(K-Medoids) Using Partitional Clustering Methods to Describe Data

• Focus: Experiments in WEKA (K-Medoids)
• Course: Databases and Data Mining
• Instructor: Jamolbek Mattiev

Learning Objectives

• • Understand K-Medoids clustering
• • Perform experiments in WEKA
• • Analyze clustering cost
• • Compare with K-Means

What is Partitional Clustering?

• • Divides dataset into K clusters
• • Each object belongs to one cluster
• • Optimizes objective function

K-Medoids Overview

• • Similar to K-Means
• • Uses real data points as medoids
• • More robust to noise and outliers

Medoid Definition

• • Central representative object
• • Minimizes total distance within cluster
• • Must be actual dataset instance

Objective Function

• Minimize total dissimilarity:
• Cost = Σ distance(point, medoid)
• Lower cost → better clustering

Algorithm Steps (PAM)

• 1. Select K initial medoids
• 2. Assign points to nearest medoid
• 3. Try swapping medoids
• 4. Keep swap if cost decreases
• 5. Repeat until stable

Distance Measures

• • Manhattan distance (common)
• • Euclidean distance
• • Any valid dissimilarity measure

Step 1: Open WEKA Explorer

• • Launch WEKA
• • Click Explorer
• • Load dataset (.arff)
• • Go to Cluster tab

Step 2: Select K-Medoids

• • Click Choose
• • Select SimpleKMedoids (if available)
• • Or use PAM implementation

Step 3: Configure Parameters

• • Set number of clusters (K)
• • Choose distance function
• • Set seed value
• • Configure max iterations

Step 4: Run Clustering

• • Click Start
• • Observe medoids
• • Check cluster sizes
• • Record total cost

Experiment Design

• • Run K from 2 to 10
• • Record total cost
• • Identify optimal K
• • Compare cluster compactness

Interpreting Output

• • Selected medoids
• • Cluster assignments
• • Total within-cluster cost
• • Distribution of instances

Comparison: K-Means vs K-Medoids

• K-Means → mean centroid
• K-Medoids → actual data point
• K-Medoids more robust to outliers

Advantages of K-Medoids

• • Robust to noise
• • Works with arbitrary distances
• • Interpretable representatives

Limitations

• • Higher computational cost
• • Less scalable than K-Means
• • Sensitive to initial medoids

Advanced Variants

• • CLARA (large datasets)
• • CLARANS (randomized search)

Discussion Questions

• • When prefer K-Medoids over K-Means?
• • How does distance metric affect results?

Summary

• • K-Medoids minimizes total dissimilarity
• • Uses real data points as centers
• • WEKA allows experimental comparison
• • Suitable for noisy datasets

Cost vs Number of Clusters (Example)

Cost Reduction Over Iterations (Example)