Open access peer-reviewed chapter - ONLINE FIRST

Semantic Map: Bringing Together Groups and Discourses

Written By

Theodore Chadjipadelis and Georgia Panagiotidou

Submitted: February 1st, 2022Reviewed: February 21st, 2022Published: April 21st, 2022

DOI: 10.5772/intechopen.103818

IntechOpen
Data ClusteringEdited by Niansheng Tang

From the Edited Volume

Data Clustering [Working Title]

Prof. Niansheng Tang

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Abstract

This chapter presents a multivariate analysis method which is developed in two steps using a combination of Hierarchical cluster analysis (HCA) and Factorial Correspondence Analysis (AFC). To explain and describe the steps of the method, we use an application example on a survey dataset from young students in Thessaloniki trying to investigate their behavioral profiles in terms of political characteristics and how these may be affected about their attendance to a civic education course offered by the Political Science department in the Aristotle University of Thessaloniki. The method is explained step by step on this example serving as a manual of its application to the researcher. HCA assigns subjects into cluster membership variables and in the next stage, these new variables are jointly analyzed with AFC. Correspondence analysis manages to extract the dimensions of the phenomenon in the study, explaining the inner antithesis between the categories but also giving the opportunity to visualize the information in a two-dimensional space, a semantic map, making interpretation more comprehensive. HCA is then applied again to the AFC’s coordinates of the categories constructing profiles of subjects, assigning them to the categories of the variables.

Keywords

  • hierarchical cluster analysis
  • correspondence analysis
  • political analysis
  • multivariate methods
  • data analysis

1. Introduction

This chapter presents a multivariate analysis method, using a combination of Hierarchical Cluster Analysis (HCA) [1] and Factorial Correspondence Analysis (AFC) in two steps [2]. The method provides the advantage of jointly handling multiple variables with many levels. The approach exploits HCA in reducing many variables into fewer ones that represent the individuals within them and then with Correspondence analysis it manages to reduce the information even further and express it upon dimensions.

These dimensions not only organize the information within the data to be explained more thoroughly but also visualizes the inner relationships among categories of the variables. By analyzing the antagonism of the clusters on different sets of dimensions, as we can also have a three-dimensional or more system of axes [3], we can understand further the behavior of the variables and their categories, as well as the associations among them.

Clustering in the final step of the coordinates of the categories on the dimensions we link the initial clusters with the categories, creating a semantic map [4] that can visualize the phenomenon in a Cartesian field or a three-dimensional space [3]. In this chapter, we present the application of the method in a specific case, which works only as an example.

The sample consists of students in Thessaloniki, Greece measuring specifically their political attitudes and their views on democracy, on moral values and the way they are informed in general about politics. In the example that is developed through the chapter we describe the application of the method and the interpretation of the results step by step.

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2. Methodology

Our data analysis is based on Hierarchical Cluster Analysis (HCA) and Factorial Correspondence Analysis (AFC) in two steps [5]. The dataset is analyzed using advanced multivariate methods (Hierarchical Cluster analysis, Factorial correspondence Analysis (Analyse factorielle des correspondences AFC) [2]. Using this mixed-method approach, enables the detection of profiles of similar behavior, the association of each profile to the distinct categories that compose it and the detection of the dimension which describes the dynamics of the phenomenon, enabling the visualization of these dynamics in its final output.

In the first step, HCA assigns subjects into distinct groups according to their response patterns [2]. The main output of HCA is a group or cluster membership variable, which reflects the partitioning of the subjects into groups. Furthermore, for each group, the contribution of each question (variable) to the group formation is investigated [2], to reveal a typology of behavioral patterns. To determine the number of clusters, we use the empirical criterion of the change in the ratio of between-cluster inertia to total inertia, when moving from a partition with r clusters to a partition with r-1 clusters [6]. The metric used is chi-square. Analysis was conducted with the software M.A.D. (Methodes de l’ Analyse des Donnees) [7]. In the second step, the group membership variable, obtained from the first step, is jointly analyzed with the existing variables via Multiple Correspondence Analysis on the so-called Burt table [8]. At this stage, correspondence extracts the dimensions that constitute the overall phenomenon, explaining the inner inertia between all subjects. To determine the number of factors, the empirical criterion of Benzecri was used. According to the empirical criterion of Benzecri [2], two specific sub-criteria should be fulfilled.

