i
`Title
`
`A new method of modeling and clustering for citation relationship
`
`Author(s)
`
`Saito, Tatsuki; Asano, Chooichiro
`
`fL1'1'i:k"¥::k"¥~1G*ftE!fltli'+Eff~fl.¥~a 1111 (3) II p327-337; Engineering
`sciences reports, Kyushu University 1111 (3) II p327 -337
`
`1989-12-01
`
`http://hdl.handle.net/2324/17162
`
`Citation
`
`,,
`
`Issue Date
`
`URL
`
`Right
`
`This document is downloaded at: 2013-02-21T02:49:54Z
`
`Kyushu University Institutional Repository (QIR)
`
`Facebook Ex. 1011
`
`0001
`
`

`

`Engineering Sciences Reports, Kyushu University
`(KYUSHU DAIGAKU SOGORIKOGAKU .KENKYUKA HOKOKU)
`Vol. 11, No.3, pp. 327-337, December 1989
`
`A new method of modeling and clustering
`for citation relationship
`
`Tatsuki SAITO* and Chooichiro• ASANO* *
`
`(Received August 22, 1989)
`
`Recently some researcher-databases have been constructed to obtain detailed information for their
`citation relationship.
`In the present paper, a fundamental methodology of modeling is proposed for a
`scientific article-space with the relational structure among scientific articles, where the techniques of
`clustering are studied on the basis of a-valued and directed graphs and the asymmetrical similarity
`matrix.
`
`I
`
`Introduction
`
`There exists impotant and characteristic information involved in various relations
`among scientific articles. However, most of bibliographic databases in market do not give
`such accurate information11 . Consequently, the direct acquisitions are not able to help the
`users on essential information involved in the origins! set of articles.
`From this viewpoint,
`a researcher-database 21 31 is newly-proposed to obtain detailed information regarding citation
`Basing on the application of such a database, it may be
`relations among original articles.
`expected to grasp some dynamic trends of further development of scientific researches in the
`field.2J.JU3J -lBJ
`The purpose of the present paper is to propose a new methodology to make clear the
`structure of relationship among articles to promote the above study.
`Also the clustering
`methods are given with graphic consideration.
`The ordinary graphs applied are dual(cid:173)
`directional and are easily processed191 201 . However, information involved in scientific arti(cid:173)
`cles is one-directional, i. e. one-way between a citing article and a cited article.
`Therefore,
`in order to represent such one-dimensional graphs with strength values and to construct
`more precise model of article relationship, a method is studied with the validity of represent(cid:173)
`ing relationship based on asymmetric similarity matrices among articles.
`Combinatorial
`cluster analyses are ordinarily suitable211 - 271 , when the relation matrix is symmetric.
`In
`Thus a
`this case, however, it is required to transform the matrix to a symmetric matrix.
`new method of clustering is obtained for asymmetric similarity matrix, aborting such a
`the clustering method with binary reiationship is based on the strength among
`trouble.
`articles as a criterion, and actually this method has shown the better performance than the
`combinatorial methods.
`
`2. Modeling by citation relation graph
`
`2.1 Valued graph
`Graph consists of a non-empty finite set P with P points, and it consists of a specified
`
`*Research Assistant, Faculty of Engineering, Hokkaido University
`**Interdisciplinary Graduate School of Engineering Science, Dept. of Information Sciences
`
`0002
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`Face book Ex. 1011
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`-328-
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`A new method of modeling and clustering
`
`The pair l = (i, j) of points i and j be-
`set L that has nonordered q pairs to belong to P.
`longs to the set L, and it is called a line of a graph. A graph that hasp points and q lines
`is called an (p, q) graph, or a graph G = (P; L) . Graph is applicable to model structural
`object. Namely it is a relational graph that a point is corresponding to an objective article
`The nondirected graph is thought to be the
`and a line is corresponding to the relation.
`special directed graph that always accompanies a directed line of reverse direction.
`In
`case of directed graph, the finite point set P that is not empty and specified set L that has
`ordered pairs of two different points are dealt simultaneously.
`Scientific articles by the
`The relation of author is not directed, but the rela(cid:173)
`same author are connected by lines.
`tion of citation is directed.
`Therefore, the citation relation is represented by a directed
`graph. While directed graph can express the presence or absence of a relation among arti(cid:173)
`cles, the strength of relation cannot be expressed only by it.
`Consequently, valued graph
`is introduced to enable an expression of the strength of relation. Valued graph (P; L; Y)
`is the graph that a line of the set L of lines is accompanied with the value r that is mapped
