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Quantitative Definitions of Collaborative Research Fields in Science and Engineering

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Practical methodology for categorizing collaborative disciplines or research in a quantitative manner is presented by developing a Correlation Matrix of Major Disciplines (CMMD) using bibliometric data collected between 2009 and 2014. First, 21 major disciplines in science and engineering are defined based on journal publication frequency. Second, major disciplines using a comparing discipline correlation matrix is created and correlation score using CMMD is calculated based on an analyzer function that is given to the matrix elements. Third, a correlation between the major disciplines and 14 research fields using CMMD is calculated for validation. Collaborative researches are classified into three groups by partially accepting the definition of pluri-discipline from peer review manual, European Science Foundation, inner-discipline, inter-discipline and cross-discipline. Applying simple categorization criteria identifies three groups of collaborative research and also those results can be visualized. Overall, the proposed methodology supports the categorization for each research field. Keywords Collaborative research, inner-disciplinary research, interdisciplinary research, cross-disciplinary research, quantification method, correlation matrix of major disciplines(CMMD), bibliometric data
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Asian Journal of Innovation and Policy (2016) 5.3:251-274
251
Quantitative Definitions of Collaborative Research
Fields in Science and Engineering
Mathew Schwartz*, Kwisun Park**, Sung-Jong Lee***
Abstract Practical methodology for categorizing collaborative disciplines or
research in a quantitative manner is presented by developing a Correlation Matrix of
Major Disciplines (CMMD) using bibliometric data collected between 2009 and 2014.
First, 21 major disciplines in science and engineering are defined based on journal
publication frequency. Second, major disciplines using a comparing discipline
correlation matrix is created and correlation score using CMMD is calculated based on
an analyzer function that is given to the matrix elements. Third, a correlation between
the major disciplines and 14 research fields using CMMD is calculated for validation.
Collaborative researches are classified into three groups by partially accepting the
definition of pluri-discipline from peer review manual, European Science Foundation,
inner-discipline, inter-discipline and cross-discipline. Applying simple categorization
criteria identifies three groups of collaborative research and also those results can be
visualized. Overall, the proposed methodology supports the categorization for each
research field.
Keywords Collaborative research, inner-disciplinary research, interdisciplinary
research, cross-disciplinary research, quantification method, correlation matrix of
major disciplines(CMMD), bibliometric data
I. Introduction
In recent decades, complementary collaboration between disciplines, as well
as the re-purposing and reuse of methodologies or theoretical foundations
between disciplines has become increasingly normal in academia (Aboelela et
al., 2007; Bourke and Butler, 1998; Broto, Gislason and Ehlers, 2009; Cameron
R., 2016; Huutoniemi et al., 2010; National Academies, 2004; Roco, 2008).
Submitted, Devember 13 , 2016; 1st Revised, December 27; Accepted, December 27
* Advanced Institutes of Convergence Technology, Seoul National University, Suwon, 443-
270, Korea; New Jersey Institute of Technology, College of Architecture and Design, New
Jersey, USA; umcadop@gmail.com
** National R&D Planning Team, National Research Foundation of Korea, Daejeon, 34113,
Korea; kwisun_park@nrf.re.kr
*** Corresponding author, Biotechnology Team; chris@nrf.re.kr
Asian Journal of Innovation and Policy (2016) 5.003:251-274
DOI: http//dx.doi.org/10.7545/ajip.2016.5.3.251
Asian Journal of Innovation and Policy (2016) 5.3:251-274
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Although interdisciplinary collaboration has traditionally been associated with
technological applications, it has proven a valuable practice in research,
contributing to the development of several fields. As a result, interdisciplinary
characteristics have emerged as a major issue in research and development
(R&D) funding and knowledge production (Bruun et al., 2005; Han and
Kyung 2011; Huutoniemi et al., 2010; Lee and Choi, 2010; Mansilla, 2005;
Van Rijnsoever and Hessels, 2011;, 2008).
The National Research Foundation of Korea (NRF), one of the largest
science and engineering (S&E) funding agencies in the world, organized the
Division of Interdisciplinary Research, under the supervision of the directorate
for basic research in science and engineering, in early 2000. The division’s
funding is mandated to support the development and success of research
requiring significant collaboration between S&E disciplines; while this
mandate is specific to the NRF, funding agencies around the world continue to
go through similar challenges. Additionally, the division is tasked with
developing a convergence research support framework to promote creative
and transformative research (Park et al., 2012/2013).
For many years, this division has categorized research applications as
interdisciplinary based on applicant proposals’ self-reported status as well as
partial sorting by reviewers. This process has brought up a few important
questions: are proposals interdisciplinary enough? How can inter-
disciplinarity be defined? Are there indicators for interdisciplinary fields that
can lead to general agreement? If so, what are these key factors and how can
they be analyzed?
