---
title: "Lab4: K-means, DB-scan and dendrograms"
author: "Vladislav Litvinov <vlad@sek1ro>"
output:
  pdf_document:
  toc_float: TRUE
---
# Data preparationc
```{r}
setwd('/home/sek1ro/git/public/lab/ds/25-1/r')
load("./income_elec_state.Rdata")
df = income_elec_state
df$incomelog = log10(df$income)
remove(income_elec_state)
```
# Function to compute Within-Cluster Sum of Squares for choosing optimal K
```{r}
elbow_wss = function(df) {
  max_k = 10
  wss = numeric(max_k)
  
  for (i in 1:max_k) {
    res = kmeans(df[,1:2], centers = i)
    wss[i] = res$tot.withinss 
  }
  
  plot(1:max_k, wss, type="b")
  
  wss_diff = diff(wss)
  wss_ratio = wss_diff[-1] / wss_diff[-length(wss_diff)]
  return(which.min(wss_ratio))
}
```
# Scatter-plot: elec vs income and log-income
```{r}
library(ggplot2)

plot_kmeans = function(data, k, log) {
  res = kmeans(data, centers = k)
  centers = as.data.frame(res$centers)
  centers$cluster = as.factor(1:k)
  data$cluster = as.factor(res$cluster)
  data$state = rownames(df)
  
  plt = ggplot() +
    geom_point(
      data = data,
      aes(
        x = income,
        y = elec, 
        color = cluster
      )
    ) +
    geom_text(
      data = data,
      vjust = 1.5,
      size = 2,
      aes(
        x = income,
        y = elec,
        label = state
      )
    ) +
    geom_point(
      data = centers,
      shape = 17,
      size = 5,
      aes(
        x = income,
        y = elec,
        color = cluster,
      )
    ) +
    theme_minimal()
  
  if (log) {
    plt = plt + scale_x_log10() + scale_y_log10()
  }
  
  print(plt)
}

data = df[,c("income", "elec")]
datalog = df[,c("incomelog", "elec")]
k = elbow_wss(data)
klog = elbow_wss(datalog)
plot_kmeans(data, k, log=FALSE)
plot_kmeans(data, klog, log=TRUE)

```
# Map of USA
```{r}
library(maps)
res = kmeans(data, centers = k)
map_color = res$cluster[order(names(res$cluster))]
map("state", fill = TRUE, col = map_color)

Q1 = quantile(df$elec, 0.25)
Q3 = quantile(df$elec, 0.75)
IQR = Q3 - Q1
min = Q1 - 1.5 * IQR
max = Q3 + 1.5 * IQR
df = subset(df,  df$elec > min & df$elec < max)

data = df[,c("income", "elec")]
datalog = df[,c("incomelog", "elec")]
k = elbow_wss(data)
klog = elbow_wss(datalog)
plot_kmeans(data, k, log=FALSE)
plot_kmeans(data, klog, log=TRUE)

```
# Differences within dendrogramm algo: 'single', 'complete', 'ward.D', 'average'
```{r}

library(ggdendro)


plot_hclust = function(df, linkage, k) {
  data = df[,c("income", "elec")]
  distance = dist(data, method = "euclidean")
  clust = hclust(distance, method = linkage)
  data$cluster = as.factor(cutree(clust, k = k))
  data$state = rownames(df)
  print(cutree(clust, k = k))
  print(data)
  plt = ggplot() +
    geom_point(
      data = data,
      aes(
        x = income,
        y = elec, 
        color = cluster
      )
    ) +
    geom_text(
      data = data,
      vjust = 1.5,
      size = 2,
      aes(
        x = income,
        y = elec,
        label = state
      )
    )
    theme_minimal()
    print(plt)
}

plot_hclust(data, "average", 5)

distance = dist(data, method = "euclidean")

clust = hclust(distance, method = "single")
plot(ggdendrogram(clust))

cutree(clust, k = 3)
```
