Use the wine quality data set (located in Week 6 files folder) to answer the following questions. Present any figures that assist you in your analysis:

Use K Means Cluster Analysis to identify cluster(s) of observations that have high and low values of the wine quality. (Assume all variables are continuous.)

Describe variables that cluster with higher values of wine quality. Describe variables that cluster with lower values of wine quality.

If you want to make a good bottle of wine, then what characteristics are most important according to this analysis?

Wine_data<-read.csv("Data/Wine_data.csv")
Wine<-na.omit(Wine_data)
Wine<-scale(Wine)
set.seed(2)
w2 <- kmeans(Wine, 2, nstart = 25)
set.seed(3)
w3 <- kmeans(Wine, 3, nstart = 25)
set.seed(4)
w4 <- kmeans(Wine, 4, nstart = 25)
set.seed(5)
w5 <- kmeans(Wine, 5, nstart = 25)
set.seed(10)
library(factoextra)

## Loading required package: ggplot2

## Welcome! Related Books: `Practical Guide To Cluster Analysis in R` at https://goo.gl/13EFCZ

q2 <- fviz_cluster(w2, data = Wine) + ggtitle("k = 2")
q3 <- fviz_cluster(w3, data= Wine) + ggtitle("k = 3")
q4 <- fviz_cluster(w4, data = Wine) + ggtitle("k = 4")
q5 <- fviz_cluster(w5, data = Wine) + ggtitle("k = 5")
library(gridExtra)
grid.arrange(q2, q3, q4,q5, nrow = 2)

set.seed(2345)
fviz_nbclust(Wine, kmeans, method = "wss")

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following object is masked from 'package:gridExtra':
## 
##     combine

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

Wine_data %>%
  mutate(Cluster3 = w3$cluster) %>%
  group_by(Cluster3) %>%
  summarise_all("mean")

## # A tibble: 3 x 13
##   Cluster3 fixed.acidity volatile.acidity citric.acid residual.sugar
##      <int>         <dbl>            <dbl>       <dbl>          <dbl>
## 1        1          9.97            0.397       0.467           2.59
## 2        2          8.20            0.537       0.290           3.05
## 3        3          7.19            0.617       0.119           2.22
## # ... with 8 more variables: chlorides <dbl>, free.sulfur.dioxide <dbl>,
## #   total.sulfur.dioxide <dbl>, density <dbl>, pH <dbl>, sulphates <dbl>,
## #   alcohol <dbl>, quality <dbl>

library(dplyr)
Wine_data %>%
  mutate(Cluster2 = w2$cluster) %>%
  group_by(Cluster2) %>%
  summarise_all("mean")

## # A tibble: 2 x 13
##   Cluster2 fixed.acidity volatile.acidity citric.acid residual.sugar
##      <int>         <dbl>            <dbl>       <dbl>          <dbl>
## 1        1          9.86            0.397       0.464           2.72
## 2        2          7.43            0.603       0.160           2.44
## # ... with 8 more variables: chlorides <dbl>, free.sulfur.dioxide <dbl>,
## #   total.sulfur.dioxide <dbl>, density <dbl>, pH <dbl>, sulphates <dbl>,
## #   alcohol <dbl>, quality <dbl>

names(Wine_data)

##  [1] "fixed.acidity"        "volatile.acidity"     "citric.acid"         
##  [4] "residual.sugar"       "chlorides"            "free.sulfur.dioxide" 
##  [7] "total.sulfur.dioxide" "density"              "pH"                  
## [10] "sulphates"            "alcohol"              "quality"

###Because there is an obvious elbow after k=3, I chose three clusters. The high quanlity has mean around 61, the medium quanlity has mean around 55, the low quanlity has mean around 53.
###The variables that cluster with higher values of wine quality includes: "alcohol", "sulphates", "density", "chlorides", "chlorides", "residual.sugar", "citric.acid" and "fixed.acidity".
###The variables that cluster with lower values of wine quality includes:"total.sulfur.dioxide", "free.sulfur.dioxide", "residual.sugar" and "volatile.acidity".
###The characters which can reflect obvious difference between different quanlities are "free.sulfur.dioxide","total.sulfur.dioxide","alcohol" and "fixed.acidity".

Use Hierarchical Cluster Analysis to identify cluster(s) of observations that have high and low values of the wine quality. (Assume all variables are continuous.) Use complete linkage and the same number of groups that you found to be the most meaningful in question 1.

Describe variables that cluster with higher values of wine quality. Describe variables that cluster with lower values of wine quality.

If you want to make a good bottle of wine, then what characteristics are most important according to this analysis? Have your conclusions changed using Hierarchical clustering rather than k means clustering? Present any figures that assist you in your analysis.

dwine <- dist(Wine, method = "euclidean")
hclust_wine <- hclust(dwine, method = "complete" )
plot(hclust_wine, cex = 0.6, hang = -1)

sub_group <- cutree(hclust_wine, k = 3)

library(dplyr)
Wine_data %>%
  mutate(cluster_Hi = sub_group) %>%
  group_by(cluster_Hi) %>%
  summarise_all("mean")

## # A tibble: 3 x 13
##   cluster_Hi fixed.acidity volatile.acidity citric.acid residual.sugar
##        <int>         <dbl>            <dbl>       <dbl>          <dbl>
## 1          1          8.32            0.529       0.269           2.45
## 2          2          8.45            0.465       0.880           2.60
## 3          3          8.52            0.398       0.421          11.8 
## # ... with 8 more variables: chlorides <dbl>, free.sulfur.dioxide <dbl>,
## #   total.sulfur.dioxide <dbl>, density <dbl>, pH <dbl>, sulphates <dbl>,
## #   alcohol <dbl>, quality <dbl>

plot(hclust_wine, cex = 0.6)
rect.hclust(hclust_wine, k = 3, border = 1:2)

library(factoextra)
fviz_cluster(list(data = Wine, cluster = sub_group))

###The variables that cluster with higher values of wine quality includes:"alcohol", "total.sulfur.dioxide", "free.sulfur.dioxide", "residual.sugar", "citric.acid".
###The variables that cluster with lower values of wine quality includes:"sulphates", "sulphates", "PH", "density", "chlorides", "volatile.acidity", "fixed.acidity".
###If I want to make a good bottle of wine, then the most important characteristics which can reflect the differnce between quanlities are "total.sulfur.dioxide", "free.sulfur.dioxide", "alcohol","free.sulfur.dioxide".

Use Principal Components Analysis to reduce the dimensions of your data. How much of the variation in your data is explained by the first two principal components. How might you use the first two components to do supervised learning on some other variable tied to wine (e.g. - wine price)?

pr.out_wine=prcomp(Wine, scale=TRUE)
biplot(pr.out_wine, scale=0)

pr.out_wine$rotation=-pr.out_wine$rotation 
pr.out_wine$x=-pr.out_wine$x
biplot(pr.out_wine, scale=0)

pr.var_wine=pr.out_wine$sdev^2
pve_wine=pr.var_wine/sum(pr.var_wine)
plot(pve_wine, xlab="Principal Component", ylab="Proportion of Variance Explained", ylim=c(0,1),
     type="b")

plot(cumsum(pve_wine), xlab="Principal Component", ylab="Cumulative Proportion of Variance Explained", 
     ylim=c(0,1),type="b")

###There are almost 40% variation explained by the first two principal components.