In order to answer these questions and develop a better approach to
collaborative research funding, a more meaningful definition of a ‘discipline
is required. Both researchers and funding agencies have made attempts to
create this distinction, with varying degrees of success (Beers and Bots, 2009;
Brandt et al., 2013; Bruun et al., 2005; Fagerberg, Landström and Martin,
2012; Huutoniemi et al., 2010; Klein, 2006; Rafols et al., 2012; Rinia et al.,
2001; Tijssen, 1992). In fact, attempts to define and classify individual fields
have met with difficulty since the earliest division of classical disciplines;
because there are so many topics and several of them overlap, it is difficult to
definitively and rigidly categorize them (Mansilla, 2005; Repko, 2008). For
example, mathematics is originally defined by the Oxford English Dictionary
as:
Originally: (a collective term for) geometry, arithmetic, and certain
physical sciences involving geometrical reasoning, such as astronomy and
optics; spec. the disciplines of the quadrivium collectively. In later use: the
science of space, number, quantity, and arrangement, whose methods
involve logical reasoning and usually the use of symbolic notation, and
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which includes geometry, arithmetic, algebra, and analysis; mathematical
operations or calculations” (Stevenson, 2010).
This definition, relying mostly on exemplum, shows how early distinctions
were created through the combination of smaller fields. As science advances
and new fields emerge, it is difficult to keep to such qualitative definitions.
There must be a limit in place when accounting for these new fields. Instead,
as shown in Repko's 2008 study, the definitions become social constructs that
have evolved and changed through additional qualitative measures. Sugimoto
provides an in-depth discussion on how disciplines are perceived through
various conceptual frameworks, but fails to give a specific metric or
quantitative definition (Sugimoto and Weingart, 2015).
While many mappings of the academic landscape have been created, they
problematically rely on selecting disciplines subjectively (Klavans and
Boyack, 2009) or utilizing existing map classifications (Rafols, Porter and
Leydesdorff, 2010), making it difficult to continuously update the ever-
changing landscape. As the work of Klavans and Boyack combines and finds
common features among 20 existing maps, the resulting disciplines are
abstracted twice. For a funding agency relying on transparent and consistent
evaluations, an automated process for defining these main disciplines based
on academic institutions and not subjective discourse is required. As such,
rather than consolidating multiple expert opinions each year, department
names of the academic institutions provide a more direct categorization
method. While it has not always been easy to parse this data, the
improvements to databases have allowed access to author addresses, including
department names. Furthermore, this method allows for a democratized
system, where if many academic institutions were to consider a topic such as
graphene to be regarded a major discipline, hence creating a Department of
Graphene, this would automatically be included in the yearly discipline
categorization.
In this study, the researchers present novel and practical methodology for
categorizing collaborative disciplines, such as inter-disciplines and cross-
disciplines, in a quantitative manner by developing a Correlation Matrix of
Major Disciplines (CMMD) using bibliometric data. Research shows that
collaborative disciplines can be identified quantitatively by first defining the
major disciplines and then measuring the correlation between the major
disciplines and a compared discipline. Disciplines were categorized as major
disciplines, inner-disciplines of a specific major discipline, inter-disciplines or
cross-disciplines of the major disciplines in this research, or emerging
disciplines in which the data has yet to stabilize.
The conceptual framework of the proposed methodology was introduced by
the NRF in the 2013 Society of Research Administrators International annual
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254
meeting, in a session designed for sponsors and agencies (Park, Cha and Lee,
2013). In a previous study, the authors presented the possibility that major
disciplines could be differentiated based on knowledge productivity, such as
the number of publications in a specific discipline, while other disciplinary
categories such as inner-discipline, inter-discipline, multidiscipline, and trans-
discipline might be explained by their relationship with the predefined major
disciplines.
In this paper, preceding work was refined and simplified to identify
collaborative disciplines and classify disciplines based on types and levels of
collaboration or academic dependency for practical implementation. The
suggested approach could be an effective complimentary tool to manage the
proposal review process in early stages and could simplify proposal
classification and review panel organization for both funders and proposal
applicants.
II. Background
Since the mid-to-late 1990s, the literature has recorded the frequent
combination of knowledge between disciplines, including multi-, inter-, cross-,
and trans-disciplinarity (Aboelela et al., 2007; European Science Foundation,
2011, National Academies, 2004; Huutoniemi et al., 2010; Nordmann, 2004).
The prefixes multi, inter, cross and trans have been applied to the word
discipline; however, it is difficult to find a quantitative definition that enables
academics around the world to find shared meaning in these terms (Mansilla,
2005; Rafols et al., 2012). NRF defines interdisciplinary research as any
research that breaks down disciplinary boundaries (Song and Seol, 1999; Seol
and Song, 1999; Park et al., 2012/2013). NRF has used the national science
and technology (S&T) standard classification system to measure
interdisciplinarity of R&D proposals statistically by mapping multiple S&T
classifications, but it still remains subjective manner by applicants (Song and
Seol, 1999; Seol and Song, 1999). In order to rank the relevance of a
proposal’s topic to the category of funding in detail, subjective measures are
used. For example, in some cases, reviewers are asked to do the ranking
themselves. This can cause problems for both the grant applicants and the
funding foundation since many categories are not clear for specific topics,
especially in interdisciplinary fields (Park, Cha and Lee, 2013; Porter and
Rossini, 1985).
