Blogs / Introduction to Clustering Algorithms: Concepts, Applications, and Key Algorithms

Introduction to Clustering Algorithms: Concepts, Applications, and Key Algorithms

آشنایی با الگوریتم‌های خوشه‌بندی: مفاهیم، کاربردها و الگوریتم‌های کلیدی

Introduction

Imagine you own an online store with millions of customers. How can you categorize them to offer the best recommendations? Or suppose you're a doctor wanting to group patients based on symptoms and genetics. This is exactly what Clustering does - discovering hidden patterns in unlabeled data and organizing them automatically.
Clustering is one of the foundational techniques in machine learning that plays a vital role in data analysis. This technique allows us to group similar data into meaningful clusters without manual labeling. From detecting financial fraud to discovering new drugs, clustering lies at the heart of many modern innovations.

What is Clustering and Why Does it Matter?

Clustering is a process where data is divided into groups (clusters) such that:
  • Data within each cluster has maximum similarity to each other
  • Data between different clusters has maximum difference from each other
This technique is part of unsupervised learning methods, as it doesn't require labeled data. Clustering helps us to:
  • Discover hidden patterns in complex data
  • Reduce data volume and simplify analysis
  • Improve machine learning model accuracy through proper preprocessing
  • Optimize business decisions with better customer understanding

Real-World and Amazing Applications of Clustering

1. Smart Marketing and Customer Experience Personalization

Major companies like Amazon and Netflix use clustering for customer segmentation. Instead of offering one generic suggestion to all customers, they divide them into different groups:
  • High-spending loyal customers interested in premium products
  • Seasonal buyers who only shop during sales
  • Price-sensitive customers looking for the best deals
  • Browsing users who view products but rarely purchase
This categorization helps digital marketing design more targeted and effective campaigns.

2. Disease Diagnosis and Precision Medicine

In AI in diagnosis and treatment, clustering helps physicians to:
  • Categorize cancer types based on genetics and symptoms
  • Divide diabetic patients into high-risk and low-risk groups
  • Discover patterns of unknown diseases in clinical data
  • Design personalized treatments for each patient group
For example, researchers using genetic data clustering have identified different Alzheimer's disease subgroups, each responding to specific treatments.

3. Fraud Detection and Security Anomalies

AI in cybersecurity systems uses clustering to identify unusual behaviors:
  • Suspicious bank transactions that violate user purchase patterns
  • Cyber attacks that deviate from normal traffic patterns
  • Phishing emails with different structures from regular emails
  • Suspicious user activities in organizational systems
Banks can determine within milliseconds whether a transaction is legitimate or likely fraudulent using clustering.

4. Social Network Analysis and Community Discovery

In social networks like Facebook and Twitter, clustering is used for:
  • Identifying user groups with common interests
  • Detecting online communities and influencers in each group
  • Predicting information spread and viral content
  • Discovering bots and fake accounts
These analyses help companies understand how information spreads through social networks and who the most influential people in each community are.

5. Image Processing and Computer Vision

In machine vision, clustering is used for:
  • Image segmentation into objects and background
  • Object and people recognition in images
  • Image compression by reducing color count
  • Visual pattern identification in medical analysis
For example, clustering is used in brain tumor detection from MRI images to separate healthy tissue from damaged tissue.

6. Intelligent Recommendation Systems

Recommendation systems use clustering for:
  • Grouping movies and series by content and style
  • Automatically categorizing products in online stores
  • Identifying similar users for new content suggestions
  • Discovering new trends in user preferences
Spotify uses clustering to categorize songs based on audio features and create personalized playlists.

7. Biology and Genomics

In autonomous scientific discovery, clustering is used for:
  • Classifying animal species based on DNA
  • Identifying genes related to diseases
  • Discovering new drugs by analyzing molecular structure
  • Evolutionary studies and understanding relationships between species
Researchers using COVID-19 genetic data clustering were able to identify and track different virus strains.

Basic and Fundamental Clustering Concepts

To understand clustering more deeply, we need to familiarize ourselves with its key concepts:

1. Distance and Similarity Metrics

Distance is a measure for assessing similarity or difference between data points. The most common metrics include:
Euclidean Distance: The straight-line distance between two points, calculated using the Pythagorean formula in 2D space. This distance is suitable for numerical data.
Manhattan Distance: The sum of coordinate differences, like moving in a city with perpendicular streets. This distance is useful when movement is only possible in horizontal and vertical directions.
Cosine Distance: Measures the angle between two vectors, suitable for text data and content analysis. This metric ignores vector magnitude and only compares their direction.
Mahalanobis Distance: A distance that considers variance and covariance of data, suitable for data with different scales.
Choosing the appropriate distance metric depends on data type and problem nature and directly impacts clustering quality.

