SV: [SIGMETRICS] On the Normalization and Visualization of Co-citation Data
Loet Leydesdorff
loet at LEYDESDORFF.NET
Mon Jan 22 04:25:46 EST 2007
Dear Jesper,
That is a pleasant surprise!
Thank you so much.
With best wishes,
Loet
_____
From: ASIS&T Special Interest Group on Metrics
[mailto:SIGMETRICS at LISTSERV.UTK.EDU] On Behalf Of Jesper Wiborg Schneider
Sent: Monday, January 22, 2007 9:36 AM
To: SIGMETRICS at LISTSERV.UTK.EDU
Subject: [SIGMETRICS] SV: [SIGMETRICS] On the Normalization and
Visualization of Co-citation Data
Dear Loet and colleagues;
In connection with the ongoing debate on proximity measures in co-citation
studies, you may find the following forthcoming two-part article of
interest:
* Schneider, J. & Borlund, P. [
<http://www.db.dk/binaries/JASIST_%20part1_preprint.pdf> PDF]
Matrix comparison, Part 1: Motivation and important issues for measuring the
resemblance between proximity measures or ordination results.
Accepted for publication in the Journal of the American Society for
Information Science and Technology.
* Abstract: The present two-part article introduces matrix
comparison as a formal means for evaluation purposes in informetric studies
such as co-citation analysis. In this, the first part, the motivation
behind introducing matrix comparison to informetric studies, as well as two
important issues influencing such comparisons, are introduced and discussed.
The motivation is spurred by the recent debate on choice of proximity
measures and their potential influence upon clustering and ordination
results. The two important issues discussed in the present first part are
matrix generation and the composition of proximity measures. The present
part of the article demonstrates that the approach to matrix generation for
the same data set, that is how data is represented and transformed in a
matrix, evidently determines the ‘behaviour’ of proximity measures. Two
different matrix generation approaches, will therefore in all probability,
lead to different proximity rankings of objects, which further lead to
different ordination and clustering results for the same set of objects.
Further, this part of the article also demonstrates that a resemblance in
the composition of formulas indicates whether two proximity measures may
produce similar ordination and clustering results. However, as shown in the
case of the angular correlation and cosine measures, a small deviation in
otherwise similar formulas, can lead to different rankings depending on the
contour of the data matrix transformed. Eventually, the ‘behaviour’ of
proximity measures, that is whether they produce similar rankings of
objects, is more or less data-specific. Consequently, we recommend the use
of empirical matrix comparison techniques for individual studies in order to
investigate the degree of resemblance between proximity measures or their
ordination results. Part two of the article introduces and demonstrates two
related statistical matrix comparison techniques the Mantel test and
Procrustes analysis, respectively. These techniques can compare and
evaluate the degree of monotonicity between different proximity measures or
their ordination results. As such, the Mantel test and Procrustes analysis
can be used as statistical validation tools in informetric studies and thus
help choosing suitable proximity measures.
* Schneider, J. & Borlund, P. [
<http://www.db.dk/binaries/JASIST_%20part2_preprint.pdf> PDF]
Matrix comparison, Part 2: Measuring the resemblance between proximity
measures or ordination results by use of the Mantel and Procrustes
statistics.
Accepted for publication in the Journal of the American Society for
Information Science and Technology.
* Abstract: The present two-part article introduces matrix
comparison as a formal means for evaluation purposes in informetric studies
such as co-citation analysis. In the first part, the motivation behind
introducing matrix comparison to informetric studies, as well as two
important issues influencing such comparisons, matrix generation and the
composition of proximity measures, are introduced and discussed. .In this
second part of the article, we introduce and thoroughly demonstrate two
related matrix comparison techniques the Mantel test and Procrustes
analysis, respectively. These techniques can compare and evaluate the
degree of monotonicity between different proximity measures or their
ordination results. In common to these techniques is the application of
permutation procedures in order to test hypotheses about matrix
resemblances. The choice of technique is related to the validation at hand.
In the case of the Mantel test, the degree of resemblance between two
measures forecast their potentially different affect upon ordination and
clustering results. In principle, two proximity measures with a very strong
resemblance most likely produce identical results, thus, choice of measure
between the two becomes less important. Alternatively, or as a supplement,
Procrustes analysis compares the actual ordination results without
investigating the underlying proximity measures, by matching two
configurations of the same objects in a multidimensional space. An
advantage of the Procrustes analysis though, is the graphical solution
provided by the superimposition plot and the resulting decomposition of
variance components. Accordingly, the Procrustes analysis provides, not
only a measure of general fit between configurations, but also values for
individual objects enabling more elaborate validations. As such, the Mantel
test and Procrustes analysis can be used as statistical validation tools in
informetric studies and thus help choosing suitable proximity measures.
Kind regards - Jesper
**********************************************
Jesper Wiborg Schneider, PhD, Assistant Professor
Department of Information Studies Royal School of Library & Information
Science
Sohngårdsholmsvej 2, DK-9000 Aalborg, DENMARK Tel. +45 98773041, Fax. +45
98151042
E-mail: <mailto:jws at db.dk> jws at db.dk
Homepage:http://www.db.dk/jws
**********************************************
_____
Fra: ASIS&T Special Interest Group on Metrics
[mailto:SIGMETRICS at LISTSERV.UTK.EDU] På vegne af Loet Leydesdorff
Sendt: 21. januar 2007 19:46
Til: SIGMETRICS at LISTSERV.UTK.EDU
Emne: [SIGMETRICS] On the Normalization and Visualization of Co-citation
Data
On the Normalization and <http://www.leydesdorff.net/aca07/index.htm>
Visualization of Author Co-Citation Data
Click here for <http://www.leydesdorff.net/aca07/aca07.pdf> PDF
The debate about which similarity measure one should use for the
normalization in the case of Author Co-citation Analysis (ACA) is further
complicated when one distinguishes between the symmetrical co-citation—or,
more generally, co-occurrence—matrix and the underlying asymmetrical
citation—occurrence—matrix. In the Web environment, the approach of
retrieving original citation data and then using Salton’s cosine or the
Pearson correlation to construct a similarity matrix is often not feasible.
In that case, one should use the Jaccard index, but preferentially after
adding the number of total citations (occurrences) on the main diagonal.
Unlike Salton’s cosine and the Pearson correlation, the Jaccard index
abstracts from the distribution and focuses only on the intersection and the
sum of the two sets. Since the distributions in the co-occurrence matrix may
partially be based on spurious correlations, this property of the Jaccard
index can be considered as an advantage in this case. The argument is
illustrated with empirical data.
_____
Loet Leydesdorff
Amsterdam School of Communications Research (ASCoR)
Kloveniersburgwal 48, 1012 CX Amsterdam
Tel.: +31-20- 525 6598; fax: +31-20- 525 3681
loet at leydesdorff.net <mailto:loet at leydesdorff.net> ;
http://www.leydesdorff.net/
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