Disciplines as a whole can be valuable references in identifying inter-
disciplinarity (Broto, Gislason and Ehlers, 2009). A discipline refers “to a
particular branch of learning or body of knowledge” (Repko, 2008) and can be
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categorized by its social organizations, based on factors such as mutual
dependence and uncertainty (Broto, Gislason and Ehlers, 2009). Researchers
have used existing data to create a journal-journal citation matrix on document
sets in relation to each other, but have not arrived at a quantifying value
(Leydesdorff, Rafols and Chen, 2013). As such, the publication trends of
major disciplines were used for the CMMD in this study.
Many conceptual definitions of interdisciplinary research have been
suggested by scholars (Aboelela et al., 2007; Apostel, 1972; European Science
Foundation, 2011, National Academies, 2004; Huutoniemi et al., 2010; Klein,
1990/ 1996; Lattuca, 2001; Repko, 2008; Rosenfield, 1992; Stember, 1991).
Wagner et al. (2011) gives an in-depth analysis of past analysis methods of
interdisciplinary research. Among these definitions, the European Science
Foundation (ESF) provides relatively comprehensive meanings for practical
use and a guideline for peer review (European Science Foundation, 2011).
ESF suggested pluri-disciplinary research as the contrary term of mono-
discipline (European Science Foundation, 2011). Pluri-discipline was broken
down into four categories: multidisciplinary, interdisciplinary, crossdisciplinary
and transdisciplinary research. Each of them are then defined as follows:
Multidisciplinarity is concerned with the study of a research topic within
one discipline, with support from other disciplines, bringing together
multiple dimensions, but always in the service of the driving discipline.
Disciplinary elements retain their original identity. It fosters wider
knowledge, information and methods.
Interdisciplinarity is concerned with the study of a research topic within
multiple disciplines, and with the transfer of methods from one discipline
to another. The research topic integrates different disciplinary approaches
and methods
Crossdisciplinarity is concerned with the study of a research topic at the
intersection of multiple disciplines, and with the commonalities among the
disciplines involved
Transdisciplinarity is concerned at once with what is between, across and
beyond all the disciplines with the goal of understanding the present world
under an imperative of unity of knowledge (European Science Foundation,
2011).
For the purpose of this research, we accepted these proposed definitions of
inter-disciplinary and cross-disciplinary research and specified our own term,
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‘inner-discipline,’ which is a discipline or field that belongs to a larger
discipline but has yet to qualify as a major discipline.
Because the characteristics of inter-disciplinarity are not fully known,
several scholars have attempted to identify underlying factors of such
collaboration, although these are mostly qualitative studies (Broto, Gislason
and Ehlers, 2009; Ho, Choi and Lee, 2013; Van Rijnsoever and Hessels,
2011). Some studies sought factors associated with disciplinary and
interdisciplinary research collaboration by quantifying individual researchers’
characteristics, such as global innovativeness, work experience, dynamics of
the scientific fields, and gender collected through surveys (Van Rijnsoever
and Hessels, 2011). Others used indicators of inter-disciplinarity typology,
such as the scope of inter-disciplinarity, type of inter-disciplinary interaction,
and type of goals (Huutoniemi et al., 2010). These studies still remain largely
qualitative and act as conceptual guidelines, while some are designed using
empirical analysis for practical use for funders and policy-makers.
Past literature has shown a recent trend toward defining inter-disciplinarity
in a quantitative way (Bourke and Butler 1998; Kaur et al., 2012; Pan et al.,
2012; Schoolman et al., 2012; Tijssen, 1992; Xie et al., 2015; Yang and Heo
2014; Yang, Park and Heo, 2010). Bibliometrics is a useful tool for
identifying publication trends, authors’ academic fields, and authors’ co-
workers. Combined with citation and bibliometric analysis, which uses
citation data, these methods provide an effective way to better examine the
nature or characteristics of inter-disciplinary activity. Recent studies have
utilized citation information and constructed a network analysis to
quantitatively and visually measure inter-disciplinarity (Kaur et al., 2012;
Schoolman et al., 2012; Small, 2009; Xie et al., 2015; Yang and Heo, 2014).
Although this approach offers some value in individual measurement, it is
difficult to apply in macro scale analysis, including the S&E field.
Furthermore, previous studies initially assumed the inter-disciplinarity of
certain research and used such assumptions as basis for later analyses (Kaur et
al., 2012; Schoolman et al., 2012; Small, 2009; Xie et al., 2015).
Other quantitative assessments of inter-disciplinarity in science and
technology have been conducted based on co-occurrence of publication in
predefined classifications using bibliometric information (Börner et al., 2012;
Bourke and Butler, 1998; Pan et al., 2012; Tijssen, 1992). This approach is
quite practical and simple; however, it has limitations, such as the lack of
generalization of co-occurrence, absence of quantitatively defined core
disciplines that can be compared with other fields of study, disregard for
diversity of publication size in different disciplines, and the restriction of
testing to specific fields.
This paper proposes a method for quantifying the relevance of a research
topic to the major disciplines within S&E, where a topic can be considered a
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type of research field or discipline that does not fall within the list of major
disciplines. Instead of starting from a boundary condition that initially
assumes a certain discipline or research topic that is inter-disciplinary, the
major disciplines are identified by the NRF in a quantitative manner using
bibliometric data and lists of R&D fields in S&E, and correlation over the
major disciplines is calculated using the CMMD. Both the frequency of
publications and co-occurrences of specific journal publication are used as a
function representing collaboration of and relation to the major disciplines.