COR > 200 and CTR value >1000/(n + 1).

where n = total number of categories.

We proceed by applying again HCA for the coordinates of the categories on the dimensions. Bringing these two analyses steps together, we can construct a semantic map that can visualize the behavioral structure of the variables and the subjects, creating behavioral patterns and abstract discourses [4].

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3. An application example in political analysis

To demonstrate the method of HCA and MCA in two steps, an example was selected to be described in the following sections. This example refers to the analysis of data collected during a survey in Thessaloniki, Greece in the period 2019–2020. The topic of the survey is to collect data about the political characteristics of young students who participated in a civic education course offered by the Department of Political Sciences in the Aristotle University of Thessaloniki. The sample consists of 1618 participants, allocated into four groups:

Group 1: random university students within the campus of the university who were not part of the civic education course.

Group 2: university students who attended the course in-classroom.

Group 3: university students who attended the course through e-learning, due to covid-19 restrictions and measures.

Group 4: high-school students who attended the course.

The tool of the survey was a questionnaire, structured in three sections: 1) demographics, 2) political behavior, 3) information means, views on democracy and moral context.

The objective of the research is to investigate the students’ levels of political knowledge, political interest, preferable way of political mobilization and distinguish the different profiles among the four groups of participants. The variables of the research -associated with each one of the questions- correspond to: a) political interest, c) political knowledge, b) political mobilization, c) their self-positioning on the ideological left–right axis, d) sources of information on politics e) structure of the “political” and f) “moral” self [9, 10].

More specifically, the respondents are asked directly for their level of political interest (ordinal scale) and the way they prefer to mobilize themselves on political issues which may arise (nominal scale). The variable of political knowledge (ordinal scale) is composed through the answers of the respondents on basic questions about politics, many correct answers produce a high score of political knowledge. Next, the respondents are asked to position themselves on a scale of 0 to 10 resembling the left–right ideological axis.

In the last section of the questionnaire, the questions on information sources, democratic and moral self are found. Regarding the preferable source of information, the respondents are asked to choose the two sources they use more often to get informed about politics. Moving on to the variable of “democratic self” [10], the respondent finds a set of 12 pictures, which conceptualize different versions of democracy. They are asked to choose three of them that symbolize in the best way how they understand democracy. Same wise, in the next question they are asked again to choose 3 pictures from a new set of 12 pictures, representing attitudes and views on life and moral values in general. These two sets of pictures construct symbolic representations of democratic institutions and of their personal moral compass (Table 1) [9].

3.1 First step of the analysis: clustering subjects into distinct groups

In this step of the analysis, we select the three variables of the last section, these are the sources of information (E13), the understanding of democracy (E14) and the moral values (E15). For these variables, we have a dataset comprising of 0–1 values, where 0 equals to a not selected picture or source and 1 to a selected one. For each one of these three sets of variables, we apply HCA, aiming to summarize the information. HCA’s output is the dendrogram in Figure 1 visualizing the clusters created in each step.

Figure 1.

Dendrogram (HCA) indicating the clusters for E14 variable.

Initially, we cluster the variables to see patterns of categories. In the example below, we cluster the pictures for democracy, getting 5 clusters (38, 40, 41, 46 and 44). As seen in Figure 2, cluster 38 is created by the selection of pictures 3, 10 and 11, cluster 40 consists of selecting picture 1 etc.

Figure 2.

Classification process of the 12 pictures-variables of E14 (from E141 to E1412).

Processing the same HCA analysis, to cluster the variables for each one of the three selected variables, we get 5 clusters for E14, 5 clusters for E15 and 4 clusters for E13, as shown in the Table 2.

CodeVariableCategories
groupgroup1: random students2: students in-class3: students e-learning4: high school students
lr_cideology1: left2: left-left3: left4: left-right5: right
PMpolitical mobilization (nominal)1: I personally address the authorities2: I participate with others in collective mobilizations3: I take action through Social Media4: I let the authorities to do their job5: I do not know / I do not answer
PIpolitical interest (ordinal)1: very much2: quite3: a little4: not at all
PKpolitical knowledge (ordinal)1: low2: moderate3: high
E13political info source (categorical, binary 0–1)1: TV-Radio2: Online newspapers-Internet3: Social media4: Family-relatives5: Friends6: Newspapers
E14perception of democracy (categorical, binary 0–1)12 pictures which visualize concepts for how they perceive democracy
E15personal values (categorical, binary 0–1)12 pictures which visualize concepts of moral values

Table 1.

