Clustering

library(ggplot2)

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library(cluster)
library(tidyverse)    # Pour la manipulation des données 

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library(formattable)  # Pour la visualisation du tableau coloré

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library(factoextra)   # Pour la fonction fviz_cluster

## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

library(cluster)
library(formattable)

Context: Piranhas (Serrasalmus sp.) is known to exhibit a variety of behaviors. Often associated with aggressive behavior, they can also show fear or flight responses. Behavioural traits were measured in 150 individuals to identify personality traits/syndromes.

Aim:

1. Clustering on individuals to separate them into groups to identify personality traits

2. Determine how many personality traits can be identified

fish_behaviour <- read_csv2("fish_behaviour.csv")

## ℹ Using "','" as decimal and "'.'" as grouping mark. Use `read_delim()` for more control.

## Rows: 150 Columns: 7
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ";"
## dbl (7): Fish_ID, Average_activity, Hiding_time, Social_interactions, Observ...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
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View(fish_behaviour)

summary(fish_behaviour)

##     Fish_ID       Average_activity  Hiding_time      Social_interactions
##  Min.   :  1.00   Min.   : 1.355   Min.   :-0.4965   Min.   :-0.03569   
##  1st Qu.: 38.25   1st Qu.: 3.993   1st Qu.: 1.5204   1st Qu.: 1.73644   
##  Median : 75.50   Median : 5.708   Median : 2.1575   Median : 3.73136   
##  Mean   : 75.50   Mean   : 5.619   Mean   : 3.3049   Mean   : 4.24929   
##  3rd Qu.:112.75   3rd Qu.: 7.353   3rd Qu.: 4.3177   3rd Qu.: 5.94535   
##  Max.   :150.00   Max.   :10.287   Max.   : 9.5205   Max.   :11.22353   
##  Observed_attacks  Exploration      Stimuli_reaction
##  Min.   :-0.509   Min.   :0.07505   Min.   : 2.698  
##  1st Qu.: 1.075   1st Qu.:2.57534   1st Qu.: 4.522  
##  Median : 2.045   Median :4.20172   Median : 5.934  
##  Mean   : 3.351   Mean   :4.50436   Mean   : 6.191  
##  3rd Qu.: 4.616   3rd Qu.:6.63353   3rd Qu.: 7.563  
##  Max.   :11.702   Max.   :9.80938   Max.   :12.229

fish_behaviour <-  transform(fish_behaviour, Fish_ID=factor(Fish_ID))

Standardize data

fish_num <- fish_behaviour[,c(2:7)]

# scale = TRUE réalise le centrage (moyenne = 0) et la réduction (écart-type = 1)
fish_std <- scale(fish_num)

Optimal number of clusters determination: WSS or another method

fviz_nbclust(fish_std, # Méthode du coude (Elbow method)
             kmeans, 
             method = "wss") +  # WCSS - Within-Cluster Sum of Squares
  labs(subtitle = "Méthode du coude")

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fviz_nbclust(fish_std, # Méthode du coefficient de silhouette
             kmeans, 
             method = "silhouette") + 
  labs(subtitle = "Méthode du coefficient de silhouette")

fviz_nbclust(fish_std,  # Statistique du Gap
             kmeans, 
             method = "gap_stat", 
             nboot = 50) + # Nombre de simulations de référence 
  labs(subtitle = "Statistique du Gap")

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Choose which clustering method to apply

# Effectuer le clustering Single: K-means avec k=5
# nstart = 25 assure que l'algorithme est exécuté 25 fois 
# Avec des centres initiaux aléatoires différents pour trouver la meilleure solution globale.
set.seed(123) # Pour la reproductibilité des résultats aléatoires, K-means commence par placer des centres au hasard
km.fish <- kmeans(fish_std,
                  centers = 5,
                  nstart = 25)
fish_behaviour$cluster <- as.factor(km.fish$cluster)

Clustering on scaled/standardized data giving a specific number of clusters

# Visualisation des clusters sur le plan de l'ACP pour réduire vos 6 variables en 2 dimensions (Dim1 et Dim2) pour la visualisation.

fviz_cluster(km.fish, data = fish_std, # utilise par défaut une ACP 
             palette = "jco",
             geom = "point",
             star.plot = TRUE,
             ellipse.type = "convex", 
             ggtheme = theme_minimal(),
             main = "Partitionnement des personnalités (Plan ACP), 
             Clustering K-means des Piranhas (k=5)")

Compare cluster results with different numbers of clusters

# Calcul de la moyenne de chaque comportement par cluster
analyse_profils <- fish_behaviour %>%
  group_by(cluster) %>%
  summarise(across(where(is.numeric), mean))

formattable(analyse_profils, 
            list(area(col = 2:ncol(analyse_profils)) ~ 
                   color_tile("white", "orange")))

cluster	Average_activity	Hiding_time	Social_interactions	Observed_attacks	Exploration	Stimuli_reaction
1	8.068587	0.9390457	2.190769	8.9811603	2.737690	5.983181
2	6.858792	1.9964016	4.988406	2.1027304	7.979879	6.889457
3	6.087402	1.9233174	9.159670	0.9031698	5.987675	4.626971
4	3.910136	3.8211131	3.893799	3.7799962	4.026532	4.339162
5	3.169023	7.8447460	1.013823	0.9877609	1.790026	9.114561

# cluster 1 : aggressive, 2 : verry mobile and exploratore = curious, 3 : social, 4 : neutral, 5 : scared/shy