Towards Enhancing Historical Analogy: Clustering
Users Having Different Aspects of Events
Ryohei Ikejiri1 , Ryo Yoshikawa2 , and Yasunobu Sumikawa3
1

2

Interfaculty Initiative in Information Studies, The University of Tokyo, Japan
Department of Information and Media Studies, Nagoya Bunri University, Japan
3
University Education Center, Tokyo Metropolitan University, Japanikejiri@iii.u-tokyo.ac.jp, yoshikawa.ryo@nagoya-bunri.ac.jp,
sumikawa-yasunobu@tmu.ac.jp

Abstract. Studying history can provide numerous benefits for finding meaningful connections or analogies over time. Several researchers have studied how to
support promoting historical analogy by computer supported learning; however,supporting group discussions to promote the analogy still remains unexplored. In
this paper, we propose a novel clustering algorithm to form users who have different aspects of the same past event in order to ease exchange ideas of what aspects
they focus to analyze the event. We implemented our algorithms and evaluatedthem in terms of getting accuracies of forming users having different aspects.
Experimental results proved that only our algorithm creates suitable groups.
Keywords: Clustering, analogy, collaborative learning, history education

1

Introduction

Studying and analyzing history-related data can provide numerous benefits including
improved comprehension of the past and support for finding meaningful connections or
analogies over time. Indeed, a researcher claims that history provides not only information on the past but also alternative solutions to similar modern issues [4]. One of thecommon goals of teaching and spreading the knowledge of history is to allow studying
how people in the past tried to solve issues and problems, and then apply the acquired
knowledge for proposing creative solutions to present issues [19]. Especially, teachingguidelines for high school education published by the Japanese government considers
fostering the ability to apply historical knowledge to modern issues to be the advanced
goal [6]. To support the modern history learning, researchers have developed effective
learning methods [2, 16], algorithms mining past events similar to a given present event[25], and an interactive system that is useful in class [15].
For promoting historical analogy, finding similar past and present events plays a
key role. However, how each person feels a similarity between past and present eventsis up to the person [12]. Furthermore, Fischer found that historical analogy often causes
the misuse of analogy; in other words, we should do careful discussions in the case ofusing historical analogy [8]. According to [16], group learning in history with their discussions is effective to check the validity of each historical analogy. This study founds

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a potential of the group learning; however, there is no algorithmic method to creategroups consisted of persons.
Contributions. In this paper, we propose a novel clustering algorithm to promotehistorical analogy through group discussions. Our algorithm has two objectives to creategroups: 1) finding two users, we call them a pair, who focus on the same aspects ofan event and 2) aggregating two pairs, we call the aggregated two pairs a group, thathave different aspects in the same event. Through these two steps, users can confirm
correctness of their ideas within own pairs and can exchange them with members in theother pair. Compared to past works of clustering, the key contribution of this algorithm
is to combine not similar data into a group as performed in the second step. Traditional
clustering algorithms basically make groups by similar data such as finding similar
documents to organize them [1], pixels to identify any parts of an image like face andlandscape [9].
Example. We present examples of how to use our algorithm in a real situation.
Recently, history teachers working in Japanese high school are required to have collaborative learning in class. If they can make good groups, students can have several
positive effects, for example, from their discussions about connectivity between pastand present events like Industrial Revolution and IT Revolution, they make their own
knowledge deeper by explaining their ideas, know what other persons have ideas forthe same learned things, find common things between the two events, think analogy
between past and present, and so on. However, making groups for stimulating goodcollaborative learning is challenging; it is required to predict how well every student
can get good outcomes. Our algorithm is useful to perform combining students who
have same and different ideas about same things.
The contributions of this study are summarized as follows:
1. We present a novel clustering algorithm for creating a new environment for modern
learning history.
2. Our clustering algorithm makes groups by combining not only similar users but
also not similar pairs for promoting historical analogy through group discussions.
3. We evaluate that our algorithm creates groups composed of different aspects for thesame event.
The remainder of this paper is organized as follows: Section 2 provides definitions
we tackle in this paper. Section 3 summaries several related works. Section 4 explains
our data collections. Section 5 describes how to create clusters. Section 6 shows experimental results, and Section 7 contains our conclusions.