2. Centroid

A centroid is a point representing the average coordinates of all points in a cluster. Simply put, the centroid is the "heart" of that group. This concept plays a fundamental role in algorithms like K-Means.
In some algorithms, instead of centroid, medoid is used, which is one of the actual data points (not a computational average) and is less sensitive to outliers.

3. Number of Clusters (K)

One of the most important challenges in clustering is determining the optimal number of clusters. Incorrect selection of this parameter can lead to:
  • Overfitting: Too many clusters where each cluster has only a few points
  • Underfitting: Too few clusters where different groups are placed in one cluster
Methods like Elbow Method and Silhouette Score are used to determine the optimal number of clusters.

4. Intra-cluster vs Inter-cluster

Good clustering should have:
  • Low intra-cluster distance (points within clusters are close together)
  • High inter-cluster distance (clusters are far apart)
These criteria are used to evaluate clustering quality.

5. Outliers and Noise

Outliers are points that don't belong to any cluster and deviate from the overall data pattern. Some algorithms like DBSCAN can identify these points as noise.

Main Clustering Algorithms and Their Comparison

1. K-Means: Simple, Fast, and Popular

K-Means is the most popular and well-known clustering algorithm that, due to its simplicity and high speed, is the first choice of many data science experts.

How K-Means Works:

  1. Choose number of clusters (K): First, specify the desired number of clusters
  2. Initialize centers: K points are randomly selected as initial centers
  3. Assign points: Each point is assigned to the nearest center
  4. Update centers: Cluster centers are calculated based on the mean of points in each cluster
  5. Iterate: Steps 3 and 4 are repeated until convergence

K-Means Advantages:

  • High speed: Very fast for large datasets
  • Implementation simplicity: Easy to implement and understand
  • Scalability: Works with millions of data points
  • Memory efficiency: Requires minimal memory

K-Means Limitations:

  • Need to specify K beforehand: You must know the number of clusters in advance
  • Sensitivity to initial centers: Results depend on random initial selection
  • Only spherical clusters: Cannot detect complex shapes
  • Sensitivity to outliers: Outliers can corrupt results

K-Means Improvements:

K-Means++: A smarter method for selecting initial centers that ensures faster convergence and better results.
Mini-Batch K-Means: For very large datasets, uses small subsets instead of all data and increases speed several times.

2. Hierarchical Clustering: Data Hierarchy

Hierarchical clustering creates a tree structure of clusters called a dendrogram, instead of dividing data into a specific number of clusters.

Two Types of Hierarchical Clustering:

1. Agglomerative - Bottom-up:
  • Each point initially is an independent cluster
  • At each step, two close clusters are merged
  • This process continues until reaching one large cluster
2. Divisive - Top-down:
  • All points initially are in one cluster
  • At each step, one cluster is divided into two clusters
  • This process continues until reaching single-point clusters

Linkage Criteria:

  • Single Linkage: Minimum distance between two points from different clusters
  • Complete Linkage: Maximum distance between two points from different clusters
  • Average Linkage: Average distance between all point pairs
  • Ward's Method: Minimum increase in intra-cluster variance

Hierarchical Clustering Advantages:

  • No need to specify number of clusters: You can later choose the number by cutting the dendrogram
  • Overall view of data structure: Dendrogram provides good visual representation of relationships
  • High interpretability: Results are easily interpretable

Limitations:

  • High time complexity: Very slow for large data (O(n³))
  • Sensitivity to noise: Noise can corrupt the tree structure
  • Irreversible: Once two clusters merge, they cannot be separated

3. DBSCAN: Detecting Complex Shapes and Anomalies

DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based algorithm considered one of the most powerful methods for clustering data with irregular shapes and detecting anomalies.

DBSCAN Key Concepts:

Epsilon (ε): Neighborhood radius - the distance within which points are considered neighbors.
MinPts: Minimum points - minimum number of points required to form a cluster.

Point Types in DBSCAN:

  1. Core Points: Points with at least MinPts neighbors within radius ε
  2. Border Points: Points within radius ε of a core point but not core themselves
  3. Noise Points: Points that are neither core nor in the neighborhood of any core point

How DBSCAN Works:

  1. A random point is selected
  2. If the point is core, a new cluster starts
  3. All reachable points from this core point are added to the cluster
  4. Process repeats for unvisited points

DBSCAN Advantages:

  • Arbitrary shape detection: Detects clusters with complex and irregular shapes
  • Automatic noise detection: Automatically identifies anomalies
  • No need for cluster count: Automatically determines the number of clusters
  • Robust against outliers: Outliers don't affect clustering

Limitations:

  • Parameter sensitivity: Selection of ε and MinPts greatly affects results
  • Problem with varying densities: Poor performance if clusters have different densities
  • Lower efficiency in high dimensions: In high dimensions, distance concept loses meaning
Practical Note: DBSCAN is very suitable for geographic data like store locations or identifying crime-prone urban areas.