`Expressing the value that is accompanied wi_th a line (i, j) as r
`onto a real number set Y.
`(i, j), it is called a value of the line.
`The production of the valued graph and its relational
`similarity matrix are describad in 2. 2.
`2.2 Modeling by similarity matrix
`Fundamental Procedure for Modeling
`The fundamental procedure for modeling is as follows,
`1. Consider a binary citation relation between articles i andj. ·
`2. Represent the binary relation as a relational graph expressed by points i and j.
`3. Generate a directed valued-relation graph that corresponds to citation relations
`among articles.
`4. Represent those graphs as similarity matrices.
`The generation of direct citation graph and the formation of its similarity matrix are de(cid:173)
`scribed as below,
`Direct Citation Relation Matrix
`Define direct citation relation matrix A= [au] . This is so-called an adjacency matrix~
`where au= 1 ; if article i cites article j.
`0; otherwise.
`Citation Relation Matrix
`Considering a total citation relation that involves indirect citation, define citation rela(cid:173)
`tion matrix S= [Su], where
`
`(1)
`
`k means the length of a directed walk, and kaiJ means the number of a directed walk of which
`the length is k between article i and article j.
`The upper bound n is less than Max (k)
`(maxim urn length of directed walk) , wk is a weight and takes a value such as 1/ k or 1/ C
`The kaii can be obtained by kth power of matrix A as resetting diagonal elements 0. An
`efficient algorithm that calculates only the nonzero elements of a matrix A has been de(cid:173)
`veloped.
`
`0003
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`-329-
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`3. Cluster analysis for relational graph model
`
`3.1 Characteristics of relational graph model
`In this section, we introduce new methods of clustering which analyze the relational
`graph represented by the similarity matrix.
`Traditional techniques of the combinatorial
`cluster analyses are discussed in 3. 2 and the present method is described in 3. 3.
`As mentioned in the previous section, the analyzed matrix is given by
`
`(2)
`
`where P is an enhancing factor (ordinarily P= 1).
`The characteristics of this matrix are summarized as follows.
`1. Each element of the matrix has a positive real quantity.
`Element su is the similarity as a correlation-like measure, then element ru has a positive
`real quantity.
`2. The matrix is asymmetric.
`The similarity matrix of the citation relation is asymmetric. because there is a time
`In consequ(cid:173)
`sequence in the incidental relation between a citing article and a cited article.
`ence, the matrix R becomes asymmetric. When the methods of the combinatorial cluster
`analyses discussed in 3. 2 are applied, it is necessary to change to the symmetric matrix.
`However, it is not desirable due to occurring the distortion of the original matrix. We
`propose a new clustering method for the asymmetric matrix in 3. 3.
`3.2 Application of combinatorial clustering analysis
`The combinatorial cluster analysis is also called the method of hierarchical cluster
`analysis, because it constructs a tree. All computer programs of the following combinato(cid:173)
`rial methods have been implemented and applied for the analysis of the relational graph
`model.
`Since the original similarity matrix of the relational graph model is asymmetric, it
`is necessary to change to a symmetric matrix, because the combinatorial methods are only
`applied to symmetric matrices.
`The nearest neighbour method
`Seven hierarchical clustering methods are examined.
`is based on single linkages, because clusters are joined at each stage in view of the single
`shortest or strongest link among them.
`The furthest neighbour method is called the com(cid:173)
`plete-linkage method, since all articles in a cluster are linked to each other in view of some
`The median method adopts the middle value of the nearest neighbour
`minimum similarity.
`value and furthest neighbour value.
`The method of average linkage within the new group
`is not influenced by extreme values for clustering and cannqt make any statement about the
`minimum or maximum similarity within a cluster. Average linkage between amerged
`group, called the group average method, evaluates the potential merger of clusters i and j in
`terms of the average similarity betwe.en the two clusters.
`The centroid method uses both
`the mean values of similaries i"nd number of articles for the merger.
`The minimum
`variance method, called Ward method, is generally reasonable, because those merger give the
`minimum increase at each stage for the total within group error-sum of squares.
`When these combinatorial methods are applied. a symmetric similarity matrix R is
`
`0004
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`Facebook Ex. 1011
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`

