Student Name: Senet Manandhar

Data received: Built in R studi0 - Gravdes TV & mtcars dataset

Dendrogram

Explaining Cluster Dendrogram

library(openintro)
## Please visit openintro.org for free statistics materials
## 
## Attaching package: 'openintro'
## The following objects are masked from 'package:datasets':
## 
##     cars, trees
data("gradesTV")
head(gradesTV,25)
##    TV Grades
## 1   0     82
## 2   0     93
## 3   0     65
## 4   5     90
## 5   7     85
## 6  10    100
## 7  11     90
## 8  12     95
## 9  14     84
## 10 15     75
## 11 15     75
## 12 16     90
## 13 17     79
## 14 19     75
## 15 20     85
## 16 20     78
## 17 20     80
## 18 23     67
## 19 24     75
## 20 25     70
## 21 27     68
## 22 28     63
## 23 30     60
## 24 30     65
## 25 32     85

Cluster Dendrogram is the grahical build of cluster hierarchy that is commonly displayed as a tree diagram

hc = hclust(dist(gradesTV))
plot(hc)

The goal of dendrogram is compare the dissimilarites between each objects.

mtcars
##                      mpg cyl  disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
## Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
## Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
## Merc 240D           24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
## Merc 230            22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
## Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
## Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
## Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
## Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
## Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
## Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4
## Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
## Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
## Fiat 128            32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
## Honda Civic         30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
## Toyota Corolla      33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
## Toyota Corona       21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
## Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
## AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
## Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
## Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
## Fiat X1-9           27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
## Porsche 914-2       26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
## Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
## Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
## Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
## Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8
## Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2
str(mtcars)
## 'data.frame':    32 obs. of  11 variables:
##  $ mpg : num  21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
##  $ cyl : num  6 6 4 6 8 6 8 4 4 6 ...
##  $ disp: num  160 160 108 258 360 ...
##  $ hp  : num  110 110 93 110 175 105 245 62 95 123 ...
##  $ drat: num  3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
##  $ wt  : num  2.62 2.88 2.32 3.21 3.44 ...
##  $ qsec: num  16.5 17 18.6 19.4 17 ...
##  $ vs  : num  0 0 1 1 0 1 0 1 1 1 ...
##  $ am  : num  1 1 1 0 0 0 0 0 0 0 ...
##  $ gear: num  4 4 4 3 3 3 3 4 4 4 ...
##  $ carb: num  4 4 1 1 2 1 4 2 2 4 ...
library(ggplot2)
## 
## Attaching package: 'ggplot2'
## The following object is masked from 'package:openintro':
## 
##     diamonds
#theme_set(theme_bw())
hc <- hclust(dist(mtcars), "ave")
hc
## 
## Call:
## hclust(d = dist(mtcars), method = "ave")
## 
## Cluster method   : average 
## Distance         : euclidean 
## Number of objects: 32
plot(hc)

plot(hc, hang = -1, cex=0.9)

##Hierarchical cluster analysis on a set of dissimilarities and methods for analyzing it.

To rotate have to download ggdendro package.

library(ggdendro)
ggdendrogram(hc, rotate = TRUE, size = 2)

The horizontal axis of the dendrogram represents the distance or dissimilarity between clusters. The vertical axis represents the objects and clusters.Our main interestis in similarity and clustering. Each joining (fusion) of two clusters is represented on the graph by the splitting of a horizontal line into two horizontal lines. The horizontal position of the split, shown by the short vertical bar,gives the distance (dissimilarity) between the two clusters.

#model <- hclust(dist(mtcars), "ave")
#dhc <- as.dendrogram(model)
# Rectangular lines
#ddata <- dendro_data(dhc, type = "rectangle")
# p <- ggplot(segment(ddata)) + 
#  geom_segment(aes(x = x, y = y, xend = xend, yend = yend)) + 
#  coord_flip() + 
#  scale_y_reverse(expand = c(.2, 0))
# p



ggdendrogram(hc, rotate = TRUE, size = 4, theme_dendro = FALSE, color = "tomato")

NOTE: After downloading APE package works.

The plot.phylo function has four more different types for plotting a dendrogram. Here they are:

library(ape)
plot(as.phylo(hc), type = "unrooted")

plot(as.phylo(hc), type = "cladogram", cex = 0.9, label.offset = 2)

plot(as.phylo(hc), type = "fan")