : current year, as of your PC's wall clock.

Functions:

Aggregate functions are available: these come in two possible forms:

funcName(start,end,variable,expression)

or

funcName(start,end,variable,booleanExpression,expression)

Where start and end are expressions denoting respectively the numeric range which variable will sweep on; variable is an identifier of choice, which is allowed to appear in expression. A booleanExpression is in the form expr relOp expr where relOp can be one among <,>,>=,<=,==,!=.

Currently available aggregate functions are min, max, sum and prod. In order to exemplify how aggregates work, assume to have a set of 5 papers with respectively 10, 6, 4, 2 and 1 citations. Then

    min(1,N,i,citations[i]) = 1
    max(1,N,i,citations[i]) = 10
    sum(1,N,i,citations[i]) = 23

Boolean expressions can be used to select which papers should be filtered out in the aggregate function. For instance, the Google My Citations i10-index (the number of publications with at least 10 citations) is

   sum(1,N,i,citations[i] >= 10,1)

As in normalization formulas, allowed expression comprehend +, -, /, *, ^, (, ), with intuitive meaning.

Some examples

  • The h-index itself:  max(1,N,x, sum(1,x,i,citations[i]>=x,1) ) 

  • The g-index: max(1,N,x,sum(1,x,i,citations[i])>=x*x,x)

  • Equivalent impact of the Top-10 articles: sum(1,10,i,citations[i])^0.5

  • e-index : sum(1,h,i,citations[i])-h^2

  • AR-index: sum(1,h,i,citations[i])^0.5 (corresponds to the AR index when citations are normalized by age).

  • Sum of citations in the last five years: sum(1,N,i,age[i] <= 5,citations[i])

  • H-Index points per year of scientific production: h/max(1,N,i,year[i]>1900,age[i]), where the condition year[i]>1900 avoids selecting papers of unknown date of publication. This is one of the criteria which was tentatively prescribed by the Italian Research Ministry for selecting Associate and Full professors.

  • Citations per year since first publications sum(1,N,i,citations[i])/max(1,N,i,year[i]>1900,age[i])

Indices used in the 2012 Italian "Abilitazione Scientifica Nazionale"

These can be programmed in the following way:

  • Total number of citations normalized by the academic age of the author: add as index formula

sum(1,N,i,citations[i])/max(1,N,i,year[i]>1900,age[i])

Here sum(1,N,i,citations[i]) is the total number of citations reported, while max(1,N,i,year[i]>1900,age[i]) estimates the academic age of an author as the age of the oldest paper appearing in the current set of papers.

  • The h-c index: add as normalization formula 4*citations/age. The column displaying the h-index will have a new row. The content of this new row will report the h-c index in the h-index column (as well as, in other rows, the h-index with several other normalizations).

  • Number of journal papers in the last 10 years of activity, possibly normalized if the academic age is less than 10: this cannot currently be obtained, due to technical constraints on how Scholar presents data about whether a paper is published in a journal or not.


Support for CiteseerX

Automatic index calculation when visiting CiteseerX has been discontinued since version 2.0.

Release Notes and history

May-Jun 2012. 3.0 Release with many new features:

  • Possibility to add custom normalization and indices formulas see the Custom Formulas section

  • 'Refine author list' and 'Refine all bibliographic entries' functions now much more accurate (can correctly extract lists of thousands of authors in almost all cases)
  • Can now compute h-index values greater than 100
  • Support for the new Scholar Modern look
  • Many bug fixes and internal code optimization
  • Jan 13th, 2012. 2.3.5 Adapted to Google Scholar page layout changes. Other minor bug fixing.
  • May 31th, 2011. 2.3 Improved layout. Added indices normalized per age.
  • Apr 26th, 2011. 2.2 Authors names are now clickable and point to the corresponding query on Scholar.
  • Feb 24th, 2011. 2.1 New advanced refinement button per paper. Other minor improvements and bug fixing.
  • Oct 23th, 2010. 2.0 Introduction of the advanced fine-tuning interface. Minor bug fixing and accuracy improvement in border cases.
  • Nov 26th, 2009. 1.4 and 1.4.1 Added radio buttons for selecting the query type on the fly. Improved author parsing.
  • Nov 21th, 2009. 1.3.3 Added on hover tooltips.
  • Nov 19th, 2009. 1.3.2 Improved appearance. Added link to the same query with 100 results if h-index and g-index fail to compute properly.
  • Nov 17th, 2009. 1.3 Introduced normalized indices and support for CiteSeerX (discontinued as of 2.0 version).
  • Oct 26th, 2009. 1.2.3 Introduced checks for overflow of h,g,e,deltah,deltag values.
  • Oct 21th, 2009. 1.2.1 A minor fix on delta-H computation.
  • Oct 20th, 2009. 1.2. Introduced delta-H and delta-G. Minor fixes.
  • Oct 16th, 2009. 1.1.1. Fix bug on e-index computation.
  • Oct 11th, 2009. 1.1. Fix bug related to Google Scholar not strictly respecting citation descending order. Fix some citation values evaluated as NaN.



Selected Publications

mwiki: ScholarHIndexCalculator (last edited 2020-02-10 16:30:47 by GiovambattistaIanni)