4. Mean Shift: Following Data Density

Mean Shift is an algorithm that tries to move cluster centers toward areas with highest data density. This algorithm is like a ball rolling down a slope to the lowest point.

How it Works:

  1. A point is selected as initial center
  2. Mean of all points within a specific radius is calculated
  3. Center moves toward this mean
  4. Process repeats until convergence

Advantages:

  • No need for cluster count: Automatically determines number of clusters
  • Arbitrary shape detection: Not limited to specific shapes
  • Finding multiple modes: Can identify multiple density centers

Limitations:

  • Bandwidth parameter sensitivity: Choosing appropriate radius is very important
  • High computational complexity: Slow for large datasets
  • Memory intensive: Requires significant memory

5. Gaussian Mixture Models (GMM): Probabilistic Clustering

GMM is a probabilistic approach to clustering that assumes data is generated from a mixture of multiple Gaussian (normal) distributions. Unlike K-Means which assigns each point to one cluster, GMM gives each point probability of belonging to each cluster.

How GMM Works:

  1. Initial parameters of Gaussian distributions (mean, variance, weight) are set
  2. Expectation (E) step: Probability of each point belonging to each distribution is calculated
  3. Maximization (M) step: Distribution parameters are updated based on probabilities
  4. Steps 2 and 3 are repeated until convergence (EM algorithm)

GMM Advantages:

  • Soft Clustering: Each point can belong to multiple clusters
  • High flexibility: Can model elliptical clusters with different orientations and sizes
  • Probabilistic basis: Enables statistical analysis and uncertainty calculation
  • Covariance learning: Learns relationships between features

Limitations:

  • Need to specify component count: Must specify number of Gaussian distributions
  • Computational complexity: More intensive computations than K-Means
  • Sensitivity to initial values: May reach local optimum
  • Gaussian distribution assumption: May not be suitable for non-Gaussian distributed data
Real Application: GMM is used in facial recognition and image processing for modeling image pixels and separating background from foreground.

6. OPTICS: Advanced DBSCAN Version

OPTICS (Ordering Points To Identify the Clustering Structure) is a density-based algorithm that solves DBSCAN's problem with varying densities.

OPTICS Advantages:

  • Robust against density changes: Can identify clusters with different densities
  • Less parameter tuning needed: Only needs one main parameter
  • Generates ordering: Output is visualizable with Reachability plot

7. Spectral Clustering: Clustering with Graph Theory

Spectral Clustering uses concepts from graph theory and is especially suitable for data with complex relationships.

How it Works:

  1. A graph is constructed from data (each point is a vertex)
  2. Similarity matrix is calculated
  3. Eigenvectors of this matrix are extracted
  4. K-Means is applied on eigenvectors

Advantages:

  • Non-convex structure detection: Can detect clusters with very complex shapes
  • Good performance in high dimensions: Robust to high dimensions
  • Strong mathematical foundation: Graph theory provides solid mathematical backing

Limitations:

  • High computational complexity: Computing eigenvectors for large data is time-consuming
  • High memory requirement: Similarity matrix can be very large

Methods for Determining Optimal Number of Clusters

One of the main challenges in clustering is determining the optimal number of clusters. Various methods exist for this purpose:

1. Elbow Method

In this method, we plot the Within-Cluster Sum of Squares (WCSS) for different numbers of clusters. The point where the graph slope sharply decreases (like an elbow) is chosen as the optimal number.

2. Silhouette Score

Silhouette coefficient measures how similar a point is to its own cluster compared to other clusters. This coefficient ranges from -1 to 1:
  • Close to 1: Point is in appropriate cluster
  • Close to 0: Point is on the border of two clusters
  • Negative: Point is likely in wrong cluster

3. Davies-Bouldin Index

This criterion calculates the ratio of intra-cluster distance to inter-cluster distance. Lower value indicates better clustering.

4. Calinski-Harabasz Index

This criterion calculates the ratio of between-cluster variance to within-cluster variance. Higher value indicates better clustering.

5. Gap Statistic

This method compares clustering of real data with clustering of random data and selects the number of clusters that creates the maximum difference (gap).