2

Problem Definitions

Assumption. We assume that every user selects several event categories for a same
event. Each user can select the one or more categories by what he/she focuses on analyzing aspects of the event. In this paper, we regard the selected event categories asaspects of the event and use them to create feature vectors as described in Section 5.2.
Input & Output. Let C be a set of event categories, C 0 be a power set of C. Given
selected event categories by users C 00 , our algorithm outputs clusters of users Cu. EventClustering for Promoting Historical Analogy

3categories are usually predicted from given feature vectors. However, we treat them tocreate clusters; we first define feature vectors from the given event categories (C 00 ) andmake groups from the vectors.

3

Related Works

3.1

History Education

Drie and Boxtel reviewed previous studies on historical reasoning [5] and found six
components of historical reasoning: asking historical questions, using sources, contextualization, argumentation, using substantive concepts, and using meta-concepts. However, previous studies did not take into account the students’ ability to use historicalcausations as a means of solving present and future problems.
Mansilla examined in depth how students apply history to current problems successfully [2]. She used the Rwandan Genocide of 1994 as an example of a modern social
problem and the Holocaust as a similar event in the past. As a result of her research,
students were able to successfully use history to build an informed comparison basebetween both cases of genocide, recognize historical differences between them, appropriately apply historical modes of thinking to examine the genocide in Rwanda, andgenerate new questions and hypotheses about the genocide. However, Mansilla did notinvestigate what themes could enable other historical causations to connect with othermodern problems.
Lee insists that an usable historical framework can make connections between
events in the past and potentially between events in the past and present [19]. This
framework must be an overview of long-term patterns of change, and be an open structure, capable of being modified, tested, improved, and even abandoned. This would
enable students to assimilate new history to the existing framework. In addition, its subject should be human history, not some privileged sub-set of it. This is the underlying
concept of a theoretical framework for using historical causations as a means of solving present and future problems. However, Lee did not explain how to create concrete
themes for the usable historical framework and learning environment.
Ikejiri designed a competitive card game for high school students studying world
history, where players can construct causal relations in the modern age by using historical causal relations [13]. This educational material includes a staged learning method
for identifying causal relationships within modern societal problems by using references to historical causal relations. The effectiveness of this game was tested, and theresults proved that this educational tool is effective in improving both the ability to associate past and current events with similar characteristics and to analyze causal relations
in modern problems by referencing historical problems. Further, Ikejiri et al. designed
another competitive card game that high school students can use to apply learning fromthe policies created in world history to create new policies that would revitalize Japan’s
economy [16]. The effectiveness of this game was tested, and it revealed that the number of policies proposed to invigorate Japan’s economy increased after the high school
students’ use of this card game. These two studies provide effective methods for highschool students to use history to analyze causal relations in modern problems by ref-4

R.Ikejiri et.al.

erencing historical problems and to cultivate alternative solutions to confront contemporary social problems. However, the theme that can connect historical contexts withmodern society is set by a researcher each time manually. Thus, these learning methods
are not automated according to modern context.
3.2

