This page contains the R scripts to replicate the results of the paper “Learning to learn in Collective Self-adaptive Systems: Automated Reasoning for System Design Patterns” (under revision at eCAS2020).

The following packages has been used for the analysis:

if (!require("pacman")) install.packages("pacman")
pacman::p_load(pacman, rio, tidyverse, cluster, fpc, ggplot2, reshape2, purrr, dplyr, dendextend, PCAmixdata, klaR, factoextra, bootcluster, kmed, FactoMineR, factoextra, corrplot,ExPosition,ape,circlize, kableExtra, knitr)

Dataset

To visualize the dataset:

kable(dataset) %>%
  kable_styling(full_width = F, font_size = 10, bootstrap_options = c("striped", "hover", "condensed"))
ID Title Application Domain Emergent Behaviour Cooperative (agent level) Behaviour Autonomy Knowledge Access Trigger - first Trigger - update Technique
1 Pervasive Self-Learning with Multi-modal Distributed Sensors CPS No Yes Selfish but collaborative Restricted Autonomy Neighborhood No initial knowledge (random) Periodic Probabilistic
2 Distributed W-Learning: Multi-Policy Optimization in Self-Organizing Systems Traffic No Yes Altruistic locally / Selfish globally Full Autonomy Neighborhood No initial knowledge (random) Not mentioned Reinforcement Learning
3 Self-organized Fault-tolerant Routing in Peer-to-Peer Overlays Network Yes No Selfish Full Autonomy Minimal From peers and other agents Periodic Reinforcement Learning
4 Self-organizing Bandwidth Sharing in Priority-Based Medium Access Network Yes No Selfish Full Autonomy Limited No initial knowledge (random) Action Game Theory
5 Incremental Social Learning Applied to a Decentralized Decision-Making Mechanism: Collective Learning Made Faster Other Yes No Selfish Full Autonomy Minimal From peers and other agents Not mentioned Statistics
6 Simulating Human Single Motor Units Using Self-Organizing Agents Other No Yes Altruistic Full Autonomy Limited No initial knowledge (random) Periodic Evolutionary Process
7 Learning to be Different: Heterogeneity and Efficiency in Distributed Smart Camera Networks CPS Yes No Selfish Full Autonomy Maximal No initial knowledge (random) Periodic Reinforcement Learning
8 Self-Organizational Reciprocal Agents for Conflict Avoidance in Allocation Problems Other No Yes Selfish but collaborative Full Autonomy Limited No initial knowledge (random) Periodic Reinforcement Learning
9 A Mutual Influence Detection Algorithm for Systems with Local Performance Measurement CPS Yes No Selfish Full Autonomy Neighborhood No initial knowledge (random) Periodic Reinforcement Learning
10 Towards Dynamic Epistemic Learning of Actions in Autonomic Multi-agent Systems Other No No Selfish Full Autonomy Maximal No initial knowledge (random) Task/Episode Applied Logic
11 Cooperative Resource Allocation in Open Systems of Systems CPS No No Both versions explored Full Autonomy Tunable Domain knowledge / humans Learning task threshold achieved Supervised Learning
12 Multiagent Reinforcement Social Learning Toward Coordination in Cooperative Multiagent Systems Cooperative Game No No Both versions explored Full Autonomy Neighborhood No initial knowledge (random) Task/Episode Reinforcement Learning
13 Efficient and Robust Emergence of Norms Through Heuristic Collective Learning Cooperative Game No No Altruistic Full Autonomy Neighborhood No initial knowledge (random) Task/Episode Game Theory
14 Reinforcement Learning of Informed Initial Policies for Decentralized Planning CPS No No Selfish Full Autonomy Minimal From peers and other agents Learning task threshold achieved Reinforcement Learning
15 Prediction-Based Multi-Agent Reinforcement Learning in Inherently Non-Stationary Environments CPS Yes No Selfish Full Autonomy Minimal Domain knowledge / humans Periodic Reinforcement Learning
16 A Reinforcement Learning Approach for Interdomain Routing with Link Prices Network Yes No Selfish Full Autonomy Minimal No initial knowledge (random) Action Reinforcement Learning
17 Machine Learning in Disruption-tolerant MANETs Network No Yes Altruistic (collaborative) Full Autonomy Neighborhood No initial knowledge (random) Social interaction Probabilistic
