04-feature-selection.Rmd

---
title: "Feature Selection"
author: "Kundan K. Rao"
date: "01/12/2021"
output: html_document
---

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

```{r}
#principle component
pr.out<-prcomp(data,scale=T)
```

```{r}
names(pr.out)
```

```{r}
pr.out$center
```

```{r}
pr.out$scale
```

```{r}
pr.out$sdev
```

```{r}
# principle component loading vector
pr.out$rotation
```

```{r}
#principle component score vectors dimention
dim(pr.out$x)
```

```{r}
#principle component score vector
head(pr.out$x)
```
assessing clustering tendency:-
```{r}
# Plot the random df
fviz_pca_ind(pr.out, title = "PCA - Random data",
geom = "point", ggtheme = theme_classic())
```



```{r}
# biplot
ggbiplot::ggbiplot(pr.out)
#biplot(pr.out,scale=0)
```
Observation:-
1. Alcohol, Color intensity, Proline, Magnesium, Ash seems to form a cluster
2. Hue, Total phenols, Flavanoids, 0D280/0D315 of diluted wines seems to form another cluster
3. Malic acid, Nonflavanoid phenols, Alcalinity of ash seems to form yet another cluster

```{r}
# variances explained by principle components
pr.var <- pr.out$sdev^2
pr.var
```


```{r}
#PVE proportion of variance explained by each principle components
pve <- pr.var/sum(pr.var)
pve
```

```{r}
# plot of PVE explained by each principle component
par(mfwow=c(2,1))
plot(pve, xlab="Principle Component", ylab = "Proportion of variance explained", ylim=c(0,1), type="b")
plot(cumsum(pve), xlab="principle component",ylab="Cumulative proportion of variance explained", ylim=c(0,1), type="b")
```
# Matrix completion

```{r}
x <- data.matrix(scale(data))
pcob <- prcomp(x)
summary(pcob)
```

```{r}
# singular value decomposition
sX<-svd(x)
names(sX)
round(sX$v,3)
```

```{r}
# compare with the above , both is same i.e. loading matrix
pcob$rotation
```

# Assesing clustering tendency:-

Statistical method:-
```{r}
library(clustertend)
# Compute Hopkins statistic for wine dataset
set.seed(123)
hopkin <-hopkins(data, n = nrow(data)-1)
hopkin
```

Visual method:-
```{r}
fviz_dist(dist(data), show_labels = FALSE)+
labs(title = "Wine data")
```
```{r}
fviz_dist(dist(data.scaled), show_labels = FALSE)+
labs(title = "Wine data")
```
The visual assessment of cluster tendency (VAT) detects the clustering tendency in a visual form by counting the number of
square shaped dark blocks along the diagonal in a VAT image.



# determining optimum number of clusters:-
Kmeans
```{r}
# Elbow method
fviz_nbclust(data.scaled, kmeans, method = "wss") +
#geom_vline(xintercept = 4, linetype = 2)+
labs(subtitle = "Elbow method")
```

```{r}
# Silhouette method
fviz_nbclust(data.scaled, kmeans, method = "silhouette")+
labs(subtitle = "Silhouette method")
```

```{r}
# Gap statistic
# nboot = 50 to keep the function speedy.
# recommended value: nboot= 500 for your analysis.
# Use verbose = FALSE to hide computing progression.
set.seed(123)
fviz_nbclust(data.scaled, kmeans, nstart = 25, method = "gap_stat", nboot = 50)+
labs(subtitle = "Gap statistic method")
```

## pam
```{r}
# Elbow method
fviz_nbclust(data.scaled, pam, method = "wss") +
#geom_vline(xintercept = 4, linetype = 2)+
labs(subtitle = "Elbow method")
```

```{r}
# Silhouette method
fviz_nbclust(data.scaled, pam, method = "silhouette")+
labs(subtitle = "Silhouette method")
```

```{r}
# Gap statistic
# nboot = 50 to keep the function speedy.
# recommended value: nboot= 500 for your analysis.
# Use verbose = FALSE to hide computing progression.
set.seed(123)
fviz_nbclust(data.scaled, pam, nstart = 25, method = "gap_stat", nboot = 50)+
labs(subtitle = "Gap statistic method")
```

## Hierarchical
```{r}
# Elbow method
fviz_nbclust(data.scaled, hcut, method = "wss") +
#geom_vline(xintercept = 4, linetype = 2)+
labs(subtitle = "Elbow method")
```

```{r}
# Silhouette method
fviz_nbclust(data.scaled, hcut, method = "silhouette")+
labs(subtitle = "Silhouette method")
```

```{r}
# Gap statistic
# nboot = 50 to keep the function speedy.
# recommended value: nboot= 500 for your analysis.
# Use verbose = FALSE to hide computing progression.
set.seed(123)
fviz_nbclust(data.scaled, hcut, nstart = 25, method = "gap_stat", nboot = 50)+
labs(subtitle = "Gap statistic method")
```


# NbClust() Method
## Majority rule
## Kmeans
```{r}
library(NbClust)
nb <- NbClust(data.scaled, distance = "euclidean", min.nc = 2,
max.nc = 10, method = "kmeans")

# visualising the result
fviz_nbclust(nb)
```

##  hierarchical
ward.D
```{r}
library(NbClust)
nb.ward2 <- NbClust(data.scaled, distance = "euclidean", min.nc = 2,
max.nc = 10, method = "ward.D")

# visualising the result
fviz_nbclust(nb.ward2)
```

average
```{r}
library(NbClust)
nb.avg <- NbClust(data.scaled, distance = "euclidean", min.nc = 2,
max.nc = 10, method = "average")

# visualising the result
fviz_nbclust(nb.avg)
```

complete
```{r}
library(NbClust)
nb.complete <- NbClust(data.scaled, distance = "euclidean", min.nc = 2,
max.nc = 10, method = "complete")

# visualising the result
fviz_nbclust(nb.complete)
```