---
title: "Banknotes with K-Means"
author: "Milica Cudina"
output:
  pdf_document: default
---

First, we need to import data:

```{r}
notes<-read.csv("banknotes.csv")
head(notes)
```

Now, a bit of exploratory data analysis:

```{r}
attach(notes)
plot(V1, V2,
     col="yellow", pch=20,
     xlab="Property 1", 
     ylab="Property 2")
```

The function `kmeans()` performs $K$-means clustering in
`R`. 

```{r}
km.out <- kmeans(notes, 5, nstart = 20)
km.out
#here are the cluster assignments
km.out$cluster
#here are the cluster centers
km.out$centers
```
It all works out much better visually. 

```{r}
#cloud of points with colors corresponding to cluster
plot(notes, col = (km.out$cluster + 1),
    main = "K-Means Clustering Results with K = 2",
    xlab = "Property 1", ylab = "Property 2", pch = 20, cex = 0.5)
#adding the centers
points(km.out$centers, col="blue", pch=20)
```