Materials for Applied Data Science profile course INFOMDA2 *Battling the curse of dimensionality*.

In this practical, we will apply hierarchical and k-means clustering to two synthetic datasets. We use the following packages:

```
library(MASS)
library(tidyverse)
library(patchwork)
library(ggdendro)
```

The data can be generated by running the code below.

**1. The code does not have comments. Add descriptive comments to the
code below.**

```
set.seed(123)
sigma <- matrix(c(1, .5, .5, 1), 2, 2)
sim_matrix <- mvrnorm(n = 100, mu = c(5, 5),
Sigma = sigma)
colnames(sim_matrix) <- c("x1", "x2")
sim_df <-
sim_matrix %>%
as_tibble() %>%
mutate(class = sample(c("A", "B", "C"), size = 100,
replace = TRUE))
sim_df_small <-
sim_df %>%
mutate(x2 = case_when(class == "A" ~ x2 + .5,
class == "B" ~ x2 - .5,
class == "C" ~ x2 + .5),
x1 = case_when(class == "A" ~ x1 - .5,
class == "B" ~ x1 - 0,
class == "C" ~ x1 + .5))
sim_df_large <-
sim_df %>%
mutate(x2 = case_when(class == "A" ~ x2 + 2.5,
class == "B" ~ x2 - 2.5,
class == "C" ~ x2 + 2.5),
x1 = case_when(class == "A" ~ x1 - 2.5,
class == "B" ~ x1 - 0,
class == "C" ~ x1 + 2.5))
```

**2. Prepare two unsupervised datasets by removing the class feature.**

**3. For each of these datasets, create a scatterplot. Combine the two
plots into a single frame (look up the patchwork package to see how to
do this!) What is the difference between the two datasets?**

**4. Run a hierarchical clustering on these datasets and display the
result as dendrograms. Use euclidian distances and the complete
agglomeration method. Make sure the two plots have the same y-scale.
What is the difference between the dendrograms? (Hint: functions youâ€™ll
need are hclust, ggdendrogram, and ylim)**

**5. For the dataset with small differences, also run a complete
agglomeration hierarchical cluster with manhattan distance.**

**6. Use the cutree() function to obtain the cluster assignments for
three clusters and compare the cluster assignments to the 3-cluster
euclidian solution. Do this comparison by creating two scatter plots
with cluster assignment mapped to the colour aesthetic. Which difference
do you see?**

**7. Create k-means clusterings with 2, 3, 4, and 6 classes on the large
difference data. Again, create coloured scatter plots for these
clusterings.**

**8. Do the same thing again a few times. Do you see the same results
every time? where do you see differences?**

**9. Find a way online to perform bootstrap stability assessment for the
3 and 6-cluster solutions.**

**10. Create a function to perform k-medians clustering**

Write this function from scratch: you may use base-R and tidyverse functions. Use Euclidean distance as your distance metric.

Input: - dataset (as a data frame) - K (number of clusters)

Output: - a vector of cluster assignments

Tip: use the unsupervised version of `sim_df_large`

with `K = 3`

as a
tryout-dataset

**11. Add an input parameter smart_init. If this is set to TRUE,
initialize cluster assignments using hierarchical clustering (from
hclust). Using the unsupervised sim_df_small, look at the number of
iterations needed when you use this method vs when you randomly
initialize.**