Understanding K-Means Clustering for Unsupervised Learning
๐ Understanding K-Means Clustering for Unsupervised Learning
๐ง What is K-Means Clustering?
K-Means Clustering is an unsupervised learning algorithm that groups data into K distinct clusters based on similarity.
It finds centroids (cluster centers) such that data points are as close as possible to the centroid of their assigned cluster.
You don’t need labeled data. The algorithm learns patterns and structure from the input features alone.
๐ฏ Goal of K-Means
To partition a dataset into K clusters where:
Each data point belongs to the cluster with the nearest mean (centroid).
The total within-cluster variance (inertia) is minimized.
๐ How the K-Means Algorithm Works
Step-by-Step Process:
Initialize: Choose K (number of clusters) and randomly initialize K centroids.
Assign: Assign each data point to the nearest centroid.
Update: Recalculate centroids as the mean of all data points in a cluster.
Repeat steps 2 and 3 until:
Centroids stop changing (convergence), or
A maximum number of iterations is reached
๐ Objective Function
K-Means minimizes the Sum of Squared Errors (SSE):
SSE
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SSE=
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Where:
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: Cluster k
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ฮผ
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: Centroid of cluster k
๐ฅ
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x
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: A data point in cluster k
๐ Key Concepts
Term Meaning
Centroid The "center" of a cluster (mean position of all points in the cluster)
Cluster A group of similar data points
Inertia Measure of how internally coherent the clusters are (lower is better)
K Number of clusters (a hyperparameter you must choose)
๐ป K-Means in Python (Scikit-learn)
from sklearn.cluster import KMeans
from sklearn.datasets import make_blobs
import matplotlib.pyplot as plt
# Generate sample data
X, _ = make_blobs(n_samples=300, centers=4, random_state=42)
# Apply K-Means
kmeans = KMeans(n_clusters=4, random_state=42)
kmeans.fit(X)
# Plotting the clusters
plt.scatter(X[:, 0], X[:, 1], c=kmeans.labels_, cmap='viridis')
plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], s=200, c='red', marker='X')
plt.title("K-Means Clustering")
plt.show()
❓ How to Choose the Right K
1. Elbow Method
Plot the inertia (SSE) vs. number of clusters K.
The "elbow point" where SSE decreases sharply but levels off indicates the best K.
2. Silhouette Score
Measures how similar a point is to its cluster vs. other clusters.
Ranges from -1 to 1 (higher is better).
⚖️ Advantages of K-Means
✅ Simple and fast
✅ Efficient for large datasets
✅ Easy to interpret results
✅ Works well with spherical, equally sized clusters
❗ Limitations of K-Means
❌ Must choose K in advance
❌ Sensitive to initialization
❌ Sensitive to outliers and non-spherical clusters
❌ Doesn't handle overlapping or varying density well
๐ง Solution: Use K-Means++ initialization or try advanced clustering methods like DBSCAN, Gaussian Mixture Models (GMM), or Hierarchical Clustering.
๐ Real-World Applications
Domain Use Case
๐ฏ Marketing Customer segmentation
๐ E-commerce Product recommendation clustering
๐ธ Image Processing Image compression, color quantization
๐งฌ Bioinformatics Gene expression data clustering
๐ Finance Risk categorization, fraud pattern grouping
๐ Summary Table
Feature Description
Learning Type Unsupervised
Algorithm Type Clustering
Input Unlabeled data
Output Cluster assignments
Key Parameter Number of clusters (K)
Evaluation Methods Inertia, Silhouette Score, Davies-Bouldin Index
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