Coding and categories of the variables used in the analysis.

Clusters for democracy3840414446
pictures selectedE1431E1411E1461E1451
E14101E1491E1421
E14111E1481
E1471
E1441
E14121
Clusters for values3738394041
pictures selectedE1531E1591E1511E1571E1541
E1581E1521E15121E1551
E1561
clusters for information23242526
pictures selectede1311e1361e1321e1381
e1331e1351
e1341

Table 2.

The clusters for each one of the variables (E4, E15 and E13) and the selected pictures they are linked to.

We proceed by clustering now the subjects. Instead of having 12 binary variables to represent the democratic self, we produce clusters of similar choices and assign each one of the respondents to the clusters he is closer to according to this profile of answers. HCA again produces a dendrogram with the steps of the clustering process (Figure 3).

Figure 3.

Dendrogram (HCA) indicating the clusters of subjects for E14 variable.

In the example shown in Figure 4 we see how the answers on the 12 pictures on democratic self are transformed into one clustering variable (gr_dem), assigning each respondent into one of the clusters of HCA. Following the same method, a separate application of HCA for information sources and for the moral self we get the clustering variables (gr_inf) and (gr_val).

Figure 4.

Transforming the dataset by replacing the binary E141-E1412 with the cluster membership variable gr_dem.

After we have completed a separate HCA, to classify the subjects (respondents) for each one of the selected variables (E14, E15 and E13) we get 8 clusters of respondents for E14 (renamed to gr_dem), 9 clusters for E15 (renamed to gr_val) and 8 clusters for E13 (renamed to gr_inf). Table 3 shows a summary of the clusters of subjects for each one of the three variables we get the following table including the clusters and their relative frequency.

gr_demfreq%gr_valfreq%gr_inffreq%
320112%31874%313611%
32047%31917%31984%
320714%319210%320612%
320914%32009%320815%
32106%320213%321115%
321215%320315%321313%
321314%320412%321516%
321418%320613%321613%
320716%

Table 3.

Cluster membership variables and their categories for E14, E15 and E13.

We investigate further the profile of each cluster for the variable E14. Each cluster is associated with selecting a set of pictures. As shown in Table 4 cluster 3201 consists of the respondents who are more likely to select picture number 12, which corresponds to the symbolic representation for religion (Table 5). Cluster 3204 relates to selecting pictures 4,5,9 and 12 (e-democracy, representative, clientelism and religion). The sets of pictures connected to the clusters, depict the different profiles of the respondents according to the way they comprehend democracy.

E14/gr_dem32013204320732093210321232133214
E141140,45127,1001
E142121,53418,638327,784
E143157,62620,2902
E144141,86582,1471
E145116,43711,927317,5035
E1461154,0449
E147167,2476
E148111,812511,1089
E1491122,653922,5595
E1410130,12710,289634,607
E1411113,397871,9056
E1412193,99697021

Table 4.

Weight of selecting each picture to the creation of the clusters for E14.

Democracy32013204320732093210321232133214
dem_1dem_2dem_3dem_4dem_5dem_6dem_7dem_8
MovementE1411XX
Ancient GreeceE1421XXX
DirectE1431XX
e-DemocracyE1441XX
RepresentativeE1451XXX
RiotE1461X
DeliberationE1471X
VolunteerismE1481XX
ClientelismE1491XX
RebellionE14101XXX
ProtestE14111XX
ReligionE14121XX
%Count11.9%7.4%14.0%13.6%6.0%15.0%14.2%18.1%

Table 5.

Summarizing the content of each cluster and renaming the clusters for E14.

Similarly, for variable E15, we describe the profiles of the cluster of the respondents regarding the pictures they are more likely to select. In Table 6 we see that cluster 3187 is connected to the pictures 1, 2, 4 and 11 which correspond to riot, anonymous, army and protest, a representation of expressivist moral values (Table 7). In contrast, we see cluster 3207 having a completely naturalist moral values as it is connected to pictures 7, 8, 9, 12 (mountain, family, intimacy and concert).