Through correlation, these disciplines are then shown to be inner-disciplines,
cross-disciplines or inter-disciplines. This classification is made by defining
the major disciplines, creating a function representative of journal frequency,
and analyzing the correlation of a compared discipline over the major
disciplines. The correlation values describe the relation between a research
topic and the major discipline. For example, if a recent research topic such as
graphene shows high correlation with major disciplines such as physics,
material science and electrical engineering, it can be considered
crossdisciplinary, as it is strongly related to those fields. Conversely, algebra
can be considered an inner-discipline due to its high correlation with
mathematics only.
As a funding agency, the motivation for this work is not in performance
evaluations of researchers, but instead in the interest of appropriating funds
designated to emerging and collaborative research topics. The ability for a
funding agency to make decisions based on repeatable and quantitative
methods is vital to a transparent and fair system. While subjective measures
can judge aspects not easily seen in data, they are also a problem when
comparing several reviewers for the same funds. This work presents a
quantitative method of classifying emerging and collaborative research topics
that can supplement the subjective measures currently used. However, it is not
meant to replace the entire process. Finally, while numerous researchers have
developed maps of the academic landscape, the methods that follow a
completely quantitative approach are difficult to implement and lack
methodology within the literature, an important aspect of this work and the
likelihood of implementation.
III. Methods
1. Major Discipline Definition
In order to correlate either major disciplines to each other, or different
research topics to major disciplines, it is necessary to quantitatively define
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what a major discipline is. As the main funding agency for South Korea, the
NRF has built a list over the last five years of fields in which it funds (NRF,
2016). The list has over one thousand fields broken into three categories; chief
review board, review board, and sub review board. From this list, all entries
from chief review boards and review boards, the more general categories,
were used as the candidates for a major discipline. This list of fields is not
determined by a subjective measure; rather, it is a culmination of all fields and
topics utilized in funded applications. Additions to the list in the future are
possible, and would easily be analyzed for inclusion of major disciplines, but
within the immediate term no additions would seem likely to contribute as a
major discipline based on the following criteria.
With a large initial set of keywords, the online database from the Web of
Science (WOS) was used to determine the presence of each keyword in the
academic community based on publications. The search filters available for
the WOS were used to find articles published that were relevant to a specific
field. Specifically, the option to search for author address was used. By using
the address, the list of major discipline candidates were compared against the
word the Universities use to define their department, i.e. Department of
Chemistry. The number of queries returned for each candidate discipline for
the entire period that had been stored in WOS was recorded. In order to define
a limitation to the number of major disciplines while including a significant
number, a value of 300,000 articles was decided as the cut-off point for a
major discipline. This number provided 22 major disciplines and did not leave
any obvious major disciplines out of the group, which was reduced further to
21 major disciplines by the criteria in the following subsection due to
duplications in the dataset.
2. Data Collection
All data used in this research was accessed either through the Web Of
Science online or the API (Web of Knowledge Web Services v. 3.0) using the
python programming language. When using data from the WOS database, it is
important to note the methods in which the data is stored and searched. For
most disciplines, the full name of the discipline is not stored in the WOS
database; instead, a concatenated version is kept in place. For example,
Chemistry is stored as Chem. This introduces errors when a word is
concatenated to a different less common word. However, the full string
Chemistry is still allowed to be used in the search, only the user must be
aware of the automatic concatenation done by the database as other terms,
such as Chemical Engineering must be searched as Chem* Eng*. For this
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259
research, the search term for address is used as the WOS search tag AD, and
when searching for keywords as the topic, the search tag TS is used.
2.1 Major Disciplines
After defining the major disciplines total search results, all data from the
years 2009 through 2014 were downloaded for each discipline with full
inclusion. Using the most recent six years of publication data is both more
representational of the current academic landscape and a reasonable limit to
the amount of data collected. In order to download the most accurate image of
the database, a python script was used to both query the search terms and store
the full raw data through the University account. Although the WOS API has
a download limit of 100,000 results, the search for each discipline is split into
yearly data. On a few disciplines, the yearly data exceeds 100,000, yet is
under 200,000. In this case, the data is sorted in reverse order, downloaded,
and parsed for duplicates in combination with the first set of 100,000,
allowing any search term under 200,000 to be downloaded.
For the search of major disciplines, a single keyword was used in the
address search field. In this case, for a given search term, i.e. Chemistry, the
results Department of Chemistry and Department of Chemistry and Chemical
Engineering are both valid results. Additionally, multiple authors may have
different addresses, resulting in a publication counting for two different search
terms. The presence of multiple authors with different departments, or
departments with multiple keywords, creates duplicate publications in each
field. In order to check the overlaps, the total duplicates in one field to another
were found. In the case of Chemical Engineering, the resulting data was
included at a rate of 99.36% in Chemistry. This is caused by both the WOS
concatenating search terms and the frequency of which departments are
named as Chemistry and Chemical Engineering. The second most duplicated
data was Biology containing 35.6% of publications from Biochemistry.
