index.Rmd

---
title: "Pokemons Classification based on Characteristics"
author: "Imen Bouzidi"
date: "11/3/2019"
output:
 html_document:
    theme: united
    highlight: tango
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)

```

## Data Set:

Pokemon dataset contains information on a total of 801 Pokemon.

it includes:

* The English name of the Pokemon
* percentage_male: The percentage of the species that are male. Blank if the Pokemon is genderless.
* height_m: Height of the Pokemon in metres
* weight_kg: The Weight of the Pokemon in kilograms
* hp: The Base HP of the Pokemon
* attack: The Base Attack of the Pokemon
* defense: The Base Defense of the Pokemon
* speed: The Base Speed of the Pokemon
* base_egg_steps: The number of steps required to hatch an egg of the Pokemon
* base_happiness: Base Happiness of the Pokemon
* capture_rate: Capture Rate of the Pokemon
* experience_growth: The Experience Growth of the Pokemon
* sp_attack: The Base Special Attack of the Pokemon
* sp_defense: The Base Special Defense of the Pokemon
* generation: The numbered generation which the Pokemon was first introduced
* is_legendary: Denotes if the Pokemon is legendary(two major classes: legendary pokemons and not legendary pokemons)



Data are downloaded from: https://www.kaggle.com/rounakbanik/pokemon/data

## Packages needed:
```{r loadlib, echo=T, results='hide', message=F, warning=F}

library('DT')
library('missMDA')
library('NbClust')
library("FactoMineR")
library('factoextra')
library('fossil')
library("corrplot")
library('plotly')
library('kohonen')
library('mclust')

```




```{r data}
D=read.csv('Pokemon.csv',header = T,row.names = 1)
datatable(D, rownames = 1, filter="top", options = list(pageLength = 5, scrollX=T) )
summary(D)

```
## PCA on Characteristics of Pokemons:

Variables from height_m to sp_defense are the quantitatives variables for the PCA.

Supplementary qualitative variable are generation and 'is_legendary'. 
```{r pca }
impData=imputePCA(D[,3:14], ncp = 2, scale = TRUE, method = c("Regularized","EM")) # Impute missing data
ImputData=data.frame(cbind(impData[["completeObs"]],D[,15:16]))
res.pca = PCA(ImputData[,1:14], graph = FALSE,quali.sup = c(13,14))

head(res.pca$eig,4)
fviz_eig(res.pca, addlabels = TRUE, ylim = c(0, 50))


```

In our case, we are studying the 2 first dimensions ( but taking three is the optimal choice with a 60.44% variance cumulative percentage and eigenvalues >1)

### Visualizing the first 2 dimensions:


```{r carte}
corrplot(res.pca$var$cos2, is.corr=FALSE)
fviz_pca_var(res.pca, col.var = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),repel = T
             )


```

From the plots above (corrplot and variables plot), The first dimension represents the variables : height_m, weight_kg, hp, attack, Capture_rate(negatively), sp_attack and sp_defense while the second dimension represents especially the base_happinesss variables and experience_growth(negatively).


Pokemons will be projected on the factor map after clustering.

## Optimal number of clusters:
NbCLust will be used to determine the optimal number of clusters for the k means and for hierarchical clustering, bellow is the code:

```{r Validation }

X=scale(ImputData[,1:12]) # Contains scaled charasteristics of each pokemon

res_nbclust<-NbClust(X,min.nc = 2, max.nc = 20, index="silhouette",method = "kmeans")
res_nbclust$All.index

```
 In the following, 3 is considered the optimal cluster's number with a silhouette index equal to 0.2342.

## Clustering Using kmeans:

```{r kmeans}

km=kmeans(X,3)

fviz_cluster(list(data = X, cluster = km$cluster), geom = "point", stand = FALSE )+
  scale_colour_manual(values = c("#ffa64d","#00b33c", "#ff3333"))+
  scale_fill_manual(values = c("#ffa64d","#00b33c", "#ff3333")) 

```

Group 1 is characterised mainly by high score in every characteristics of dimension 1( height, weight, hp, attack, sp_attack and sp_defense). It seems that Pokemons of group1 are the most powerful Pokemons but don't have high values in base_happiness. 

Group2 is characterised by lower values on dimension 1 but higher values on dimension 2 (having higher base happiness than group 2 (see RadarPlot)).

Group 3 of Pokemons have the lowest values on the two dimensions but have a higher capture rate than other Pokemons.