Practical Challenges and Solutions in Clustering

1. Curse of Dimensionality

In high-dimensional spaces, the concept of distance loses meaning and all points are at approximately the same distance from each other.
Solution: Use dimensionality reduction methods like PCA, t-SNE, or UMAP before clustering.

2. Feature Scaling

Features with different scales can distort clustering results.
Solution: Normalize or standardize data before clustering (StandardScaler or MinMaxScaler).

3. Sensitivity to Outliers

Many algorithms like K-Means are sensitive to outliers.
Solution: Use robust algorithms like DBSCAN, or preprocess and remove outliers with methods like Isolation Forest.

4. Categorical Data

Most clustering algorithms are designed for numerical data and don't work with categorical data.
Solution: Use distance metrics specific to categorical data (like Hamming Distance) or algorithms like K-Modes.

5. Result Interpretability

Understanding and explaining clustering results, especially for non-experts, can be challenging.
Solution: Use visualization techniques, analyze characteristics of each cluster, and document the clustering process carefully.

Clustering Tools and Libraries

For implementing clustering algorithms, powerful tools are available:

Python

Scikit-learn: The most comprehensive Python library with implementations of most clustering algorithms.
python
from sklearn.cluster import KMeans, DBSCAN, AgglomerativeClustering
from sklearn.mixture import GaussianMixture
SciPy: For hierarchical clustering with excellent visualization capabilities.
HDBSCAN: Improved version of DBSCAN for varying densities.

R

stats package: Basic clustering implementations.
cluster package: More advanced algorithms.

Other Tools

MATLAB: Clustering tools in Statistics and Machine Learning Toolbox.
Apache Spark MLlib: For very large and distributed data clustering.
TensorFlow and PyTorch: For implementing deep clustering algorithms.

Deep Clustering

With advances in deep learning, new clustering methods have emerged:

Autoencoders for Clustering

Autoencoders are neural networks that can map data to lower-dimensional space. Clustering in this compressed space usually yields better results.

Deep Embedded Clustering (DEC)

This method simultaneously performs representation learning and clustering and can discover more complex patterns.

Clustering in Vision Transformers

Vision Transformers (ViT) models can be used for clustering images without labels.

Advanced and Emerging Applications

1. Clustering in NLP and Text Analysis

In natural language processing, clustering is used for:
  • Document categorization and news articles: Automatic grouping of thousands of articles by topic and content for better information organization
  • Sentiment analysis and opinion grouping: Separating positive, negative, and neutral customer reviews for better feedback understanding
  • Topic discovery (Topic Modeling): Automatic identification of main topics in large text collections without manual labeling
  • Automatic text summarization: Selecting key and representative sentences from each cluster to create meaningful summaries
Transformer models like BERT generate rich embeddings that can be clustered.

2. Clustering in Time Series

Time series forecasting can benefit from clustering:
  • Identifying seasonal patterns in sales data: Discovering recurring trends like sales increases during holidays or seasonal changes
  • Customer grouping based on purchase behavior over time: Detecting customers with similar purchase patterns for better recommendations
  • Anomaly detection in sensor data: Identifying unusual behaviors in industrial equipment before complete failure
Specific algorithms like TimeClust and k-Shape are designed for time series clustering.

3. Clustering in IoT and Edge AI

With the growth of IoT and Edge AI, clustering is used for:
  • Grouping sensors with similar behavior: Identifying sensors producing similar data to reduce redundancy and optimize network
  • Fault detection in industrial devices: Predictive maintenance by analyzing performance patterns and identifying deviations from normal behavior
  • Energy consumption optimization in smart homes: Grouping devices by consumption pattern for intelligent energy management

4. Clustering in Smart Cities

AI in smart city development uses clustering for:
  • Traffic analysis and congestion point identification: Discovering areas facing heavy traffic at specific times for better urban planning
  • Public transportation route optimization: Determining best routes based on citizen mobility pattern analysis
  • High energy consumption area identification: Finding urban areas with highest energy consumption for optimization actions
  • Urban service need prediction: Estimating needs for services like waste collection or park maintenance based on past patterns

5. Clustering in Metaverse and Virtual Reality

  • User categorization based on virtual space behavior: Identifying user groups with similar interests and behaviors for better social experiences
  • Experience personalization for each user group: Delivering customized content and environments based on each cluster's preferences
  • Community identification and social groups in Metaverse: Automatic discovery of friendship groups and online communities to strengthen interactions

