Jason's Notebook

Density-Based Spatial Clustering of Application with Noise (DBSCAN)

2 min read

INFO

An unsupervised machine learning algorithm used for clustering data points based on density

  • Developed by: Martin Ester, Hans-Peter Kriegel, Jörg Sander, and Xiaowei Xu (1996)
  • Core Principle: Groups points into clusters based on the density of surrounding data, identifying core, border, and noise points
  • Search Strategy:
    • Define epsilon () — the neighborhood radius
    • Define minPts — minimum number of points to form a dense region
    • Expand clusters from core points using density reachability

Workflow

  1. Parameter Definition
    • Set : radius around each point
    • Set minPts: minimum number of neighbors required
  2. Cluster Formation
    • Identify core points with ≥ minPts neighbors within \epsilon
    • Label border points that are within \epsilon of a core point but not core themselves
    • Mark remaining points as noise

Code Example

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.cluster import DBSCAN
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import make_moons
 
# Generate synthetic transaction data (two interleaving patterns)
X, _ = make_moons(n_samples=300, noise=0.1, random_state=42)
 
# Standardize features
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
 
# Apply DBSCAN
dbscan = DBSCAN(eps=0.3, min_samples=5)
labels = dbscan.fit_predict(X_scaled)
 
# Convert results to DataFrame for analysis
df = pd.DataFrame(X_scaled, columns=['Transaction Amount', 'Transaction Frequency'])
df['Cluster'] = labels
 
# Visualizing the results
plt.figure(figsize=(8,6))
unique_labels = set(labels)
colors = [plt.cm.jet(float(i) / max(unique_labels + {1})) for i in unique_labels]
 
for label, color in zip(unique_labels, colors):
    subset = df[df['Cluster'] == label]
    plt.scatter(subset['Transaction Amount'], subset['Transaction Frequency'], color=color, label=f'Cluster {label}', edgecolors='k')
 
plt.xlabel("Transaction Amount (Standardized)")
plt.ylabel("Transaction Frequency (Standardized)")
plt.title("DBSCAN Clustering of Financial Transactions")
plt.legend()
plt.show()

Advantages

  • Detects clusters of arbitrary shapes
  • Robust to noise and outliers
  • Density-based approach uncovers meaningful structure without requiring number of clusters

Disadvantages

  • Sensitive to and minPts selection
  • Struggles with high-dimensional data
  • Computationally expensive for large datasets due to nearest-neighbor searches

Graph View

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