18 Mobilized ad-hoc networks: a reinforcement learning approach Network No Yes Altruistic (collaborative) Full Autonomy Neighborhood No initial knowledge (random) Social interaction Reinforcement Learning
19 Autonomous smart routing for network QoS Network No Yes Altruistic (collaborative) Full Autonomy Neighborhood No initial knowledge (random) Action Reinforcement Learning
20 Decentralized Bayesian Reinforcement Learning for Online Agent Collaboration CPS No Yes Altruistic (collaborative) Full Autonomy Neighborhood No initial knowledge (random) Social interaction Reinforcement Learning
21 Modeling Assistant s Autonomy Constraints As a Means for Improving Autonomous Assistant-Agent Design Market No Yes Selfish Full Autonomy Minimal Not mentioned Action Supervised Learning
22 Adaptivity at Every Layer: A Modular Approach for Evolving Societies of Learning Autonomous Systems CPS No Yes Altruistic (collaborative) Full Autonomy Minimal Not mentioned Social interaction Reinforcement Learning
23 Bayesian Interaction Shaping: Learning to Influence Strategic Interactions in Mixed Robotic Domains CPS No No Altruistic locally / Selfish globally Full Autonomy Limited Domain knowledge / humans Action Probabilistic
24 Resource Abstraction for Reinforcement Learning in Multiagent Congestion Problems Traffic Yes No Selfish Full Autonomy Minimal No initial knowledge (random) Not mentioned Reinforcement Learning
25 Multiagent Reinforcement Learning and Self-organization in a Network of Agents Distributed Task Allocation Problem No Yes Selfish but collaborative Full Autonomy Minimal No initial knowledge (random) Action Reinforcement Learning
26 Batch Reinforcement Learning in a Complex Domain CPS No Yes Selfish but collaborative Full Autonomy Maximal Domain knowledge / humans Learning task threshold achieved Reinforcement Learning
27 Co-evolution of Agent Strategies in N-player Dilemmas Cooperative Game Yes No Selfish Full Autonomy Neighborhood No initial knowledge (random) Learning task threshold achieved Game Theory
28 Self-organisation in an Agent Network via Learning Distributed Task Allocation Problem No Yes Selfish but collaborative Full Autonomy Neighborhood No initial knowledge (random) Action Reinforcement Learning
29 Self-organization for Coordinating Decentralized Reinforcement Learning Distributed Task Allocation Problem Yes No Selfish Full Autonomy Tunable No initial knowledge (random) Action Reinforcement Learning
30 Adjustable Autonomy in Real-world Multi-agent Environments Other No Yes Altruistic Restricted Autonomy Maximal Domain knowledge / humans Task/Episode Reinforcement Learning
31 How Autonomy Oriented Computing (AOC) Tackles a Computationally Hard Optimization Problem Cooperative Game No Yes Altruistic Full Autonomy Maximal Domain knowledge / humans Action Game Theory
32 A Bartering Approach to Improve Multiagent Learning Other No Yes Selfish Full Autonomy Maximal Domain knowledge / humans Action Supervised Learning
33 Learning Sequences of Actions in Collectives of Autonomous Agents CPS Yes No Selfish Full Autonomy Minimal No initial knowledge (random) Action Reinforcement Learning
34 Learning and Decision: Making for Intention Reconciliation Market No Yes Selfish Restricted Autonomy Minimal No initial knowledge (random) Action Reinforcement Learning
35 Continuous Collaboration: A Case Study on the Development of an Adaptive Cyber-physical System CPS No Yes Altruistic (collaborative) Full Autonomy Maximal No initial knowledge (random) Learning task threshold achieved Reinforcement Learning
36 RPLLEARN: Extending an Autonomous Robot Control Language to Perform CPS No No Selfish Full Autonomy Minimal No initial knowledge (random) Task/Episode Statistics
37 Coordination Through Mutual Notification in Cooperative Multiagent Reinforcement Learning CPS No No Altruistic Full Autonomy Limited No initial knowledge (random) Task/Episode Reinforcement Learning
38 On Topic Selection Strategies in Multi-agent Naming Game Cooperative Game Yes No Selfish Full Autonomy Minimal No initial knowledge (random) Action Game Theory