Clustering

Clustering is an important and fundamental technique in NLP, ML, and other computerscience related research fields. Indeed, there are lots of survey papers such as comparing
algorithms in theory and/or practical views [7, 27, 26] and domain-specific comparisons
like text clustering [1], image processing [9]. We summarize the closest algorithms with
their categories in this paper. More detailed categorizations are presented in the above
survey papers.
Partitioning-based algorithm. We fist summarize one of the most basic and popular algorithms in many research fields. The intuitive idea of this kind algorithm is todivide data into groups satisfying 1) each group must contain at least one object, and(2) each object must belong to exactly one group. One of the most famous algorithms ofis K-means [20] that updates the centers of clusters by iteratively computing averagesof all points and coordinates representing the arithmetic mean. This process continues
until some criteria are satisfied. In addition to K-means, PAM [18], CLARA [17], and
CLARANS [21] are also famous and used widely.
Hierarchy-based algorithm. For many data, we can naturally define hierarchicalrelationship among data and can represent them as a dendrogram whose leaves represent the data. To construct the hierarchical clusters, there are two kinds of algorithms:
agglomerative (bottom-up) or divisive (top-down) ones. The former algorithm createsclusters for each data and recursively merges them. The latter one starts with the wholedataset and recursively dived them into sub-clusters. These processes are basically performed until some criteria are satisfied, such as k clusters can be created. As for thehierarchy-based algorithms, BIRCH [29], CURE [10], and ROCK [11] are proposed.
Distribution-based algorithm. This kind of algorithms assumes that each datain the same cluster is generated from the same distribution. Gaussian mixture model(GMM) [23] is one of the most popular algorithms of this kind category. GMM considers that every data is generated from several Gaussian distributions. DBCLASD [28] isanother popular algorithm of the distribution-based algorithm. This is a dynamic incremental algorithm considering nearest neighborhood.
Graph-based algorithm. Once we regard each data is a node, we can constructa graph by representing an edge whose weight represents a score of similarity between two data. Spectral clustering [24] is a typical algorithm performing clustering
on a graph.
Our algorithm is designed as 2 steps of partitioning-based approach; however, we
compare our algorithm with the 4 kinds of algorithms in Sec. 6. This is because it ispossible to regard the algorithm as a hierarchy- or distribution-based ones as we perform
grouping twice and generate the groups from different distributions at each step. As agraph-based algorithm is another view of clustering, we use spectral clustering as abaseline. In Sec. 6, we describe that no baselines can be fit to the purpose of this study.

Clustering for Promoting Historical Analogy

5

Table 1. Example events. The abbreviated names of categories are used: Reign (Rg), Diplomacy(Dp), War (Wr), Production (Pr), Commerce (Cr), Study (St), Religion (Rl), Literature
and Thought (LT), Technology (Tc), Popular Movement (PM), Community (Cn), Disparity(Ds) and Environment (En)
Event
Categories
Agnes Chan named UNICEF Regional Ambassador for East Asia and
Dp, Cn and TL
Pacific Region.
The World Strikes a Deal on Climate Change.
En
Paris attacks.
Dp, Rg and PM
ISIS Terrorists Strike on Three Continents.
Dp, Rl, Wr and PM
Same-Sex Marriage Debate.
TL and Cn
Ebola outbreak.
En, St and Tc
The Scottish independence referendum.
Rg, PM and Cn

4

Data Collection

4.1

Event Classes

In this paper, we use 13 categories: Reign (Rg), Diplomacy (Dp), War (Wr), Production(Pr), Commerce (Cr), Study (St), Religion (Rl), Literature and Thought (LT),Technology (Tc), Popular Movement (PM), Community (Cn), Disparity (Ds) and
Environment (En). They were described in [14, 15] as a proposal of an event category
list to define curriculum of teaching history with connecting past and present. These
categories are based on definitions of Encyclopedia of Historiography [22]. We show
example events for the 13 categories in Tab. 1.
4.2

Present Event

We assume that every user reads news papers or any other kinds of articles like Wikipedia
describing present social issues. In general, an event can be classified into several
classes. For example, if we read the Wikipedia article1 to know what the 2014 West
Africa Ebola outbreak caused in our life, we can see that it killed many both humanand nonhuman (environment event), we developed a vaccine (technology event), someresearchers report the details and their statistics (study event), and so on.
Similar to Tab. 1, users reading the contents of an article of present event selectmore than one category for each event by what they want to focus on.