`-330-
`
`A new method of modeling and clustering
`
`changed to symmetric matrix by (3).
`
`(3)
`
`3.3 Cluster analysis for relational graph model
`Though combinatorial clustering methods are versatile, when it applies to the asymilar(cid:173)
`ity matrix, the matrix must be symmetrized.
`Consequently the initial information space to
`be clustered is distorted, so that the precision of analysis often decreases. We propose a
`It is called binary relationship
`new method of clustering for asymmetric similarity matrix.
`cluster analysis that classifies objects by the binary relationship between articles.
`,
`Binary Relationship Cluster Analysis (BRCA)
`Let od (i) denote the outdegree at an anticle i, which is obtained by L au, where t is the
`total number of articles, and let Yu be
`
`j=l
`
`-
`ru
`Yu- (od(j) )' '
`
`where e is an enhancing exponent ordinarily e = 1.
`If the combinatorial analysis of total relation is required, let zu be
`
`otherwise let a matrix Z= kJ,
`
`t
`
`where zu= L wkViJ,
`
`k=l
`
`(4)
`
`(5)
`
`(6)
`
`and wk is a weight (e. g. wk = 1, ! , iz), and vu is (i, j) element which is a powered matrix
`IYuJ of k.
`article j.
`(i~k).
`This clustering procedure is realized by the pollowing way.
`Procedure 1 : Searching max (zu) row-wisely (j= 1, 2, ... , m) and denote it Zik·
`Procedure 2 : If Z;k is greater than or equal to Zki· article i is clustered to cluster k,
`otherwise article k is clustered to cluster i.
`However, if there exists Ztm which is greater
`than Zik (m~k), then article i is joined to cluster m.
`The property of this clustering method is to construct a hierarchical structure and has
`a tendency to make small cluster.
`
`The quantity zu is construed as the quantity in which article i has influence on
`Comparing zu with ZJi pairwisely, when zu?:.Zk;. article} is linked under article k
`
`4.
`
`Illustrations
`
`Scientific articles for two different research fields have been investigated in order to
`test the present method. One is 231 articles for CAD/CAM.
`The other is 140 articles of
`two or three bodies problem for nuclear physics. All of them have citation relation arti(cid:173)
`cles in each field.
`The former contains mainly the articles for computational geometry and
`several articles relevant to AI (Artificial Intelligence ) .
`In the following comparison with
`
`0005
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`

`-331-
`
`manual classification by experts, conformance percentages is the separation rates between
`AI-cluster and the other.
`Because the research filed is obviously different from CAD/(cid:173)
`CAM, it is expected to suppress the occurrence of the error by analyst's subjectivity. On
`the other hand, the latter consists of three groups, namely DIS, V AR and REAL, which are
`different in approach or methodology to solve.
`Clustering methods to be used are the
`Computer programs by M. R.
`seven combinatorial methods and the present method.
`Anderberg were utilized for the former 281
`•
`Fig. I shows the result by the average linkage within new group method, which was
`best among hierarchical methods.
`Concluding from the result, the combinatorial methods
`except the average linkege within new group method are not useful, because these clusters
`never or rarely agglomerate until last stage.
`Thus tendency appeared commonly for both
`processed objects. Accordingly, these methods are not adequate for analyzing of scientific
`article's relation structure.
`For 140 articles, the clustering result by BRCA is shown in Fig. 2.
`The result classi-
`fied by twelve physical experts is marked by superscripts (D, V, R) at upper right of arti(cid:173)
`cle's number.
`In comparison with human classification by the physicists, similarly con(cid:173)
`formance percentage is calculated and displayed the respective clusters for 140 articles.
`Superscripts as D, V and R mean the symbol of proper clusters in each figure.
`BRCA has
`the property to end in small clusters. Table I shows the summary result by the average
`linkage within new group of hierarchical clustering methods for 140 articles.
`, the combinato(cid:173)
`In order to compare BRCA with ISM (Interpretive Structural Model) 291
`rial analysis that the enhancing factor P was set 0 in (2) was examined.
`The effect of
`direct walk's length are shown in Tables 2 and 3.
`Concerning with Table 2 for 231 arti(cid:173)
`cles maximum value 72.2% is obtained at over k = 4 in case of citation relation.
`In con(cid:173)
`cerning with Table 3 for 140 articles, maximim value 65.9% is obtained at k=1 in case of
`citation.
`From this result, while citational relation spreads widely, it is necessary to con(cid:173)
`sider until the range of directed walk length four in the research field of CAD/CAM, The re(cid:173)
`lation in the field of nuclear physics is closed and accordingly it does not need to consider
`the distance more than length two. While optimal value 72.2% is obtained at greater k=4
`in case of total citation relation by hierarchical clustering method for 231 articles, the optim(cid:173)
`al value is 65.9% at most by the combinatorial method in case of direct citation relation for
`140 articles.
`In consequence, more appropriate method for clustering was required.
`Thus requirement made the present clustering method (BRCA) and the conformance percen(cid:173)
`tage attains 76. 9% by it.
`The exploratory results are summarized in the following way.
`This fact is
`1. The present modeling attains good results in comparison with ISM.
`considered that the original objects are expressed at the location in the information space.
`2.
`In comparison with combinatorial cluster analyses, the present clustering method of
`BRCA attains good conformance.
`From this fact, it is considered that the present method
`is more suitable for proper clustering of relation matrix without distortion.
`It is clarified that there are some research fields with deep citation relation as
`3.
`CAD/CAM and are to be applied simply to shallow citation relation like in the two or three
`bodies problem of nucle physics.
`
`0006
`
`Facebook Ex. 1011
`
`