39 Inter-institutional Social Capital for Self-Organising Nested Enterprises CPS Yes Yes Selfish Full Autonomy Minimal No initial knowledge (random) Learning task threshold achieved Supervised Learning
40 Dealing with Unforeseen Situations in the Context of Self-Adaptive Urban Traffic Control: How to Bridge the Gap Traffic No No Altruistic locally / Selfish globally Full Autonomy Minimal No initial knowledge (random) Learning task threshold achieved Reinforcement Learning
41 Decentralised Progressive Signal Systems for Organic Traffic Control Traffic No Yes Altruistic (collaborative) Full Autonomy Neighborhood Not mentioned Learning task threshold achieved Reinforcement Learning
42 Learning in Open Adaptive Networks Distributed Task Allocation Problem Yes No Selfish Full Autonomy Minimal Not mentioned Not mentioned Reinforcement Learning
43 A Machine Learning Approach to Performance Prediction of Total Order Broadcast Protocols Network No No Selfish Full Autonomy Minimal Not mentioned Not mentioned Supervised Learning
44 Self-Adaptive Dissemination of Data in Dynamic Sensor Networks Network Yes No Selfish Full Autonomy Limited Not mentioned Not mentioned Reinforcement Learning
45 Autonomic Multi-policy Optimization in Pervasive Systems: Overview and Evaluation Traffic No Yes Altruistic Restricted Autonomy Neighborhood Not mentioned Periodic Reinforcement Learning
46 Self-Organising Zooms for Decentralised Redundancy Management in Visual Sensor Networks CPS No Yes Altruistic Restricted Autonomy Limited No initial knowledge (random) Periodic Reinforcement Learning
47 Towards Data-centric Control of Sensor Networks through Bayesian Dynamic Linear Modelling CPS Yes No Selfish Full Autonomy Minimal No initial knowledge (random) Periodic Probabilistic
48 Firefly-Inspired Synchronization for Improved Dynamic Pricing in Online Markets Market No Yes Selfish but collaborative Full Autonomy Maximal No initial knowledge (random) Periodic Swarm System
49 Decentralized Approaches for Self-adaptation in Agent Organizations Other No Yes Selfish but collaborative Full Autonomy Neighborhood No initial knowledge (random) Periodic Reinforcement Learning
50 Static Dynamic and Adaptive Heterogeneity in Distributed Smart Camera Networks CPS No Yes Selfish but collaborative Full Autonomy Neighborhood No initial knowledge (random) Task/Episode Swarm System
51 Distributed Cooperation in Wireless Sensor Networks CPS No Yes Selfish but collaborative Full Autonomy Neighborhood Not mentioned Periodic Game Theory and Reinforcement Learning
52 Prosumers as Aggregators in the DEZENT Context of Regenerative Power Production CPS Yes No Selfish Restricted Autonomy Tunable Not mentioned Periodic Reinforcement Learning
53 Goal-Aware Team Affiliation in Collectives of Autonomous Robots CPS Yes Yes Altruistic Full Autonomy Limited No initial knowledge (random) Action Reinforcement Learning
54 Decentralized Collective Learning for Self-Managed Sharing Economies CPS Yes Yes Tunable Full Autonomy Minimal Domain knowledge / humans Action Gradiend Descend
55 Constructivist Approach to State Space Adaptation in Reinforcement Learning Traffic No No Selfish Full Autonomy Minimal Domain knowledge / humans Task/Episode Reinforcement Learning
56 TSLAM: A Trust-Enabled Self-Learning Agent Model for Service Matching in the Cloud Market Market No Yes Selfish Full Autonomy Minimal Domain knowledge / humans Periodic Supervised Learning
57 Autonomous Management of Energy-Harvesting IoT Nodes Using Deep Reinforcement Learning CPS Yes No Selfish Full Autonomy Minimal Domain knowledge / humans Task/Episode Reinforcement Learning
58 Reinforcement Learning for Cooperative Overtaking Traffic Yes Yes Altruistic Full Autonomy Neighborhood Domain knowledge / humans Periodic Reinforcement Learning
59 New quantum-genetic based OLSR protocol (QG-OLSR) for Mobile Ad hoc Network Network No No Altruistic Full Autonomy Maximal From peers and other agents Learning task threshold achieved Genetic Algorithm and Reinforcement Learning