E15/gr_val318731913192320032023203320432063207
E1511188,512
E152120,9268118,98354,775
E153112,058458,0211
E154118,172121,4029
E155179,23274,1092
E156173,3846
E157110,258748,65415,5155
E158118,88215,8182
E159144,77482,15323,8393
E1510174,8128
E1511122,457652,60380,7176
E1512123,37319,8778

Table 6.

Weight of selecting each picture to the creation of the clusters for E15.

ValuesPicture318731913192320032023203320432063207
val_1val_2val_3val_4val_5val_6val_7val_8val_9
ExpressivistRiotE1511X
ExpressivistAnonymousE1521XXX
ChristianChristE1531XX
ArmyArmyE1541XX
NaturalistMoneyE1551XX
Moon explorationAstronautE1561X
SpiritualityMountainE1571XXP
NaturalistFamilyE1581XP
NaturalistIntimacyE1591XXP
SpiritualityMeditationE15101X
ExpressivistProtestE15111XXX
NaturalistConcertE15121XP
%Count4.2%7.2%9.8%8.6%13.4%15.4%12.4%13.5%15.6%

Table 7.

Summarizing the content of each cluster and renaming the clusters for E15.

Once more, we investigate the content of each cluster for the variable E13, regarding sources of information. Cluster 3136 includes those respondents who answer 1 and 3 (Table 8) which translates into preferring to get informed about politics by TV-radio and family (Table 9).

E13/gr_inf31363198320632083211321332153216
e131129,225221,241629,2252
e132197,3186
e133152,575840,4936
e134181,3803
e135138,54626,465978,426
e136134,788236,0722
e1381181,9963

Table 8.

Weight of selecting each source of information to the creation of the clusters for E13.

Info Source31363198320632083211321332153216
inf_1inf_2inf_3inf_4inf_5inf_6inf_7inf_8
TV-Radioe1311XXX
Newspaperse1321X
Familye1331XX
Friendse1341X
Social Mediae1351XXX
internete1361XX
No informatione1381X
%Count11.0%4.5%12.3%15.1%14.6%13.0%15.9%13.5%

Table 9.

Summarizing the content of each cluster and renaming the clusters for E13.

3.2 Second step: joint analysis of the cluster membership variables

In the second step of the analysis, we jointly analyze the initial variables together with the new cluster membership variables gr_dem, gr_var and gr_inf. We repeat the steps as in the early stages of the analysis applying HCA which produced the following clusters for the subjects, as w result 8 clusters of respondents are detected (Table 10).

ClusterFreq%
31555%
31706%
31746%
31778%
318538%
318711%
319217%
31948%

Table 10.

Clustering for the subjects using all the variables together with the new cluster membership variables, produced in the first step.

These clusters relate to the categories of the variables creating a behavioral profile for each one of the clusters of the respondents, in which they have been assigned accordingly. In Table 11 the profiles of the clusters are given in full detail, e.g., cluster 3155 consists of respondents who belong to group 4, are men [sex1], they characterize themselves as center-left [lr_c2], have moderate political knowledge [PK2], they choose to mobilize by personally addressing the authorities, take action through social media and/or let the authorities to do their job [PM1, PM3 and/or PM4],have a little political interest [PI3]. Furthermore, respondents in this cluster belong also in cluster 3136, 3208 and 3216 on how they get informed on politics, they belong to clusters 3207,3209, 3213 and 3214 regarding their views on democracy, and finally they belong in cluster 3192 regarding their set of moral values.