5

Methodology

5.1

Overview

As our purpose is to stimulate users exchanging their ideas and discussing them, we
design the algorithm with the following requirements.
1

https://en.wikipedia.org/wiki/West_African_Ebola_virus_epidemic

6

R.Ikejiri et.al.
Group1

SubG1
SubG2

Creating Sim.
Sub-groups

Creating Diff.
GroupsGroup2

SubG3
SubG4

Fig. 1. Overview of our algorithm.

1. Users in each group have different aspects for the same event.
2. There are at least two users who have the same aspect in a group.
The first requirement is the key idea of our algorithm. As described in Sec. 1, grouping
users who have different ideas is an effective way to stimulate their discussions. The
last one is helpful to discuss in case that one user misses some important ideas.
Fig. 1 shows an overview of our algorithm. Our algorithm first takes information
about what aspects each user focus on for an event. Then, to satisfy the second requirement, it forms two users according to their selected event categories. We call the twousers a pair. Last, our algorithm combines two pairs for the first requirement.
We describe each step in the remainder of this section.
5.2

Feature Vector Creation

We first take event categories selected for an event by users. We then convert the categories to a feature vector whose elements are represented by 0 or 1. Formally, we createa feature vector for ith user as follows:
fik = δ(ck , C 0 ), ck ∈ C, 1 ≤ k ≤| C |(1)

where C is a set of all event categories, C 0 is a set of event categories selected by a user,
and the function δ returns 1 if the first argument is included in the second argument;
otherwise, it returns 0. This equation defines the kth element of the feature vector.
5.3

Combining Similar Two Data

After converting the categories into feature vectors, we create pairs of users by theirsimilarities. We measure the similarity by counting how many common categories areClustering for Promoting Historical Analogy

7

selected; the more the number of common categories uses select, the more they are
similar to each other.
The formal definition of measuring pair similarity is given as follows:
PairSim(fi , f j ) =|C|
X

And(fik , f jk )(2)kwhere fi and f j represent feature vectors for ith and jth users and the function And
applies the AND logical operator to the two arguments. As described in the previous
section, each element is a binary; therefore, sum of the results of And represents how
many common categories are selected by two users.
We then solve the following maximum problem.
max PairSim(P)\s.t.
Pi = ∅|Pi | ≥ 2
where P is a set of pairs, and Pi ∈ P is a set of users.
Algorithm 1 shows an algorithm solving the above minimum problem. This problem
is essentially Knapsack problem; we have several knapsacks, and then determine the
combinations of two feature vectors so that each knapsack can include at most two
users and the total variance of the pairs is as large as possible. It is well known that theits optimization problem is NP-hard; there is no known polynomial algorithm providing
a solution. To solve this problem, we traverse a tree representing candidates of pairs andthen determine the best pairs by calculating scores of all candidates.
Algorithm 1 Algorithm of combining two similar data
Input: A set of feature vectors F
Output: A set of pair P
1: Function CreatePairs(F)2: P = ∅3: WorkList = F
4: while |WorkList| > 0 do
5:(s1, s2) = FindBestPair(WorkList)
6:
P.add((s1, s2))
7:
WorkList.remove(s1)8:WorkList.remove(s2)9: end while
10: return P

5.4

Creating Groups

After creating the pairs, we combine two pairs by connecting two pairs that focus on
different aspects of an event. In other words, we combine two pairs whose common

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R.Ikejiri et.al.