The following packages has been used for the analysis:

if (!require("pacman")) install.packages("pacman")
pacman::p_load(pacman, rio, tidyverse, cluster, fpc, ggplot2, reshape2, purrr, dplyr, dendextend, PCAmixdata, klaR, factoextra, bootcluster, kmed, FactoMineR, factoextra, corrplot,ExPosition,ape,circlize, kableExtra, knitr)

Clustering Analysis

The notion of similarity between papers refersto similarity between their attributes (see dataset). Since the attributes identified by our classification are categorical, we adopt the Gower Distance measure.

gower.dist <- daisy(x, metric = c("gower"))

HAC starts by treating each observation (i.e.,paper) as a separate cluster. Then, it repeatedlyidentifies and merge the two most similar clusters.

aggl.clust.c <- hclust(gower.dist, method = "complete")
plot(aggl.clust.c,cex = 0.7)

There are two methods allowing establishing evaluation criteria for the number ofclusters K: silhouette values and the bootstrap method.

Silhouette Analysis:

ggplot(data = data.frame(t(cstats.table(gower.dist, aggl.clust.c, 10))), 
       aes(x=cluster.number, y=avg.silwidth)) + 
  geom_point(size=1.5)+
  geom_line(size=0.5)+
  scale_x_continuous(breaks = scales::pretty_breaks(n = 10), limits=c(2, 10)) +
  scale_y_continuous(breaks = scales::pretty_breaks(n = 10)) +
  ggtitle("") +
  labs(x = "K", y = "Average silhouette width") +
  theme_minimal(base_size = 15) +
  geom_hline(yintercept=0.18, linetype="dashed", 
                color = "red", size=1)

Bootstrap of Clusters and Visualization:

kchoice<-2
invisible(capture.output(cboot.hclust <- clusterboot(gower.dist,distances=TRUE,clustermethod=hclustCBI, k=kchoice,method="complete",seed="123456789")))
cboot.hclust$bootmean  

## [1] 0.8423149 0.7770231

cboot.hclust$bootbrd 

## [1] 0 2

dendro <- as.dendrogram(aggl.clust.c)
dendro.col <- dendro %>%
 set("branches_k_color", k = 2, value =   c("#2E9FDF","red")) %>% 
  set("branches_lwd", 1) %>%
  set("labels_colors", k = 2, value =   c("#2E9FDF","red")) %>% 
  set("labels_cex", 1)
circlize_dendrogram(dendro.col)


kchoice<-3
invisible(capture.output(cboot.hclust <- clusterboot(gower.dist,distances=TRUE,clustermethod=hclustCBI, k=kchoice,method="complete",seed="123456789")))
cboot.hclust$bootmean  