Finally, the removal of Chemical Engineering due to the lack of unique data
reduced the total major disciplines to 21.
After deciding on the final 21 disciplines, all duplicate data was removed
from the database to give a correlation based on a basic frequency of
publications in a specific journal. This removes duplicate publications through
database errors as well as collaborative papers. The motivation behind this is
two folds. First and foremost, the data seems to agree with conventional ideas
of disciplines when the duplicates are removed. Second, the use of duplicate
data creates a strong weight on co-authored papers, which could be analyzed
separately for their own metrics.
Table 1 lists the final major disciplines and the total number of papers
collected over each year. The data collection period occurred between May
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13th and May 15th 2015. Each discipline displayed here had an overall
publication number over 300,000 when searching through all years. Table 1
represents the full data records collected for each of the past six years.
Table 1 Yearly data downloaded for each major discipline
Discipline
Code
2009
2011
2012
2013
2014
Agriculture
A
35183
42936
45599
48809
51872
Anatomy
B
12788
13406
13758
13552
13235
Biochemistry
C
38592
43170
44564
45884
45025
Biology
D
116802
132868
141010
144436
146917
Chemistry
E
160299
176172
182105
194227
199700
Computer Science
F
18197
20605
22690
24553
26535
Dentistry
G
17667
20067
21514
22019
21155
Electrical Eng.
H
20930
24644
26715
28681
31113
Food
I
19263
23005
24519
27853
29417
Internal Medicine
J
23796
27170
29434
30417
29704
Material Science
K
29647
34596
36678
40572
44363
Mathematics
L
48438
53165
57853
61249
62425
Mechanical Eng.
M
18959
21810
23362
26210
28475
Nutrition
N
17166
20184
20872
24423
22863
Obstetrics
O
14207
16513
17510
17792
18154
Pathology
P
45851
50618
53791
53822
54168
Pharmacology
Q
26457
28298
29055
30674
29209
Physics
R
110782
121529
124636
132182
137450
Physiology
S
25850
27037
28107
29111
28690
Psychiatry
T
23512
26240
27514
28576
29147
Surgery
U
61888
72212
77397
83092
85911
2.2 Minor Disciplines
After creation of CMMD, any research topic can be used as a keyword to
find the collaboration category. A large challenge to quantifiable categories is
the lack of prior work using quantifiable measures. In order to compare the
results of this research to outside opinion, multiple keywords from various
known sources were collected. In this study, these keywords refer to minor
disciplines. Table 2 shows the selected 14 minor disciplines, the source and
defined category from the source, as well as the total number of papers for
each minor discipline of the six years. The search terms used for research
topics are in the supporting information.
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Table 2 Source, category and number of publications downloaded per year
Keyword
Code
Source
Category
2009
2010
2011
2012
2013
2014
3D Printing
AA
Gatner, 2013
Collaborative or
Emerging
143
123
168
234
379
762
Algebra
BB
NRF, 2016
Inner of
Mathematics
3497
3513
3665
3764
3915
3885
Artificial
Intelligence
CC
ESF, 2011
Transdisciplinary
589
595
669
754
807
826
Atomic Physics
DD
NRF, 2016
Inner of Physics
849
1159
1541
1586
927
634
Climate Change
EE
European
Environment
Agency, 2014
Collaborative or
Emerging
8150
9676
11585
13281
15550
16582
Cognition
FF
ESF, 2011
Transdisciplinary
4974
5296
5996
6814
7738
8156
Combinatorics
GG
NRF, 2016
Inner of
Mathematics
261
269
291
281
285
290
Differential
Equations
HH
NRF, 2016
Inner of
Mathematics
6678
6652
6963
7441
8085
8116
Graphene
II
Sanchez et al.,
2012
Collaborative or
Emerging
2134
3506
5683
8477
11892
16554
Internet of Things
JJ
Gartner, 2011
Collaborative or
Emerging
41
61
144
202
412
623
Molecular
Machines
KK
Schlick, 2010
Collaborative or
Emerging
310
309
287
324
322
357
Quantum
Mechanics
LL
NRF, 2016
Inner of Physics
1789
1826
1825
1913
1988
2009
Robotics
MM
ESF, 2011
Interdisciplinary
905
972
1024
1069
1230
1200
Synthetic Biology
NN
ESF, 2011
Transdisciplinary
424
515
641
851
912
1040
3. Analyzer Score
The correlation of two disciplines is defined by the common journals in
which each discipline publishes. By parsing the data collected through
publications, the total publications within a specific journal are counted,
referred to here as journal frequency. The journal frequency is used as a
function to correlate the importance of a specific journal in one field to
another.
With new data sets, the analyzer function can be derived by the same
method each time, without the need for future model fitting. The analyzer
function is then defined by the average of the most frequent journal frequency
of all major disciplines, which can be written as Equation 1.
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262
a(x)=
i=1
n x(Pi)
n (1)
Where n is the total number of major disciplines, P is the set of disciplines
with elements Pi, where Pi is the set containing the journal frequency of
different journals within a discipline and x(Pi) is the journal frequency of the
xth most frequent journal in a discipline.