Algorithm 2 Algorithm of finding the best pair of given list
Input: A set of feature vectors WorkList
Output: A pair of two users BestPair
1: Function FindBestPair(WorkList)
2: val = 0
3: BestPair = None
4: for i = 0; i < WorkList.size(); i + + do
5:
s1 = WorkList[i]6:
for j = i + 1; j < WorkList.size(); j + + do
7:
s2 = WorkList[ j]8:sval = PairSim(s1, s2)
9:if val < sval then10:
val = sval
11:
BestPair = (s1, s2)
12:
end if13:
end for
14: end for
15: return BestPair

event categories is as less as possible. As we consider pair-level selected event categories, we first define a feature vector for a pair. Formally, we define a feature vector
for a pair ( fi , f j ) as follows:p( fi , f j )k = fik + f jk , 1 ≤ k ≤ |C|(3)

Then, We define the scores of similarity between pairs as follows:
GroupSim(pi , p j ) =|C|Xpik ∗ p jk

(4)kwhere pi and p j represent feature vectors for ith and jth pairs.
We then solve the following minimum problem.
min GroupSim(G)\s.t.
Gi = ∅|Gi | ≥ 2
where G is a set of groups, and Gi ∈ G is a set of pairs.
Algorithm 3 shows an algorithm solving the above maximum problem. Similar to
Algorithm 1, this algorithm solves Knapsack problem. We traverse a tree representing
candidates of groups to compare scores of all candidates.

6

Experimental Evaluation

6.1

Setup

Data collection. We collect practical data that are event categories selected by 40 thirdyear high school students in Japanese public schools who learn world history for a realClustering for Promoting Historical Analogy

9

Algorithm 3 Algorithm of creating groups by combining two pairs.
Input: A set of feature vectors for pair FP
Output: A set of group G
1: Function CreateGroups(FP)2: G = ∅3: WorkList = FP
4: while |WorkList| > 0 do
5:(p1, p2) = FindBestGroup(WorkList)
6:
G.add((p1, p2))
7:
WorkList.remove(p1)8:WorkList.remove(p2)9: end while
10: return G

Algorithm 4 Algorithm of finding the best groups of given list.
Input: A set of feature vectors WorkList
Output: A group of two pairs BestGroup
1: Function FindBestGroup(WorkList)
2: val = 0
3: BestGroup = None
4: for i = 0; i < WorkList.size(); i + + do
5:
p1 = WorkList[i]6:
for j = i + 1; j < WorkList.size(); j + + do
7:
p2 = WorkList[ j]8:sval = GroupSim(p1, p2)
9:if val < sval then10:
val = sval
11:
BestGroup = (p1, p2)
12:
end if13:
end for
14: end for
15: return BestGroup
Table 2. Statistics of data collection
Number of users
Number of present events

40
1

present event. Japanese labor problem is set as the present event in this case. We show
the statistics we used in this paper in Tab. 2.
Baselines. We compare our algorithm with the following baselines.
– k-means: this is one of the most popular partitioning-based algorithms. This algorithm creates k clusters by assigning a cluster label for each point if it is closer tothe cluster’s centroid than any other centroid.

10

R.Ikejiri et.al.

– Birch: this is a hierarchy-based algorithm. Our algorithm can be seen as an agglomerative hierarchy-based one as it performs creating groups twice; therefore,
we compare our algorithm with this one.
– GMM: this algorithm is also widely used to create clusters as a distribution-based
approach.
– Spectral: this algorithm is a graph-based approach, and is a commonly used if thestructure of the individual clusters is highly non-convex.
Parameters. For our purpose, we assume that there are at least 2 users having thesame aspects and 2 pairs having different aspects in each group. Therefore, we combine
4 users as a group. For this, we set k (number of clusters) as a result of dividing thenumber of uses by 4 in all algorithms.
Measurements. We evaluate all algorithms with three measurements as follows:– Size of clusters: This measurement means that how many users are grouped foreach cluster.
– MinDist: We measure the minimum Euclidean distance for each cluster.
– Similarity of Inner-cluster: We average all Euclidean distances for all combinations of feature vectors of a cluster.
– User similarity: This means that how similar two users in the same pair in average.
We measure this score by Eq. (2).
– Pair similarity: This is an average Euclidean distance between two pairs in a group.
Eq. (4) is used to measure this similarity.
– Quality of clustering: Calinski and Harabaz (CH) score [3] is one of the widely
popular measuring qualities of clusters. This measurement is defined as follows:
CH(k) =(n − k) B(k)×(k − 1) W(k)where B(k) and W(k) are sums of squares for the k clusters of inner- and inter-clusters,
respectively. n is a number of clustered data. Intuitively, if all data in a cluster are close
to each other, and data between different clusters are not close, we can say that thequality of the clusters is high. Thus, the higher the score is, the better quality of thecluster is. Even though the purpose of our algorithm includes aggregating not similarpairs, we measure the qualities of clusters to take more in-depth discussions.
6.2