```{r plot}

Centers.km=data.frame(km$centers) #Contains the centroids of each class
datatable(Centers.km, filter="top", options = list(pageLength = 3, scrollX=T) )

plot_ly(  type = 'scatterpolar',fill = 'toself',mode='markers') %>%
  add_trace(r = as.numeric(Centers.km[1,]),theta = colnames(Centers.km),name = 'Group 1')%>%
  add_trace(r = as.numeric(Centers.km[2,]),theta = colnames(Centers.km),name = 'Group 2')%>%
  add_trace(r = as.numeric(Centers.km[3,]),theta = colnames(Centers.km),name = 'Group 3')%>%
  layout(polar = list(radialaxis = list(visible = T,range = c(-3,3))))


```



To conclude, Group1 is the most powerful group of Pokemons, Group2 is less powerful than Group1 and Group 3 is the least powerful group of pokemons but with higher Base_happiness and capture_rate.

## Clustering using Hierarchical clustering: 

```{r hier}
d=dist(X,method = 'euclidean') 
hc=hclust(d,method = 'ward.D') 
classesHC=cutree(hc,k=3)# Return Classes of the hierarchical clustering

# function to find centroid in cluster i
clust.centroid = function(i, dat, classes) {
  ind = ( classes == i)
  colMeans(dat[ind,])
}
Centers.hc=sapply(unique(classesHC), clust.centroid, X, classesHC)
Centers.hc=data.frame(t(Centers.hc))

table(km$cluster,classesHC)

```
Group1 of Pokemons of kmeans is mainly classified in Group3 of hierarchical clustering, Group2 is mainly classified in Group1 of hierarchical clustering(419 pokemons are in group1 and only 2 are in group3) and Group3 is divided between Group2 and Group3.

```{r randind}
rand.index(km$cluster,classesHC)
```
A Rand index of 0.72 indicates a similarity between kmeans results and hierarchical clustering results.

```{r clustval}


plot_ly(  type = 'scatterpolar',fill = 'toself',mode='markers') %>%
  add_trace(r = as.numeric(Centers.hc[1,]),theta = colnames(Centers.hc),name = 'Group 1')%>%
  add_trace(r = as.numeric(Centers.hc[2,]),theta = colnames(Centers.hc),name = 'Group 2')%>%
  add_trace(r = as.numeric(Centers.hc[3,]),theta = colnames(Centers.hc),name = 'Group 3')%>%
  layout(polar = list(radialaxis = list(visible = T,range = c(-3,3))))

```


Due to changes of switching Pokemons from a cluster to another in hierarchical clustering, the characteristics of the groups are mainly the same. Whereas Group2 have the loawest values of each score other than Base_happiness abd Capture_rate.

## Clustering Usins SOM (Self-Organizing Map):

```{r som}

set.seed(7)

#create SOM grid
sommap <- som(X, grid = somgrid(3, 1, "hexagonal"))
plot(sommap)


```

The first Group is characterised by a high capture_rate and base_happiness while the second group of pokemons is characterised by higher scores in every other variable.

The third group is characterised by low values in every variable other than base_happiness.


```{r rand}

somc=sommap$unit.classif
table(km$cluster,somc)
rand.index(km$cluster,somc) # to compare kmeans and Som CLustering

```
Groups of Pokemons that we obtained from Som are nearly the same as the groups we obtained with kmeans. 

The rand index in this case is 0.99. 
this proves a very good similarity between Som Clustering results and kmeans results.



## Clustering Using EM (Expectation Maximization):

```{r EM}
EMB <- Mclust(X)

summary(EMB)
summary(EMB$BIC)


```