Figure 1 xth most frequent journal frequency (journal rank)
The minimum and maximum data is displayed in grey. This graph shows
the core part of the graph with extents of 10,000 and 200 respectively. The
middle dotted line is the calculated average using Equation 1.
4. Correlation Matrix
The correlation of major discipline A to major discipline B, is referred to as
Ca,b, where Ca,b is a row-column pair of the nn matrix C. To calculate a
discipline pair A and B, a normalized analyzer score is defined as k in
Equation 2.
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k=
i=1
n a(i)2 (2)
Where i is the argument for the analyzer function in equation 1. The value
for an individual pair of journals in each discipline given ordered sets
A={x1,x2,x3,,xj:xixji<j}and B={x1,x2,x3,,xj:xixji<j}
where elements xixj are journal names ordered by journal frequency within
discipline A and B. The resulting values from the analyzer function a(i) are
multiplied. Defined in Equation 3.
h(x)=(a(i):xiA)(a(i):xiB) (3)
The final correlation value for Ca,b is given through Equation 4, where p
is the title of a journal in both discipline A and B.
ra,b=
pAB
h(p) (4)
Ca,b= ra,b
k*100
For the minor discipline to major discipline correlation, an additional factor
is applied to reduce the influence of a particular field on the correlation value.
For a given major discipline a to minor discipline m, referred to as Ca,m , a
normalizer value t acts as the divisor for the final normalized score Nm,a
defined in Equation 5.
t=
i=0
n Ca,i (5)
Nm,a= Cm,a
t
Where Ca,i is the correlation score defined in Equation 4, of discipline A
to n total major disciplines.
Asian Journal of Innovation and Policy (2016) 5.3:251-274
264
5. Categorization
Due to limited data of recently emerging fields, categorization through
bibliometric data may be unreliable. In this case, the additional tag of
Emerging is given to the research topic if the number of publications has
doubled in the past 6 years, which can be found from Table 2.
A function 𝑚𝑎𝑥𝑖(𝑥) is defined as the maximum value of the set X, where
i is the ith maximum value such that 𝑚𝑎𝑥1(𝑥)> 𝑚𝑎𝑥2(𝑥). Finally, the
categorization for a minor discipline set of normalized correlations to the
major disciplines,Nm, is defined as:
(6)
These values are defined based on the definitions given in the Introduction
section for inter-discipline and cross-discipline, for inter-discipline being a
research topic, which is not central to any one specific field, and hence will
have a lower overall correlation, which in this research was chosen as a value
of 5. In contrast, cross-discipline is defined to be the default case such that a
research topic is not inter-discipline and is also not considered inner-discipline,
requiring a high correlation (above 5) to more than one major discipline.
Further research into more research topics in the future would help in
understanding if these values can be kept as constant or must be determined
each year. While this is one drawback of the proposed method, it is acceptable
for the intended purpose of correlating research topics to the major disciplines
and being able to compare these topics against each other.
IV. Results and Discussion
1. Major Discipline
This research took a bottom up approach to defining collaborative fields by
using quantitative measures for each step of the process. The first step was in
defining what is considered a major discipline. After finding the major
disciplines, a correlation matrix between the major disciplines is created
(Table 3).
Asian Journal of Innovation and Policy (2016) 5.3:251-274
265
Table 3 Correlation matrix of the major disciplines rounded to the nearest integer
Code
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
A
*
33
38
43
10
10
11
2
33
30
3
3
2
20
7
20
18
3
33
13
11
B
33
*
44
47
3
10
19
2
10
37
1
3
1
25
13
37
35
4
58
21
19
C
38
44
*
71
21
11
20
2
21
47
6
3
2
29
13
35
43
5
58
15
16
D
43
47
71
*
10
12
17
2
16
39
3
4
2
25
10
32
33
5
54
16
14
E
10
3
21
10
*
2
3
5
18
3
36
1
10
4
1
2
8
15
5
1
1
F
10
10
11
12
2
*
3
21
3
9
2
11
6
4
2
5
6
4
11
5
4
G
11
19
20
17
3
3
*
1
5
24
3
1
1
13
9
16
15
2
20
8
11
H
2
2
2
2
5
21
1
*
1
1
22
6
17
1
0
1
1
23
2
1
1
I
33
10
21
16
18
3
5
1
*
8
5
1
2
27
3
7
11
2
11
3
3
J
30
37
47
39
3
9
24
1
8
*
1
3
1
30
15
41
32
3
47
17
25
K
3
1
6
3
36
2
3
22
5
1
*
1
29
1
0
1
2
38
2
0
1
L
3
3
3
4
1
11
1
6
1
3
1
*
5
1
1
2
2
8
3
1
1
M
2
1
2
2
10
6
1
17
2
1
29
5
*
1
0
1
1
14
2
0
1
N
20
25
29
25
4
4
13
1
27
30
1
1
1
*
12
16
24
2
35
9
10
O
7
13
13
10
1
2
9
0
3
15
0
1
0
12
*
14
10
1
13
6
10
P
20
37
35
32
2
5
16
1
7
41
1
2
1
16
14
*
21
2
26
9
18
Q
18
35
43
33
8
6
15
1
11
32
2
2
1
24
10
21
*
3
52
18
11
R
3
4
5
5
15
4
2
23
2
3
38
8
14
2
1
2
3
*
5
2
1
S
33
58
58
54
5
11
20
2
11
47
2
3
2
35
13
26
52
5
*
23
17
T
13
21
15
16
1
5
8
1
3
17
0
1
0
9
6
9
18
2
23
*
6
U
11
19
16
14
1
4
11
1
3
25
1
1
1
10
10
18
11
1
17
6
*
It is useful to see the correlation of these fields within S&E for funding
decisions as the major disciplines of researchers collaborating can be
quantified in terms of closeness through past journal publications. Easily
visible through Figure 2 is the tendency for Engineering and Medical fields to
be more correlated to their own group, a sign that the methodology produces
intuitively agreeable results.