Discussions of Results

At the beginning, we show how many users are grouped in Tab. 3. Looking at the firstrows (Size) of all algorithms, kmeans, Birch, and GMM algorithms fail to include morethan 2 users in a few clusters (C7 in GMM, C9 for Birch, and C10 for all) whereas
our algorithm included 4 users in all clusters. Spectral outputs clusters having at least 2
users for each cluster; however, all users in 4 clusters (C2, C4, C5, and C6) selected thecompletely the same event categories. As our purpose is to promote group discussions
and to combine users having different ideas, this result does not fit to the purpose.

Clustering for Promoting Historical Analogy

11

Therefore, we can conclude that our algorithm is the best for the purpose of this study.
In other words, if we create groups of users to promote historical analogy through their
discussions, our algorithm is the best way compared with the 4 baselines.
Next, we analyze the qualities of all clusters. We first show minimum distances ineach cluster created by all algorithms in Tab. 3. 4 baselines created 5 or 6 pairs whose
users input completely same categories whereas our algorithm did 7 pairs. In contrast,looking at inner-cluster (sum of distances of all combinations in each cluster), there arelarge clusters (C3 for kmeans and spectral, C7 for Birch, and C1 and C2 for GMM)
in baselines whereas our algorithm created almost same sizes for 8 clusters (from C1
to C8). Indeed, out algorithm is the smallest for scores of standard deviation for innercluster. We can find that our algorithm fails to combine different 2 pairs as a group for
2 clusters (C9 and C10). To increase the diversity of aspects, we will take variations of
selected categories to group users as a future work.
We have checked qualities of each cluster in the above discussions. Next, we analyze
the qualities of whole clusters in Tab. 4. First, we can see that our algorithm naturallyachieved the lowest CH score as our algorithm combines not similar pairs at the second
phase. This result indicates that our algorithm generates clusters whose sizes are relatively large. Indeed, in our algorithm, the average of minimum distances of inner-cluster(2nd column) is the smallest whereas the average total distances between data in eachcluster is high following to Birch.
Figs. 2, 3, 4, 5, and 6 show how each algorithm assigns a cluster label to all user. As
dimensional sizes of the feature vectors are 13, we decomposed them into 2-dimensionalby singular-value decomposition (SVD). We can see that our algorithm tends to assign
the same labels to close 2 users.