## [1] 0.8269758 0.8038819 0.4952221

cboot.hclust$bootbrd 

## [1]  1  2 57

dendro <- as.dendrogram(aggl.clust.c)
dendro.col <- dendro %>%
 set("branches_k_color", k = 3, value =   c("#2E9FDF", "red","#E7B800")) %>% 
set("branches_lwd", 1) %>%
set("labels_colors", k = 3, value =   c("#2E9FDF", "red","#E7B800")) %>% 
set("labels_cex", 1)
circlize_dendrogram(dendro.col)


kchoice<-4
invisible(capture.output(cboot.hclust <- clusterboot(gower.dist,distances=TRUE,clustermethod=hclustCBI, k=kchoice,method="complete",seed="123456789")))
cboot.hclust$bootmean  

## [1] 0.8441289 0.8300746 0.5662892 0.4727753

cboot.hclust$bootbrd 

## [1]  1  4 49 64

dendro <- as.dendrogram(aggl.clust.c)
dendro.col <- dendro %>%
  set("branches_k_color", k = 4, value =   c("#2E9FDF","red","#E7B800","darkgreen")) %>% 
  set("branches_lwd", 1) %>%
  set("labels_colors", k = 4, value =   c("#2E9FDF","red","#E7B800","darkgreen")) %>% 
  set("labels_cex", 1)
circlize_dendrogram(dendro.col)


kchoice<-9
invisible(capture.output(cboot.hclust <- clusterboot(gower.dist,distances=TRUE,clustermethod=hclustCBI, k=kchoice,method="complete",seed="123456789")))
cboot.hclust$bootmean  

## [1] 0.6946536 0.5451034 0.5109907 0.6680000 0.7800000 0.6060833 0.4335839
## [8] 0.4879693 0.3661667

cboot.hclust$bootbrd 

## [1] 21 53 64 35 28 46 72 67 86

dendro <- as.dendrogram(aggl.clust.c)
dendro.col <- dendro %>%
  set("branches_lwd", 1) %>%
  set("labels_colors", k = 9, value=c("#2E9FDF","red","#E7B800","darkgreen", "blue","darkorange","black","gray","purple")) %>% 
  set("labels_cex", 1)
circlize_dendrogram(dendro.col)

We visualize how the attributes are represented by the clustering:

colors_to_use <- as.numeric(xOrig$`Autonomy`)
colors_to_use <- colors_to_use[order.dendrogram(dendro)]
labels_colors(dendro) <- colors_to_use
dendro.list<-as.character(xOrig$`Autonomy`)

circlize_dendrogram(dendro)


colors_to_use <- as.numeric(x$`Emergent Behaviour`)
colors_to_use <- colors_to_use[order.dendrogram(dendro)]
labels_colors(dendro) <- colors_to_use
dendro.list<-as.character(x$`Emergent Behaviour`)

circlize_dendrogram(dendro)
par(mar=c(0,25,0,0),xpd=TRUE)
legend(-1.7,1, 
       legend = c("No Emergent Behaviour","Emergent Behaviour" ), 
       col = c(1,2), 
       pch = c(20,20), bty = "n",  pt.cex = 1, cex = 0.7,
       text.col = "black", horiz = FALSE)


colors_to_use <- as.numeric(x$`Cooperative(agent level)`)
colors_to_use <- colors_to_use[order.dendrogram(dendro)]
labels_colors(dendro) <- colors_to_use
dendro.list<-as.character(x$`Cooperative(agent level)`)

circlize_dendrogram(dendro) 
par(mar=c(0,25,0,0),xpd=TRUE)
legend(-1.7,1, 
       legend = c("Non cooperative agent","Cooperative agent"), 
       col = c(1,2), 
       pch = c(20,20), bty = "n",  pt.cex = 1, cex = 0.7, 
       text.col = "black", horiz = FALSE)