Asian Journal of Innovation and Policy (2016) 5.3:251-274
266
Figure 2 Correlation of the major disciplines
The color map shows the correlation values from 0 to 100 of the major
Disciplines. This map makes it easy to understand which fields have high
correlation, which is most common in similar type fields.
2. Minor Discipline
The final result of this research is the categorization of any given keyword
or research topic in relation to its collaboration within major disciplines.
Fourteen minor disciplines have been analyzed, with the correlation matrix
shown in Table 4. The resulting correlation between the referenced minor
disciplines and the suggested major disciplines using the CMMD is shown in
Table 5.
Asian Journal of Innovation and Policy (2016) 5.3:251-274
267
Table 4 Minor disciplines to the major disciplines rounded to the nearest tenth
Code
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
AA
.6
.6
.6
.6
2.3
1.1
.8
3.5
.6
.5
2.5
.6
4.1
.4
.4
.4
.4
1.5
.5
.5
.9
BB
.1
.0
.0
.1
.1
1.4
.0
.8
.0
.0
.2
17.6
.5
.0
.0
.0
.0
2.7
.0
.1
.0
CC
.4
.3
.2
.3
.3
8.0
.2
3.1
.3
.3
.3
2.9
3.5
.2
.2
.2
.2
.4
.2
.3
.2
DD
.1
.1
.2
.3
1.4
.5
.1
4.7
.1
.1
4.1
2.1
3.5
.0
.1
.1
.1
8.9
.1
.1
.1
EE
2.2
1.5
1.3
2.1
.6
1.5
1.0
.5
.9
1.4
.3
1.2
.7
.8
.8
1.1
1.0
1.0
1.3
1.5
1.2
FF
1.7
2.0
1.4
1.7
.4
1.6
1.3
.3
.7
1.6
.1
1.0
.2
1.1
1.0
1.2
1.5
.5
1.9
6.1
1.4
GG
.0
.0
.1
.1
.2
3.8
.0
.5
.1
.0
.1
12.3
.2
.0
.0
.0
.0
.9
.0
.0
.0
HH
.2
.1
.1
.1
.3
1.4
.1
1.7
.1
.1
.4
26.3
3.1
.1
.1
.1
.1
1.9
.1
.1
.1
II
.2
.1
.2
.2
5.2
.3
.2
4.1
.6
.0
6.7
.9
3.7
.1
.1
.1
.1
8.7
.1
.1
.1
JJ
.1
.1
.1
.1
.2
4.3
.1
2.7
.2
.1
.2
1.2
.8
.1
.1
.1
.1
.3
.1
.1
.1
KK
.7
.6
1.3
1.2
6.6
1.3
.5
.6
.7
.5
1.9
1.0
.8
.4
.4
.6
.7
1.8
.7
.6
.5
LL
.2
.1
.3
.3
2.4
.9
.1
1.4
.3
.1
1.7
5.8
1.1
.1
.1
.1
.2
7.8
.2
.1
.1
MM
.2
.3
.2
.2
.2
2.2
.2
1.8
.1
.2
.3
.7
2.3
.1
1.0
.3
.2
.4
.2
.3
1.1
NN
1.2
1.0
1.6
1.8
2.9
1.5
.8
.4
1.0
.9
.9
1.0
.5
.6
.6
.9
.9
.9
1.0
1.0
.8
Table 5 Categorization of the minor disciplines using CMMD
Research Topic
Code
Category
Emerging
Agreement with
Reference
3D print
AA
Inter
Yes
Yes
Algebra
BB
Inner
Yes
Artificial Intelligence
CC
Cross
Yes
Atomic Physics
DD
Inner
Yes
Climate Change
EE
Inter
Yes
Yes
Cognition
FF
Inner
No
Combinatorics
GG
Cross
No
Differential Equations
HH
Inner
Yes
Graphene
II
Cross
Yes
Yes
Internet of Things
JJ
Inter
Yes
Yes
Molecular Machines
KK
Inner
No
Quantum Mechanics
LL
Cross
No
Robotics
MM
Inter
Yes
Synthetic Biology
NN
Inter
Yes
Yes
When comparing against the categorization of the NRF disciplines, Algebra,
and Differential Equations agree as inner-disciplines of Mathematics.
