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

Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is an unsupervised learning method. It groups data points that are close to each other while also identifying those data points that are in sparse regions. This method does not require the number of clusters to be known in advance, unlike the k-means method. This method can identify clusters of varying shapes, and outliers can also be identified.

The Two Fundamental Parameters

Max Distance (Epsilon): The greatest distance at which two locations can be regarded as neighbors.
Minimum Points (MinPts): The bare minimum of data points needed to create a dense zone within a (epsilon) radius

Let's consider the following data points:
(1,2), (2,2), (2,3), (3,2)
(8,7), (8,8), (7,8), (7,7)
(5,5)

Step 1: Pick a random point
Example: (2,2)

Step 2: Count neighbors within Epsilon 1.5 radius
Points near (2,2):
(1,2)
(2,3)
(3,2)
Total = 4 → ≥ MinPts (3)
so, (2,2) becomes a Core Point

Step 3: Expand Cluster
All density-reachable points from this core point form Cluster 1
Same process finds Cluster 2.
Final Clustering Result
Cluster 1:
(1,2), (2,2), (2,3), (3,2)
Cluster 2:
(8,7), (8,8), (7,8), (7,7)
Noise:
(5,5)
USE CASE 1: Healthcare Patient Grouping using DBSCAN : Hospitals often need to group patients with similar characteristics to: Identify high-risk patients, Personalize treatment plans, Optimize resource allocation, Improve healthcare management

import pandas as pd from sklearn.preprocessing import StandardScaler from sklearn.cluster import DBSCAN import numpy as np # Load data # download from: # https://www.pythonplaza.com/healthcare_patient_dataset.html df = pd.read_csv("patients_data.csv") # Features used for clustering X = df[['Age', 'BMI', 'Blood_Pressure', 'Cholesterol', 'Hospital_Visits']] # Scale data scaler = StandardScaler() X_scaled = scaler.fit_transform(X) # Train DBSCAN model dbscan = DBSCAN(eps=1.5, min_samples=5) df['Cluster'] = dbscan.fit_predict(X_scaled) # Print cluster assignments print(df[['Cluster']].value_counts()) # New patient? new_patient = [[33, 28.0, 139, 210, 4]] # Apply SAME scaling new_patient_scaled = scaler.transform(new_patient) # ------------------------------ # DBSCAN prediction logic # ------------------------------ # DBSCAN has NO predict() method # We assign cluster using nearest core point (common approach) labels = df['Cluster'].values # Remove noise points (-1) valid_points = X_scaled[labels != -1] valid_labels = labels[labels != -1] # Compute distances from new patient to all points distances = np.linalg.norm(valid_points - new_patient_scaled, axis=1) # Find nearest point nearest_index = np.argmin(distances) cluster = valid_labels[nearest_index] print("Patient belongs to Cluster:", cluster)

USE CASE 2: Use DBSCAN for customer segmentation in Market Basket Analysis. Instead of finding which products are purchased together (like Apriori or FP-Growth), use DBSCAN to group customers based on their purchasing behavior. Once customers are clustered, you can create targeted promotions and personalized recommendations for each segment.

import pandas as pd from sklearn.cluster import DBSCAN from sklearn.preprocessing import StandardScaler import numpy as np # ---------------------------------- # Step 1: Sample Market Basket Data # ---------------------------------- data = pd.DataFrame({ 'Customer': ['C001','C002','C003','C004','C005','C006','C007','C008'], 'Bread': [12,10,11,1,0,2,6,5], 'Milk': [10,8,9,2,1,1,5,6], 'Eggs': [8,7,6,1,2,0,4,5], 'Beer': [0,1,0,10,12,9,4,5], 'Chips': [1,0,1,8,10,7,3,4] }) # Load data (if using file instead) # data = pd.read_csv("customer_shopping.csv") print("Original Data") print(data) # ---------------------------------- # Step 2: Select Features # ---------------------------------- X = data[['Bread', 'Milk', 'Eggs', 'Beer', 'Chips']] # ---------------------------------- # Step 3: Scale Features # ---------------------------------- scaler = StandardScaler() X_scaled = scaler.fit_transform(X) # ---------------------------------- # Step 4: Train DBSCAN Model # ---------------------------------- dbscan = DBSCAN(eps=1.5, min_samples=2) data['Cluster'] = dbscan.fit_predict(X_scaled) print("\nCluster Assignments") print(data[['Customer', 'Cluster']]) # ---------------------------------- # Step 5: Cluster Profiles # ---------------------------------- print("\nCluster Profiles (Mean of Original Data)") cluster_profiles = data.groupby('Cluster')[['Bread','Milk','Eggs','Beer','Chips']].mean() print(cluster_profiles.round(2)) # ---------------------------------- # Step 6: Test New Customer # ---------------------------------- new_customer = pd.DataFrame({ 'Bread': [11], 'Milk': [9], 'Eggs': [7], 'Beer': [1], 'Chips': [1] }) new_customer_scaled = scaler.transform(new_customer) # ---------------------------------- # DBSCAN has NO predict() # So we assign cluster by nearest neighbor # ---------------------------------- X_scaled_arr = np.array(X_scaled) labels = np.array(data['Cluster']) # Remove noise points (-1) valid_mask = labels != -1 valid_X = X_scaled_arr[valid_mask] valid_labels = labels[valid_mask] # Compute distances to all valid points distances = np.linalg.norm(valid_X - new_customer_scaled, axis=1) nearest_index = np.argmin(distances) predicted_cluster = valid_labels[nearest_index] print("\nNew Customer") print(new_customer) print(f"\nPredicted Cluster: {predicted_cluster}") # ---------------------------------- # Step 7: Recommendation Logic # ---------------------------------- if predicted_cluster == 0: print("Recommendation: Bread, Milk, Eggs promotions") elif predicted_cluster == 1: print("Recommendation: Beer and Chips promotions") else: print("Recommendation: Mixed basket offers")