Comprehensive Comparison of Clustering Algorithms

Algorithm Speed Scalability Need K Cluster Shape Noise Detection Complexity Best Use Case
K-Means Very Fast Excellent Yes Spherical No Low Large data with spherical clusters
Hierarchical Slow Poor No Arbitrary No High Small data needing hierarchy
DBSCAN Medium Good No Arbitrary Yes Medium Data with varying density and noise
GMM Medium Good Yes Elliptical No High Probabilistic clustering
Mean Shift Slow Poor No Arbitrary No High Small data with varying density
Spectral Slow Poor Yes Complex No High Graph data and complex relationships

Guide to Choosing the Right Algorithm

When you have large datasets:
  • K-Means or Mini-Batch K-Means: These algorithms with linear complexity can process millions of data points in short time and are optimized for large scales.
When cluster shapes are irregular:
  • DBSCAN or Spectral Clustering: These methods aren't limited to spherical shapes and can detect ring-shaped, spiral, or any arbitrary shape clusters.
When you need hierarchical clustering:
  • Hierarchical Clustering: If you want to see tree relationships between clusters or need clustering at different levels, this algorithm is ideal.
When there's a lot of noise in data:
  • DBSCAN or HDBSCAN: These algorithms automatically identify and separate outliers without negatively affecting clustering quality.
When you need membership probabilities:
  • Gaussian Mixture Models: If you need to know with what probability each point belongs to each cluster or want soft clustering, GMM is suitable.
When you don't know the number of clusters:
  • DBSCAN, Mean Shift, or HDBSCAN: These algorithms automatically determine the number of clusters based on data structure and don't need K specified beforehand.

Best Practices

1. Careful Data Preprocessing

  • Standardization: Use StandardScaler or MinMaxScaler - transform all features to the same scale so features with larger values don't dominate results.
  • Removing redundant features: Use PCA or Feature Selection - reduce dimensions to remove useless features and improve speed and accuracy.
  • Handling missing values: Imputation or deletion - fill missing values with mean, median, or more advanced methods or delete incomplete rows.
  • Detecting and managing outliers: Before clustering - identify and remove or manage outliers that can distort results.

2. Comprehensive Evaluation

  • Use multiple metrics for evaluation (Silhouette, Davies-Bouldin, Calinski-Harabasz) - no single metric is complete, so combining several provides comprehensive view.
  • Visualizing results with t-SNE or UMAP - transform multidimensional data to 2D or 3D for better viewing and understanding cluster distribution.
  • Analyzing cluster characteristics and understanding their meaning - examine common features of each cluster to understand why data is grouped together.
  • Validation with domain knowledge - compare results with expert knowledge to ensure clusters are logical.

3. Parameter Tuning

  • Use Grid Search or Random Search to find optimal parameters - systematic search in parameter space to find best combination.
  • Experiment with different K values and compare results - test different numbers of clusters and use evaluation metrics to select best number.
  • Consider trade-off between quality and execution time - sometimes a faster algorithm with slightly lower quality is better than slow algorithm with high quality.

4. Documentation

  • Record reasons for choosing algorithm and parameters - document why decisions were made for future review and learning from experiences.
  • Maintain experiment history and results - save all experiments even unsuccessful ones to avoid repeating mistakes.
  • Explain cluster meanings to stakeholders - translate technical results into understandable language for business decision-makers.

Future of Clustering and Emerging Trends

1. Federated Learning and Clustering

Federated learning enables clustering without sharing sensitive data - critical for banks and hospitals.

2. Self-Learning Clustering

Self-improving AI models can automatically adjust their parameters and optimize without human intervention.

3. Multimodal Clustering

Multimodal models can cluster text, image, and audio simultaneously.

4. Quantum Computing and Clustering

Quantum AI can dramatically increase clustering speed at very large scales.

5. Privacy-Preserving Clustering

With increasing concerns about privacy in the AI era, algorithms that cluster data without revealing sensitive information are gaining importance.

Conclusion

Clustering is one of the most powerful and practical artificial intelligence techniques that plays a fundamental role in discovering hidden patterns and organizing unlabeled data. From smart marketing to disease diagnosis, from fraud detection to building AI applications, clustering lies at the heart of today's innovations.
Choosing the right algorithm depends on data nature, analysis goals, and computational constraints. K-Means for speed, DBSCAN for complex shapes, Hierarchical for understanding relationships, and GMM for probabilistic analysis - each is unmatched in its place.
With advances in technologies like deep learning, quantum computing, and Edge AI, the future of clustering is brighter than ever. Smarter, faster, and more interpretable algorithms are coming that can analyze more complex data with greater accuracy.
Final Note: Clustering is a tool, not a goal. Real success comes when clustering results lead to better decisions, deeper data understanding, and ultimately creating real value.