colors_to_use <- as.numeric(x$Behaviour)
colors_to_use <- colors_to_use[order.dendrogram(dendro)]
labels_colors(dendro) <- colors_to_use
dendro.list<-as.character(x$Behaviour)

circlize_dendrogram(dendro)
par(mar=c(0,25,0,0),xpd=NA)
legend(-1.7,1, 
       legend = c("Altruistic" , "Altruistic (collaborative)", "Altruistic locally/Selfish globally","Both versions explored","Selfish","Selfish but collaborative","Tunable"), 
       col = c(1,2,3,4,5,6,7), 
       pch = c(20,20,20,20,20,20,20), bty = "n",  pt.cex = 1, cex = 0.7, 
       text.col = "black", horiz = FALSE)


colors_to_use <- as.numeric(x$`Knowledge Access`)
colors_to_use <- colors_to_use[order.dendrogram(dendro)]
labels_colors(dendro) <- colors_to_use
dendro.list<-as.character(x$`Knowledge Access`)

circlize_dendrogram(dendro)
par(mar=c(0,25,0,0),xpd=NA)
legend(-1.7,1, 
       legend = c("Limited","Maximal","Minimal", "Neighborhood", "Tunable"), 
       col = c(1,2,3,4,5,6), 
       pch = c(20,20,20,20,20), bty = "n",  pt.cex = 1, cex = 0.7,
       text.col = "black", horiz = FALSE)


colors_to_use <- as.numeric(x$`Trigger-first`)
colors_to_use <- colors_to_use[order.dendrogram(dendro)]
labels_colors(dendro) <- colors_to_use
dendro.list<-as.character(x$`Trigger-first`)

circlize_dendrogram(dendro)
par(mar=c(0,25,0,0),xpd=NA)
legend(-1.7,1,
       legend = c("Domain knowledge/humans","From peers and other agents","No initial knowledge (random)","Not mentrioned"), 
       col = c(1,2,3,4,5,6), 
       pch = c(20,20,20,20,20), bty = "n",  pt.cex = 1, cex = 0.7,
       text.col = "black", horiz = FALSE)


colors_to_use <- as.numeric(x$`Trigger-update`)
colors_to_use <- colors_to_use[order.dendrogram(dendro)]
labels_colors(dendro) <- colors_to_use
dendro.list<-as.character(x$`Trigger-update`)

circlize_dendrogram(dendro)
par(mar=c(0,25,0,0),xpd=NA)
legend(-1.7,1,
       legend = c("Action","Learning task\nthreshold achieved","Not mentioned","Periodic","Social interaction","Task/Episode"), 
       col = c(1,2,3,4,5,6), 
       pch = c(20,20,20,20,20,20), bty = "n",  pt.cex = 1, cex = 0.7,
       text.col = "black", horiz = FALSE)


colors_to_use <- as.numeric(x$`Technique`)
colors_to_use <- colors_to_use[order.dendrogram(dendro)]
labels_colors(dendro) <- c(8,6,"#E7B800","#E7B800","#E7B800",8,8,8,8,2,8,8,8,8,8,8,8,"darkgreen",7,"darkgreen","#E7B800",8,3,8,8,8,7,8,4,8,8,8,8,8,"purple","#E7B800",8,8,3,3,3,8,8,8,8,8,7,8,8,8,8,5,1,"purple",8,8,3,"#E7B800",7)
dendro.list<-as.character(x$`Technique`)

circlize_dendrogram(dendro)
par(mar=c(0,25,0,0),xpd=NA)
legend(-1.7,1,
       legend =c("Applied Logic","Evolutionary Process","Game Theory","Game Theory and RL","Genetic Algorithm and RL","Gradient Descent","Probabilistic","Reinforcement Learning","Statistics","Supervised Learning","Swarm System"), 
       col = c(1,2,3,4,5,6,7,8,"purple","#E7B800","darkgreen"), 
       pch = c(20,20,20,20,20,20,20,20,20,20,20), bty = "n",  pt.cex = 1, cex = 0.7,
       text.col = "black", horiz = FALSE)


