OPTICS Clustering Explanation - ML

OPTICS (Ordering Points To Identify the Clustering Structure) is a density-based clustering algorithm similar to DBSCAN clustering. Unlike DBSCAN which struggles with varying densities. OPTICS does not directly assign clusters but instead creates a reachability plot which visually represents clusters. The key concepts in OPTICS are:

• Core Distance: The minimum distance needed for a point to be classified as a core point. If a point does not have enough nearby neighbors its core distance is undefined.
• Reachability Distance: It is a measure of how difficult it is to reach from one point to another. It is calculated as the larger core distance of starting point and actual

What is Reachability Plot?

A reachability plot is a graph that helps visualize clustering structures. It shows the reachability distance of each point in the dataset. It makes it ordered way based on how OPTICS processes them.

Here clusters appear as valleys in the plot where lower reachability distances indicate dense regions while peaks represent sparse regions or noise.

Illustration of Core and Reachability Distances

To better understand the concept refer to the below image:

• Epsilon (Eps) = 6mm and MinPts = 5.
• The core distance of point p is 3mm meaning it needs at least 5 points within a 3mm radius to be considered as a core point.
• The reachability distance from q to p is 7mm (since q is farther than p's core distance).
• The reachability distance from r to p is 3mm (since r is within p's core distance).

It is more informative than DBSCAN as the reachability plot provides better understanding of clustering structure. Now we will learn about its working.

Step-by-Step Working of OPTICS

1. The algorithm selects a starting point and checks if it has at least MinPts neighbors within Eps.
2. If the point meets the density requirement it is marked as a core point and nearby points are then analyzed.
3. Reachability distance is computed for each neighboring point.
4. Points are then processed in order of their reachability distance hence forming a reachability plot.
5. Clusters appear as valleys i.e low reachability distances and noise appears as peaks i.e high reachability distances.

OPTICS vs. DBSCAN Algorithm

Implementing OPTICS in Python

Below is the Python implementation using scikit-learn to demonstrate OPTICS on a synthetic dataset of varying densities:

• OPTICS(min_samples=5, xi=0.05, min_cluster_size=0.05): Configures the OPTICS algorithm.
• labels=clustering.labels_: Retrieves cluster labels.
• plt.scatter(): Plots the clustering results.

from sklearn.cluster import OPTICS
from sklearn.datasets import make_blobs
import numpy as np
import matplotlib.pyplot as plt

X, _ = make_blobs(n_samples=300, centers=3, random_state=42)

clustering = OPTICS(min_samples=5, xi=0.05, min_cluster_size=0.05)
clustering.fit(X)

labels = clustering.labels_

plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='rainbow', edgecolor='k')
plt.title("OPTICS Clustering on Synthetic Data")
plt.xlabel("Feature 1")
plt.ylabel("Feature 2")
plt.show()

Output:

OPTICS is widely used for clustering algorithm that works well for identifying clusters of varying densities. It provides flexibility through reachability plots which allows dynamic cluster extraction. While computationally more expensive it is useful for complex datasets where density variation is significant.