Proposed Spectral GMM

Birch

kmeansTable 3. Sizes, minimum distances in a cluster, and total distances between data in a cluster foreach cluster. Each cluster is labeled by a unique name from C1 to C10. ”-” means that there is novalid data to measure
C1
C2
C3
C4
C5
C6
C7
C8
C9 C10 Ave. Std. Dev.
Size
2
11
8
4
3
2
2
2
5
1
4
3.033
MinDist 1.732 0.0
0.0 1.414 1.414 0.0
1.0 1.732 0.0 0.0 0.729 0.753
6.878 10.554
Inner-cluster 1.732 0.0 35.113 11.295 5.382 0.0
1.0 1.732 5.656 Size
3
7
2
2
2
4
16
2
1
1
4
4.335
MinDist 1.414 0.0 1.732 1.732 1.732 0.0
0.0 1.414 0.0 0.0 0.802 0.809
Inner-cluster 4.878 21.999 1.732 1.732 1.732 7.292 68.709 1.414 0.0 0.0 10.948 20.233
Size
12
8
3
2
4
2
1
5
2
1
4
3.346
MinDist0.0
0.0
0.0 1.414 1.414 1.414 0.0
0.0 1.732 0.0 0.597 0.736
9.915 11.280
Inner-cluster 19.052 35.431 2.828 1.414 11.799 1.414
5.656 1.732 Size
3
11
6
4
3
2
3
2
3
3
4
2.569
MinDist 1.414 0.0 1.414 0.0
0.0
0.0
0.0
1.0 1.732 1.732 0.729 0.753
Inner-cluster 4.878 0.0 30.381 0.0
0.0
0.0
2.0
1.0 5.464 5.464 4.918 8.772
Size
4
4
4
4
4
4
4
4
4
4
4
0.0
MinDist0.0
0.0
0.0
0.0 1.414 1.732 0.0 1.732 0.0 0.0 0.487 0.749
Inner-cluster 11.948 11.922 9.797 11.922 11.032 13.512 11.103 12.385 0.0 0.0 9.362 4.769

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R.Ikejiri et.al.
Table 4. Results of all clusters.
Algorithm
k-means
Birch
GMM
Spectral
Proposed

Quality
9.834
10.022
9.018
9.714
1.740

Ave. MinDist
0.729
0.802
0.597
0.729
0.487

Inner-cluster
6.191
10.948
7.932
4.918
9.362

1.5

1.0

0.5

0.0

-0.5
0.0

0.5

1.0

1.5

2.0

Fig. 2. Results of k-means.

1.5

1.0

0.5

0.0

-0.5
0.0

0.5

1.0

1.5

2.0

Fig. 3. Results of Birch.

Finally, we measure how well our algorithm creates groups by analyzing similaritiesof two users are in each pair and differences of two pairs are in each group, and show
them in Tab. 5. We can see that all pairs tend to have similar interesting in aspects.
In contrast, almost of distances between pairs are relatively longer than ones between
pairs. Therefore, we can conclude that our algorithm successfully created groups.

Clustering for Promoting Historical Analogy

13

1.5

1.0

0.5

0.0

-0.5
0.0

0.5

1.0

2.0

1.5

Fig. 4. Results of GMM.

1.5

1.0

0.5

0.0

-0.5
0.0

0.5

1.0

1.5

2.0

Fig. 5. Results of spectral.

1.5

1.0

0.5

0.0

-0.5
0.0

0.5

1.0

1.5

2.0

Fig. 6. Results of our algorithm.

7

Conclusions

Studying history provides numerous benefits including support for finding meaningful connections over time. In this paper, we introduce a novel clustering technique for14

R.Ikejiri et.al.
Table 5. User and pair similarities of our algorithm.
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10Dist(p1)
0.0 0.0 0.0 0.0 1.414 1.732 0.0 1.732 0.0 0.0
Dist(p2)
1.0 1.732 0.0 1.732 2.236 2.0 1.732 2.236 0.0 0.0
Dist(p1, p2) 2.692 2.397 2.449 2.397 1.322 2.061 2.179 1.581 0.0 0.0

creating new collaborative learning platform specialized for history. Our clustering algorithm has two phases: combining two users that have similar interesting in an eventand combining two pairs that have different interesting in the event.
In the future, we plan to analyze 1) how well users can discuss with their own groupmembers. In addition, 2) we will propose more sophisticated grouping algorithm. As weanalyzed in our experimentations, our algorithm combines 4 users who have completely
same aspects; it might fall into local optima. Finally, 3) we will analyze robustnessof our algorithm. In this paper, we used real data generated by Japanese high school
students; however, we will check results in different datasets.

Acknowledgments
This work was supported by JSPS KAKENHI Grant Number 16K16314.

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