colors_to_use <- as.numeric(x$`Application Domain`)
colors_to_use <- colors_to_use[order.dendrogram(dendro)]
labels_colors(dend) <- colors_to_use
dendro.list<-as.character(x$`Application Domain`)

circlize_dendrogram(dendro)
par(mar=c(0,25,0,0),xpd=NA)
legend(-1.7,1,
       legend = c("Cooperative Game","CPS","Distributed Task\nAllocation Problem","Market","Network","Other","Traffic"),
       col = c(1,2,3,4,5,6,7), 
       pch = c(20,20,20,20,20,20,20), bty = "n",  pt.cex = 1, cex = 0.7,
       text.col = "black", horiz = FALSE)

Multiple Correspondence Analysis

MCA identifies new latent dimensions, which are a combination of the original dimensions and hence can explain information not directly observable. We perform MCA to capture interaction between attributes with the aim of validating and further extending the cluster analysis.

MCA derives for each identified dimension: (i) the relative eigenvalue and, (ii) the identified proportion of variance retained (i.e., the amount of variation accounted for by the corresponding principal dimension).

We report the results obtained with the optimistic Benzécri correction.

# Benzécri + Greenacre adjustment	
mca.res.bg <- epMCA(x, graphs = FALSE, correction = c("b","g"))
eig.val <- get_eigenvalue(res.mca)
kable(eig.val) %>%
  kable_styling(full_width = F, font_size = 10, bootstrap_options = c("striped", "hover", "condensed"))
eigenvalue variance.percent cumulative.variance.percent
Dim.1 0.1016633 32.0966572 32.09666
Dim.2 0.0477599 15.0785324 47.17519
Dim.3 0.0435705 13.7558631 60.93105
Dim.4 0.0302412 9.5476127 70.47867
Dim.5 0.0237786 7.5072644 77.98593
Dim.6 0.0213798 6.7499243 84.73585
Dim.7 0.0131710 4.1583027 88.89416
Dim.8 0.0098605 3.1131107 92.00727
Dim.9 0.0082914 2.6177197 94.62499
Dim.10 0.0073535 2.3216133 96.94660
Dim.11 0.0043133 1.3617619 98.30836
Dim.12 0.0036845 1.1632455 99.47161
Dim.13 0.0009755 0.3079905 99.77960
Dim.14 0.0006243 0.1970954 99.97669
Dim.15 0.0000738 0.0233061 100.00000

To interpret the results of MCA it is necessary to choose the number of dimensions to retain. We decided, according to the average rule introduced by Lorenzo-Seva et. al., to keep all the dimensions whose variance is greater than 9%. Hence, we keep 4 dimensions.

Contributions of the attributes to PC1 (principal component one):

fviz_contrib(res.mca, choice="var", axes = 1, top =15,
             fill = "lightgray", color = "black") +
  theme_minimal() +
  labs(title = "", x = "") +
  theme(text = element_text(size=10), axis.text.x = element_text(angle=70, vjust=1, hjust=1))

Contributions of the attributes to PC2:

fviz_contrib(res.mca, choice="var", axes = 2, top =15,
             fill = "lightgray", color = "black") +
  theme_minimal() +
  labs(title = "", x = "") +
  theme(text = element_text(size=10), axis.text.x = element_text(angle=77, vjust=1, hjust=1))

Contributions of the attributes to PC3:

fviz_contrib(res.mca, choice="var", axes = 3, top =15,
             fill = "lightgray", color = "black") +
  theme_minimal() +
  labs(title = "", x = "") +
  theme(text = element_text(size=10), axis.text.x = element_text(angle=77, vjust=1, hjust=1))

Contributions of the attributes to PC4:

fviz_contrib(res.mca, choice="var", axes = 4, top =15,
             fill = "lightgray", color = "black") +
  theme_minimal() +
  labs(title = "", x = "") +
  theme(text = element_text(size=10), axis.text.x = element_text(angle=77, vjust=1, hjust=1))

