1d kmeans

library(tidyverse)

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n <- 200
x1 <- rnorm(n, mean = 5, sd = 1)
x2 <- rnorm(n, mean = 10, sd = 1)
x3 <- rnorm(n, mean = 15, sd = 1)
d <- tibble(xs = c(x1, x2, x3), cl = rep(letters[1:3], each = n))

ggplot(d, aes(x = xs, fill = cl)) +
  geom_histogram(bins = 50)

km <- kmeans(d$xs, centers = 3)
d$km <- as.character(km$cluster)

ggplot(d, aes(x = xs, fill = km)) +
  geom_histogram(bins = 50)

wss <- sapply(1:10, function(k ) kmeans(d$xs, nstart = 20, centers = k)$tot.withinss)
qplot(wss, 1:10)

library(pastecs)

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dens <- density(d$xs)
ts_y <- ts(dens$y)
tp <- turnpoints(ts_y)
plot(dens)
points(dens$x[tp$tppos], dens$y[tp$tppos], col = 'red')