`

`-332-
`
`A new method of modeling and clustering
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`Fig. I
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`Result clustered by the average linkage within new gtoup for 231 articles in the field of CAD/CAM.
`
`0007
`
`Facebook Ex. 1011
`
`

`

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`

`- 334-
`
`A new method of modeling and clustering
`
`Table 1 Coincident ratio of clustering by the average linkage within new group method, comparing
`with expert physiciocvis result for 140 articles in the field of nuclear physics.
`
`Cluster
`
`Citation Relation
`
`Direct
`
`Total
`
`34/39=87. 2%
`1/39= 2. 6%
`2/39= 5. lo/o
`2/39= 5. 1%
`
`2/44= 4. 5%
`27 /44=61. 4%
`8/44=18. 2%
`5/44=11. 4%
`1/44= 2. 3%
`1/44= 2. 3%
`
`0/57=
`0%
`26/57=45. 6%
`25/57=43. 9%
`1/57:;:: 1. 8%
`5/57-= 8. 8%
`
`8/96= 8. 3%
`44/96=45. 8%
`31/96=32. 3%
`2/96= 2. 1 o/o
`10/96=10. 4%
`1/96= 1. 0%
`
`0/6 =
`0%
`5/6 =83. 3%
`1/6 =16. 7%
`
`28/38=73. 7%
`5/38=13. 2%
`3/38= 7. 9%
`1/38= 2. 6%
`
`1/38= 2. 6%.
`
`DIS
`REAL
`VAR
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`RV
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`REAL
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`
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`REAL
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`
`1
`
`2
`
`3
`
`5. Conclusion
`
`The present cluster analysis was more adequate to make clearly the information space
`of scientific articles rather than combinatorial cluster analyses, and the space has a directed
`structure.
`These were based on two sets of articles in different research fields, where the present
`model with relational graph is more suitable for the cluster analysis of scientific articles
`than ISM.
`
`0009
`
`Face book Ex. 1 0 11
`
`

`

`Table 2
`
`Effect of directed walk's length for 231
`articles citation relation.
`
`Table 3
`
`Effect of directed walk's length for 140
`articles citation relation.
`
`: Lenath of
`k
`directe walk
`
`Citation
`Relation
`ls
`
`: Lenath of
`k
`directe walk
`
`Citation
`Ref at ion
`ls
`
`-335-
`
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`ks8
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`kS12
`k;;;;13
`
`71. lo/o
`63. 2%
`63. 2%
`72. 2%
`72. 2%
`72. 2%
`72. 2%
`72. 2%
`72. 2%
`72. 2%
`72. 2%
`72. 2%
`72. 2%
`
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`
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`65. 9%
`62. lo/o
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`49. 9%
`57. 6%
`57. 6%
`57. 6%
`57. 6%
`57. 6%
`57. 6%
`60. 3%
`
`The citation relation should be considered until k= 1 in the field of nuclear physics, but
`it should be until k =Maximum in the CAD/CAM field.
`Therefore, we must choose ade(cid:173)
`quately the range of the citation relation, depending on the goal.
`The final goal is not
`necessary to coincide completely with manual classification but is expected that the metho(cid:173)
`dology brings us
`the significant
`information, wh