DBSCAN Clustering in R

Welcome! In this lesson, we will explore the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. Using R and its powerful packages, we will implement DBSCAN and visualize its results with ggplot2. DBSCAN is a popular clustering algorithm that can identify clusters of varying shapes and sizes, as well as detect outliers (noise) in your data. In this lesson, we’ll use a synthetic "two moons" dataset, which is a classic example for demonstrating the strengths of density-based clustering. Let’s dive in and see how DBSCAN works in R!

To get started, we need to load a few essential R packages. The dbscan package provides the DBSCAN algorithm implementation, ggplot2 is used for data visualization, MASS helps with data generation, and scales is used for color palettes.

# Install packages if not already installed
if (!require(dbscan)) install.packages("dbscan")
if (!require(ggplot2)) install.packages("ggplot2")
if (!require(MASS)) install.packages("MASS")
if (!require(scales)) install.packages("scales") # for hue_pal

# Load the libraries
library(dbscan)
library(ggplot2)
library(MASS)
library(scales)

To showcase DBSCAN’s ability to find clusters of arbitrary shapes, we’ll generate a "two moons" dataset. This dataset consists of two interleaving half circles, which are not well separated by traditional clustering algorithms like k-means.

set.seed(42)
n <- 150
theta <- runif(n, 0, pi)
x1 <- cbind(cos(theta), sin(theta)) + matrix(rnorm(2 * n, sd = 0.1), ncol = 2)
x2 <- cbind(1 - cos(theta), 1 - sin(theta) - 0.5) + matrix(rnorm(2 * n, sd = 0.1), ncol = 2)
moon_data <- rbind(x1, x2)
moon_data <- as.data.frame(moon_data)
colnames(moon_data) <- c("x", "y")

Here, we generate two moon-shaped clusters by sampling points along two half circles and adding a bit of noise for realism.

It’s a good practice to standardize features before clustering, especially when features are on different scales.

# Standardize features for clustering
moon_data_scaled <- as.data.frame(scale(moon_data))

With our data ready, we can now apply the DBSCAN algorithm using the dbscan package. DBSCAN in R requires two main parameters: eps (the neighborhood radius) and minPts (the minimum number of points required to form a dense region).

# Parameters
epsilon <- 0.3
min_samples <- 5

# Run DBSCAN
db <- dbscan(moon_data_scaled, eps = epsilon, minPts = min_samples)

The cluster assignments are stored in db$cluster. In DBSCAN, points labeled as 0 are considered noise (outliers). To count the number of clusters (excluding noise):

# Number of clusters (excluding noise)
n_clusters <- length(setdiff(unique(db$cluster), 0))
cat("Estimated number of clusters:", n_clusters, "\n") # Should print 2

Here is an example of the plot you should see after running the visualization code above:

In this plot, each cluster is shown in a different color, and noise points (cluster 0) are displayed in black. The two moon-shaped clusters are clearly identified, demonstrating DBSCAN’s ability to find clusters of arbitrary shapes and to detect outliers.

Congratulations on successfully implementing the DBSCAN algorithm in R and visualizing the resulting clusters on a challenging "two moons" dataset! Practice is essential for mastering these concepts, so be sure to try out the upcoming exercises to reinforce your understanding. Good luck!