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I know I am probably late to this party but I recently found out about DBSCAN or “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise”[^1]. In a nutshell, the algorithm visits successive data point and asks whether neighbouring points are density-reachable. In other words is it possible to connect two points with a chain of points all conforming to some density criteria. This has some major advantages over other clustering algorithms that I have used before.

• It can identify clusters of arbitrary shape.
• Number of clusters is not an input parameter.
• It's fast as it only visits the data points rather than the space in between.
• A data point with no close neighbours is assigned noise rather than its nearest cluster.

Let have a go at clustering uk cities from `library(maps)`. First load the packages and the data, then subset the data to get only the UK cities.

```library(ggplot2)
library(dplyr)
library(maps)
library(dbscan)

data("world.cities")
UK <- world.cities %>% filter(country.etc == "UK")
```

Now we can run the algorithm on the latitude and longitude collumns. Then we can pull the cluster assignments out of the resulting object.

```EPS <- 0.15
clusters <- dbscan(select(UK, lat, long), eps = EPS)
UK\$cluster <- clusters\$cluster
```

Finally we can split the original data into two according to whether dbscan has assigned or cluster or noise.

```groups  <- UK %>% filter(cluster != 0)
noise  <- UK %>% filter(cluster == 0)
```

Now lets have a look at the results[^2].

```ggplot(UK, aes(x = long, y = lat, alpha = 0.5)) +
geom_point(aes(fill = "grey"), noise) +
geom_point(aes(colour = as.factor(cluster)), groups,
size = 3) +
coord_map() +
theme_stripped +
theme_empty +
theme(legend.position = "none")
``` I arbitrarily set the EPS parameter. How to tune it? Discussion for another time...

[^1]: I recommend reading the paper which is quite accesible. Martin Ester, Hans-Peter Kriegel, Joerg Sander, Xiaowei Xu (1996). A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise. Institute for Computer Science, University of Munich. Proceedings of 2nd International Conference on Knowledge Discovery and Data Mining (KDD-96).

[^2]: I am stripping out some of the ggplot defaults with two objects `theme_stripped` and `theme_empty` which I use routinely to either remove the background and gridlines or to remove everything including axes.