31553170317431773187319431853192
group111,846325,59282,31926,596
group2148,5301
group3125,4921
group410,919814,568734,22955,459
sex176,27629,35314,1511
sex223,63971,79975,205620720,234
lr_c130,83338,756590,10695,594
lr_c293,41483,84510,519
lr_c348,30862,839
lr_c4591985,217
lr_c5227479,06714,2434
PK079,32153,899
PK198,86233,42116,69725,42227,604
PK215,539976,055360526,049
PK318,350950,07719,997
PK9125,4921
PM134,84378,40845,907
PM273,69734,221730,93958,30422,388
PM392,60321,341
PM438,36121,75169,31529,301
PM918,068225,506
PI121,737199,77823,30557,641
PI286,38547,95887,02516,576
PI381,29568,02861,683
PI431,38181344
gr_inf313635,69217,13740,678740,057
gr_inf319895,479
gr_inf320617,961772,51418,0647
gr_inf320812,109713,51272,4843135
gr_inf321160,75916,94335,994
gr_inf321310,405620,232617,819
gr_inf321531,174
gr_inf321668,82668,82625,316
gr_dem320145,4001
gr_dem320436,4704
gr_dem320723,59516,314738,13136,193
gr_dem320954,34860,25445,489
gr_dem321036,148617,7273
gr_dem321248,5952
gr_dem321336,19376,896
gr_dem321414,641261,18554,36658,628
gr_val318792,596
gr_val319138,8079
gr_val3192114,202920,676
gr_val320035,4314
gr_val320222,330182,690836,965
gr_val320325,96861,13712,4995
gr_val320446,96658,266
gr_val320620,11639,9724
gr_val3207527711,5083

Table 11.

Association between the clusters produced in the second step and the categories of the analysis.

In the same way, we continue to examine each one of the clusters of the respondents to understand their behavioral profile, considering the total number of the variables used in our analysis.

In the next step, with the application of correspondence analysis, we extract the dimensions of the analysis and a set of coordinates for each one of the dimensions for each one of the variable categories (Table 12).

categoriesxy
group1−13518
group2415−276
group31192865
group4−179−221
sex1−22−160
sex215112
lr_c1726−466
lr_c278−13
lr_c3−235156
lr_c4−75141
lr_c5−38−308
PK0−20879
PK1−165−27
PK2−94−86
PK3−18−236
PK91192865
PM1−45139
PM2494−432
PM3−121
PM4−186193
PM9−211−41
PI1712−262
PI21139
PI3−20185
PI4−414−17
inf_1−270−24
inf_2−518−167
inf_3381181
inf_4160112
inf_5−21925
inf_6283−206
inf_71519
inf_8−198−70
dem_1−21731
dem_2−269−105
dem_3−44215
dem_4−1186
dem_532−703
dem_6371−316
dem_7−140140
dem_87898
val_1234−661
val_286−257
val_3−39194
val_4−149−285
val_5550−387
val_6−31309
val_7−13744
val_8−160134
val_9−192202

Table 12.

Coordinates for each one of the categories on two main dimensions (x,y).

An extra but final step of HCA is applied this time on the coordinates of the categories classifying them into groups (Figure 5).

Figure 5.

Clustering the variables using their coordinates on the dimension as input.

10 clusters51628772848586899293
6 clusters51919188909088959593
4 clusters98989894949494959593
96969696969693
groupgroup3group2group1group4
Left–Rightfar leftcenter-left/center-rightcenter-leftfar right
Political InterestVeryNot verySomewhatNot at all
Political KnowledgeNo DataNone/LittleAdequateHigh
Political MobilizationCollectivePersonalLet others to do their jobSocial MediaN/A
GenderFemaleMale
Information SourceSocial media, Internet/ NewspapersTV-Radio, InternetTV-Radio, social media/ FriendsFamily, social mediaTV-Radio, FamilyNo information
DemocracyMovement, Direct, Rebellion, ProtestAncient Greece, Representative, Deliberatione-DemocracyMovement, Ancient Greece, Representative, VolunteerismAncient Greece, Direct, Volunteerism, Rebellione-Democracy, Representative, CorruptionReligionRiot, Corruption, Rebellion, Protest
ValuesProtestAnonymous, ProtestSpirituality, meditation/ Mountain, family, intimacy, concertAstronaut, mountain, concertAnonymous, Christ, money, army/ Money intimacyChrist, family, intimacyRiot, anonymous, army, protest

Table 13.

Summarizing the association between the categories and the clusters.

The analysis highlights the existence of 10 distinct discourses of behavior (Table 13):

  1. Clusters 51, 62, 87 which is a later step are unified in one cluster 98. This cluster reflects the profile of group 2 and 3 (university students who undertook the civic education course either in-class either online). They are characterized as far left, with high political interest, collective political mobilization, get informed by social media, internet or the newspapers. They see democracy as direct and think of it as rebellion and protest, while in their moral set of values they choose protest (expressivists).

