K-Means Clustering

library(tidymodels)
library(tidyverse)

set.seed(27)

centers <- tibble(
  cluster = factor(1:3), 
  num_points = c(100, 150, 50),  # number points in each cluster
  x1 = c(5, 0, -3),              # x1 coordinate of cluster center
  x2 = c(-1, 1, -2)              # x2 coordinate of cluster center
)

labelled_points <- 
  centers %>%
  mutate(
    x1 = map2(num_points, x1, rnorm),
    x2 = map2(num_points, x2, rnorm)
  ) %>% 
  select(-num_points) %>% 
  unnest(cols = c(x1, x2))

ggplot(labelled_points, aes(x1, x2, color = cluster)) +
  geom_point(alpha = 0.3) + theme_bw()

points <- labelled_points %>% select(-cluster)
kclust <- kmeans(points, centers = 3)
kclust

K-means clustering with 3 clusters of sizes 148, 51, 101

Cluster means:
           x1        x2
1  0.08853475  1.045461
2 -3.14292460 -2.000043
3  5.00401249 -1.045811

Clustering vector:
  [1] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
 [56] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1
[111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[166] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[221] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[276] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

Within cluster sum of squares by cluster:
[1] 298.9415 108.8112 243.2092
 (between_SS / total_SS =  82.5 %)

Available components:

[1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss" "betweenss"    "size"        
[8] "iter"         "ifault"      

summary(kclust)

             Length Class  Mode   
cluster      300    -none- numeric
centers        6    -none- numeric
totss          1    -none- numeric
withinss       3    -none- numeric
tot.withinss   1    -none- numeric
betweenss      1    -none- numeric
size           3    -none- numeric
iter           1    -none- numeric
ifault         1    -none- numeric

augment(kclust,points)

tidy(kclust)

glance(kclust)

kclusts <- 
  tibble(k = 1:9) %>%
  mutate(
    kclust = map(k, ~kmeans(points, .x)),
    tidied = map(kclust, tidy),
    glanced = map(kclust, glance),
    augmented = map(kclust, augment, points)
  )

kclusts

clusters <- 
  kclusts %>%
  unnest(cols = c(tidied))

assignments <- 
  kclusts %>% 
  unnest(cols = c(augmented))

clusterings <- 
  kclusts %>%
  unnest(cols = c(glanced))

p1 <- 
  ggplot(assignments, aes(x = x1, y = x2)) +
  geom_point(aes(color = .cluster), alpha = 0.8) + 
  facet_wrap(~ k) +theme_bw()
p1

p2 <- p1 + geom_point(data = clusters, size = 10, shape = "x")
p2

ggplot(clusterings, aes(k, tot.withinss)) +
  geom_line() +
  geom_point() + theme_bw()