We show the biplots:

fviz_mca_ind(res.mca,
             legend.title = "Emergent Behaviour",
             pointsize = 1.2,
             labelsize = 3,
             habillage = x$`Emergent Behaviour`,
             palette = c("#FC4E07","#00AFBB", "#E7B800", "#FC4E07"),
             addEllipses = TRUE, 
             ellipse.level = 0.95,
             axes = c(1, 2)
             ) + labs(title = "", x = "Dim.1", y ="Dim.2")


fviz_mca_ind(res.mca,
             legend.title = "Cooperative (agent level)",
             pointsize = 1.2,
             labelsize = 3,
             habillage = data$`Cooperative (agent level)`, 
             palette = c("#FC4E07","#00AFBB", "#E7B800", "#FC4E07"),
             addEllipses = TRUE,
             ellipse.level = 0.95,
             axes = c(1, 2)
) + labs(title = "", x = "Dim.1", y ="Dim.2")


fviz_mca_ind(res.mca,
             legend.title = "Behaviour",
             pointsize = 1.2,
             labelsize = 3,
             habillage = data$`Behaviour`,
             palette = c("#2fc437","#00AFBB","#E7B800","#FC4E07","#e633ff","#FF8000","#8000FF","#0080FF","#FF0080"),
             addEllipses = TRUE, # Concentration ellipses
             ellipse.level = 0.8,
             axes = c(1,2)
) + labs(title = "", x = "Dim.1", y ="Dim.2")


fviz_mca_ind(res.mca,
             legend.title = "Trigger - first",
             pointsize = 1.2,
             labelsize = 3,
             habillage = data$`Trigger - first`,
             palette = c("#2fc437","#00AFBB","#E7B800","#FC4E07","#e633ff","#FF8000","#8000FF","#0080FF","#FF0080"),
             addEllipses = TRUE, # Concentration ellipses
             ellipse.level = 0.6,
             axes = c(2,3),
) + labs(title = "", x = "Dim.2", y ="Dim.3")


fviz_mca_ind(res.mca,
             legend.title = "Trigger - update",
             pointsize = 1.2,
             labelsize = 3,
             habillage = data$`Trigger - update`, # color by groups
             palette = c("#2fc437","#00AFBB","#E7B800","#FC4E07","#e633ff","#FF8000","#8000FF","#0080FF","#FF0080"),
             addEllipses = TRUE, # Concentration ellipses
             ellipse.level = 0.6,
             axes = c(2,3)
) + labs(title = "", x = "Dim.2", y ="Dim.3")


fviz_mca_ind(res.mca,
             legend.title = "Knowledge Access",
             pointsize = 1.2,
             labelsize = 3,
             habillage = data$`Knowledge Access`, 
             palette = c("#2fc437","#00AFBB","#E7B800","#FC4E07","#e633ff","#FF8000","#8000FF","#0080FF","#FF0080"),
             addEllipses = TRUE, # Concentration ellipses
             ellipse.level = 0.6,
             axes = c(2,3)
) + labs(title = "", x = "Dim.2", y ="Dim.3")


fviz_mca_ind(res.mca,
             legend.title = "Technique",
             pointsize = 1.2,
             labelsize = 3,
             habillage = data$`Technique`,
             addEllipses = TRUE,
             ellipse.level = 0.5,
             axes = c(3,4)
) + labs(title = "", x = "Dim.3", y ="Dim.4")


fviz_mca_ind(res.mca,
             legend.title = "Application Domain",
             pointsize = 1.2,
             labelsize = 3,
             habillage = data$`Application Domain`, # color by groups
             addEllipses = TRUE, # Concentration ellipses
             ellipse.level = 0.6,
             axes = c(3,4)
) + labs(title = "", x = "Dim.3", y ="Dim.4")