  2. Clusters 72, 84, 85, 86 which in later classification stage merge into cluster 94, including the random sample of students who were not part of the civic education course. These participants are characterized as center-left/center-right, have a moderate to low political interest, little to none political knowledge, low political mobilization (letting others do their job) or social media, they get informed by tv-radio, social media, friends and family. They view democracy as movement, representative, direct and they see a strong connection to ancient Greece. Their moral values are mainly naturalist, focusing on entertainment, family or spirituality.

  3. In clusters 89, 92 which meet later in cluster 95, we find the younger high school students, who also attended the civic education course. This cluster is characterized as closer to the righter positions of the left–right axis. They demonstrate high political knowledge, they get informed by TV-radio and family and they see democracy as e-democracy, representative and connected to corruption and religion. Their moral setting is a mixture of expressivist and naturalistic values, including a set of nationalist symbolism including army, Christ, and family.

  4. Cluster 93 concentrates respondents of no political interest, or information who understand democracy as rebellion or corruption and are closer to expressivist values such as riot, protest but also army.

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4. Final output: the semantic map

Utilizing the coordinates of the points on the two first axes which were obtained from the correspondence analysis, we construct a system of 2 axes on which we place all these points [3]. The output resembles a simple Cartesian field where x is the first dimension (horizontal), and y is the second dimension (vertical). A third dimension can be brought into the analysis by using a three-dimensional space, visualizing the objects within a cube, or by presenting the different sets of the dimension by two.

The output is a semantic map, where all objects can be seen altogether, and their positioning on the field can be explained in terms of the object’s proximity or opposition on each one of the dimensions.

In our example (Figure 6), we make the following observations:

Figure 6.

The semantic map, visualizing in a Cartesian field (x,y) the categories of all variables positioned according to their coordinates from AFC.

The first axis is created by the opposing objects of: 1) group 1 (random students) and group 4 (high school students), followed by characteristics such as low political interest, getting informed by V-radio or friend and family, center left\center right, naturalistic values, choosing not to be mobilized or act on an individual level if needed and 2) group 2 and group 3 (university students of the civic education course) with high political interest, left, getting informed by newspapers and social media, expressivists choosing collective ways of mobilization.

The second axis depicts the antithesis between group 3 (online students of the civic education course) who are connected to the online information about politics, in contrast to the in-class students of group 2 who are linked to collective ways of mobilization. Additionally, the second axis is described by the antithesis between the set val_1 (Riot, Anonymous, Army, Protest), dem_5 (Riot, Deliberation, Volunteerism, Clientelism, Rebellion, Protest) and the set val_6/val_9 (Mountain, Family/Mountain, Family, Intimacy) and dem_3/dem_4 (Ancient Greece, Representative, Deliberation /e-Democracy). This polarization is explained as the difference between the democratic and moral discourses which were detected in the analysis.

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5. Conclusion

The method presented in this chapter, as applied in the example of a survey among universities and high school in Thessaloniki, follows the application of HCA and MCA (or AFC) in two steps.

The added value of the presented methodological approach lies in its competence to utilize an advanced clustering method that incorporates the dimension reduction function of correspondence analysis. Clustering in multiple stages of the analysis, produces summarized variables that can describe the overall behavior or profile of the subjects. Then these new cluster membership variables can be associated with the categories of the variables used in the clustering analysis, therefore we can associate each cluster not only with its subjects but with the categories as well. In the second step, the joint analysis of the cluster membership variables together with the rest of the variables of the analysis, produces a comprehensive clustering of all items together, associating them again with the categories of the variables. This procedure allows the researcher to have a full and comprehensive overview of the profiles of each cluster.

Moreover, correspondence analysis brings forward the inner competition of the phenomenon, extracting multiple dimensions that explain the dynamics within it. The coordinates of each object give a better understanding of the distances between them, and when analyzed again with HCA we get the final fully described clusters. The coordinates can visualize the phenomenon in a simple two-dimensional space or even of more dimensions, where the observer can comprehend in more detail the revealed inner relationships or oppositions among the subjects and the objects of the analysis.

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Written By

Theodore Chadjipadelis and Georgia Panagiotidou

Submitted: February 1st, 2022Reviewed: February 21st, 2022Published: April 21st, 2022