Class Activity 26

# load the necessary libraries
library(tidyverse) 
library(ggthemes)
library(factoextra)
library(janitor)
library(broom)

select <- dplyr::select
theme_set(theme_stata(base_size = 10))


standardize <- function(x, na.rm = FALSE) {
  (x - mean(x, na.rm = na.rm)) / sd(x, na.rm = na.rm)
}

Group Activity 1

Let’s look at the following data tibble that randomly creates some x- and y- coordinates around the cluster centroids that we just saw in class. Please answer the questions based on this data.

set.seed(1234)

my_df <- tibble(
  X1 = rnorm(n = 120, mean = rep(c(2, 4, 7.33), each = 40)),
  X2 = rnorm(n = 120, mean = rep(c(6.33, 3, 6), each = 40))
)

my_df %>%
  ggplot(aes(X1, X2)) +
  geom_point()

  1. How many clusters can you identify in the data?
Click for answer

Answer: Answers may vary

  1. Fit kmeans algorithm to the data picking the number of clusters you previously identified in part a.
Click for answer

Answer:

set.seed(1234)
res_kmeans <- kmeans(my_df, centers = 3, nstart = 25)
  1. Add the cluster association to the dataset and make a scatter plot color-coded by the cluster association.
Click for answer

Answer:

augment(res_kmeans, data = my_df) %>%
  ggplot(aes(X1, X2, color = .cluster)) +
  geom_point()

  1. Repeat parts b-c for identifying more number of clusters than what you picked in part a.
Click for answer

Answer:

set.seed(1234)
res_kmeans <- kmeans(my_df, centers = 5, nstart = 25)
augment(res_kmeans, data = my_df) %>%
  ggplot(aes(X1, X2, color = .cluster)) +
  geom_point()

  1. Aggregate the total within sum of squares for each k to the data table multi_kmeans.
Click for answer

Answer:

multi_kmeans <- tibble(k = 1:10) %>%
  mutate(
    model = purrr::map(k, ~ kmeans(my_df, centers = .x, nstart = 25)),
    tot.withinss = purrr::map_dbl(model, ~ glance(.x)$tot.withinss)
  )
  1. Make an elbow plot modifying the code below:
Click for answer

Answer:

multi_kmeans %>%
  ggplot(aes(k, tot.withinss)) +
  geom_point() +
  geom_line()+
  scale_x_continuous(breaks = 1:15)

  1. After picking an optimal number of cluster, use the in-built function in the factoextra package to construct the final cluster plot.
Click for answer

Answer:

set.seed(1234)
kmeans.final <- kmeans(my_df, 5, nstart = 25)
fviz_cluster(kmeans.final, data = my_df, ggtheme = theme_stata())

(Extra) Group Activity 2

Let’s look at the following data tibble that randomly creates some x- and y- coordinates around the cluster centroids. Now, there are more clusters and the data points are closer to each other. Please repeat the analysis as seen above to find the optimal number of clusters.

set.seed(1234)

my_df <- tibble(
  X1 = rnorm(n = 240, mean = rep(c(2, 4, 7.33, 2.5, 5, 6), each = 40)),
  X2 = rnorm(n = 240, mean = rep(c(6.33, 3, 6, 3.5, 4.5, 5.5), each = 40))
)

my_df %>%
  ggplot(aes(X1, X2)) +
  geom_point()

Click for answer

Answer:

  1. How many clusters can you identify in the data?

Answer: Answers may vary!

  1. Fit kmeans algorithm to the data picking the number of clusters you previously identified in part a.
set.seed(1234)
res_kmeans <- kmeans(my_df, centers = 6, nstart = 25)
  1. Add the cluster association to the dataset and make a scatter plot color-coded by the cluster association.
augment(res_kmeans, data = my_df) %>%
  ggplot(aes(X1, X2, color = .cluster)) +
  geom_point()

  1. Repeat parts b-c for identifying more number of clusters than what you picked in part a.
set.seed(1234)
res_kmeans <- kmeans(my_df, centers = 8, nstart = 25)
augment(res_kmeans, data = my_df) %>%
  ggplot(aes(X1, X2, color = .cluster)) +
  geom_point()

  1. Aggregate the total within sum of squares for each k to the data table multi_kmeans.
multi_kmeans <- tibble(k = 1:15) %>%
  mutate(
    model = purrr::map(k, ~ kmeans(my_df, centers = .x, nstart = 25)),
    tot.withinss = purrr::map_dbl(model, ~ glance(.x)$tot.withinss)
  )
  1. Make an elbow plot modifying the code below:
multi_kmeans %>%
  ggplot(aes(k, tot.withinss)) +
  geom_point() +
  geom_line() +
  scale_x_continuous(breaks = 1:15)

  1. After picking an optimal number of cluster, use the in-built function in the factoextra package to construct the final cluster plot.
set.seed(1234)
kmeans.final <- kmeans(my_df, 8, nstart = 25)
fviz_cluster(kmeans.final, data = my_df, ggtheme = theme_stata())