However, the NRF has categorized Quantum Mechanics as an inner discipline
of Physics, while this research has found it to have high correlations with both
Asian Journal of Innovation and Policy (2016) 5.3:251-274
268
Mathematics and Physics, easily seen in Figure 3. Suggesting there is much
more input from the mathematics discipline than previously thought. This
color map shows the high correlation to Mathematics and Physics, suggesting
a Cross-discipline rather than an Inner-discipline of Physics.
Figure 3 Correlation color map of quantum mechanics
Atomic Physics was categorized as an inner discipline of Physics by the
NRF database, but it seems to have strong correlation with Mathematics,
Mechanical Engineering, and Physics as shown in Figure 4. However, it falls
into the inner-discipline of Physics based on the suggested categorization
criteria, equation (6).
Figure 4 Correlation color map of atomic physics
As the ESF manual uses Transdisciplinary, not being in the categories
proposed here, it is considered either Inter or Cross disciplinary to validate the
results (i.e. not Inner-disciplinary). In this view, most of the minor disciplines
were categorized similarly to the referenced categorization of minor
disciplines with a few exceptions such as Molecular Machines. The results in
Figure 5 suggest it is still strongly correlated with Chemistry, leading it to be
categorized as an Inner discipline. This color map shows the high correlation
to Chemistry, with very little correlation to the other major disciplines,
suggesting an Inner-discipline rather than a Collaborative discipline.
Figure 5 Correlation color map of molecular machines
Asian Journal of Innovation and Policy (2016) 5.3:251-274
269
Finally, a good representation of how this research represents the definitions
proposed in the ESF manual in a quantitative way is the research field
Robotics. As the ESF defines Robotics as an inter-disciplinary field due to its
application in a variety of disciplines, with no one major discipline taking
ownership, an even correlation among many disciplines is to be expected, as
seen in Figure 6. This color map shows the relatively similar correlation
among many disciplines, suggesting a research topic that is neither cross nor
inner disciplinary.
Figure 6 Correlation color map of robotics
The highest correlation value in Robotics can be seen as 2.3 with
Mechanical Engineering, an unsurprising result. Additionally, Electrical
Engineering and Obstetrics both have correlation values of approximately 1.8
and 1.0 respectively. While the former is again unsurprising, the latter is more
unique, most likely caused by the large use of robots and robotic technology
in the discipline.
10 of out 14 minor disciplines agreed with the referenced categorization; 3D
print, Algebra, Artificial Intelligence, Atomic Physics, Climate Change,
Differential Equations, Graphene, Internet of Things, Robotics, Synthetic
Biology. Cognition and Molecular Machines are in disagreement with the
references, as the proposed methodology suggests they are inner-disciplines of
Psychiatry and Chemistry, respectively. Additionally, while the reference
material refers to Molecular Machines as both collaborative and emerging, the
growth rate of bibliometric data does not suggest this. However, it is possible
the low quantity of data has skewed the results. Quantum Mechanics and
Combinatorics are considered inner-disciplines by the reference material, but
are shown to have high correlations to more than one discipline. Quantum
Mechanics is highly correlated to both Mathematics and Physics, while
Combinatorics is highly correlated to both Mathematics and Computer
Science.
Based on the criteria stated in Table 2, the research topics 3D Print, Climate
Change, Graphene, Internet of Things, and Synthetic Biology are emerging
topics. As these minor disciplines were identified by Gartner (Gartner,
2011/2013) as emerging topics, the results are in agreement.
Asian Journal of Innovation and Policy (2016) 5.3:251-274
270
V. Discussion
The purpose of this research is to introduce a quantitative method of
categorizing disciplines and research topics in terms of their correlation to one
another. The values produced from this correlation can be used to
quantitatively define frequently used terms such as Inter-disciplinary. While
this paper uses a variety of sources to ensure the accuracy of results, it is
important to note that these references act as only a guide and cannot be used
to truly test the validity of the results, as the current methods used by
organizations such as the NRF and ESF are still qualitative.
An initial search for publication frequency on a larger dataset of keywords
in S&E would be beneficial. These keywords, though, had not been
predefined as major or interdisciplinary, and were solely used as a source list
for possible search terms without access to the raw database and numbers of
keywords.
Further improvement of the work can be done in data collection. Yearly
data could be expanded to many more years, which would assist in the
development of the analyzer function. Issues with the WOS database do
introduce errors, although the error is believed to be negligible, especially as
more yearly data is collected. Additional sources of data for publication
records would also improve the accuracy of the correlations.
This work is meant to be a starting point for the quantification of disciplines,
a necessary step to improve funding allocations and allow academics to better
understand new fields and collaborations. Additionally, the work can be
applied as an indexing tool for academic institutions focusing on
interdisciplinary or convergence research. In planning and development,
institutes looking for new collaborations between seemingly unrelated
disciplines can use this method to detect lowly correlated disciplines and
focus on the possible convergence between them. As with any new method of
categorization, there will be disagreements among academics on the way a
discipline is categorized, in both the major disciplines and the categorization
of minor disciplines. The authors acknowledge this issue and encourage
further development of this method as a means for more accurately describing
a discipline and more precisely (quantifiably) defining the use of words such
as inner-,multi-,cross-,inter-, and trans-disciplinary.
Asian Journal of Innovation and Policy (2016) 5.3:251-274
271
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