Interview Prep
Career
GenAI
Prompt Engg
ChatGPT
LLM
Langchain
RAG
AI Agents
Machine Learning
Deep Learning
GenAI Tools
LLMOps
Python
NLP
SQL
AIML Projects

Reading list

Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

Spectral Clustering: A Comprehensive Guide for Beginners

K
Keerthana Last Updated : 14 Oct, 2024
6 min read

Introduction

When given a bunch of movies to organize, you might sort them based on similarity measures such as genre, year of release, casting, revenue generated, and so on. While you categorize them based on a measure, it doesn’t mean that a measure used by others is of no good. Our perception of data is greatly influenced by the clustering measure being used. When you believe that two sci-fi movies belong to the same cluster, someone else might consider two movies released in the same year to be in the same cluster. Because you might have used the genre as a measure to cluster and the other person might have used the year of release as a measure.

Learning Objectives:

  • Understand the concept of clustering and how it differs from classification
  • Learn about the two major approaches to clustering: compactness and connectivity
  • Grasp the key steps involved in the spectral clustering algorithm
  • Familiarize with the advantages and limitations of spectral clustering

This article was published as a part of the Data Science Blogathon

Table of contents

Classifications vs Clustering

In machine learning, humans widely use clustering, an unsupervised algorithm that groups unlabeled data points based on similarity and distance measures. If the data points are labeled, the grouping is known as classification. Many applications utilize clustering algorithms, such as anomaly detection, image segmentation, search result grouping, market segmentation, and social network analysis. Clustering is one of the primary steps in exploratory data analysis for visualizing similarity and identifying hidden patterns in data points. The goal of clustering is to uncover similarities within a cluster and differences between clusters.

Support Vector Machines, Decision trees, Random forests, Linear classifiers and Neural networks are few classification algorithms whereas K means clustering, Fuzzy analysis clustering, Mean shift, DBSCAN and Spectral are clustering algorithms.

Classification vs clustering

There are two major approaches in clustering. They are:

  • Compactness
  • Connectivity

In compactness, the points are closer to each other and are compact towards the cluster center. Distance is used as a measure to compute closeness. There are different types of distance metrics that are in use. A few of them are Euclidean distance, Manhattan distance, Minkowski distance, and Hamming distance. K-means algorithm uses the compactness approach. In connectivity, the points in a cluster are either immediately next to each other (epsilon distance) or connected. Even if the distance is less, the algorithm does not place them in the same cluster. Spectral Clustering Algorithm is one of the techniques that follows this approach.

types of clustering

How to do Spectral Clustering?

The three major steps involved in Spectral Clustering Algorithm are: constructing a similarity graph, projecting data onto a lower-dimensional space, and clustering the data. Given a set of points S in a higher-dimensional space, it can be elaborated as follows:

  1. Form a distance matrix
  2. Transform the distance matrix into an affinity matrix A
  3. Compute the degree matrix D and the Laplacian matrix L = D – A.
  4. Find the eigenvalues and eigenvectors of L.
  5. With the eigenvectors of k largest eigenvalues computed from the previous step form a matrix.
  6. Normalize the vectors.
  7. Cluster the data points in k-dimensional space.
How to do Spectral Clustering?

Pros and Cons of Spectral Clustering

Spectral clustering helps us overcome two major problems in clustering: one being the shape of the cluster and the other is determining the cluster centroid. K-means algorithm generally assumes that the clusters are spherical or round i.e. within k-radius from the cluster centroid. In K-means, the algorithm requires many iterations to determine the cluster centroid. In spectral clustering, the clusters do not adhere to a fixed shape or pattern. The algorithm assigns points that are far apart but connected to the same cluster, while points that are close to each other could belong to different clusters if they are not connected. This suggests that the algorithm may be effective for data with varying shapes and sizes.

When compared with other algorithms, it is computationally fast for sparse datasets of several thousand data points. You don’t need the actual dataset to work with. Although computing eigenvalues and eigenvectors for large datasets and then performing clustering may be costly, the algorithms aim to reduce the cost. One must fix the number of clusters (k) before initiating the procedure.

Where can I use spectral clustering?

Spectral clustering has its application in many areas which includes: image segmentation, educational data mining, entity resolution, speech separation, Spectral Clustering Algorithm of protein sequences, text image segmentation. Although spectral clustering is a technique based on graph theory, it is used to identify communities of vertices in a graph based on the edges connecting them. This method is flexible and allows us to cluster non-graph data as well either with or without the original data.

Python packages for spectral clustering: spectralcluster. SpectralCluster is a python library that has inbuilt code for spectral clustering. There are other packages with which we can implement the spectral clustering algorithm.
Let us try an example with spectral clustering algorithm available from sklearn package.
Python Code:

from spectralcluster import SpectralClusterer
from sklearn.cluster import SpectralClustering
from sklearn.datasets import make_blobs
import matplotlib.pyplot as plt
from numpy import random


clusterer = SpectralClusterer(
    min_clusters=2,
    max_clusters=100)


X = random.randint(1,10,(3,4))
labels = clusterer.predict(X)
print(labels)

random.seed(1)
x, _ = make_blobs(n_samples=400, centers=4, cluster_std=1.5)
plt.scatter(x[:,0], x[:,1])
plt.show()

where X is a NumPy array of shape (n_samples, n_features) and the returned labels is a NumPy array of shape (n_samples, ).

Clustering with the spectral clustering and visualizing the data

sc=SpectralClustering(n_clusters=4).fit(x)
SpectralClustering(affinity='rbf', assign_labels='kmeans', coef0=1, degree=3,
                   eigen_solver=None, eigen_tol=0.0, gamma=1.0,
                   kernel_params=None, n_clusters=4, n_components=None,
                   n_init=10, n_jobs=None, n_neighbors=10, random_state=None)
labels = sc.labels_
plt.scatter(x[:,0], x[:,1], c=labels)
plt.show()
print(sc)
Clustering with the spectral clustering and visualizing the data

Let’s try changing the number of clusters.

f = plt.figure()
f.add_subplot(2, 2, 1)
for i in range(2, 6):
 sc = SpectralClustering(n_clusters=i).fit(x)
 f.add_subplot(2, 2, i-1)
 plt.scatter(x[:,0], x[:,1], s=5, c=sc.labels_, label="n_cluster-"+str(i))
 plt.legend()
plt.show()
Let's try changing the number of clusters.

Conclusion

Spectral clustering is a powerful technique that uses eigenvectors to partition data into clusters, overcoming the limitations of traditional methods like K-means. It can effectively handle non-linearly separable data and clusters of arbitrary shapes. While computationally expensive for large datasets, Spectral Clustering Algorithm finds applications in diverse areas such as image segmentation, speech separation, and network analysis. By leveraging graph theory and linear algebra concepts, this method identifies natural groupings in data based on connectivity and affinity measures. As demonstrated, spectral clustering offers an excellent option when dealing with complex, non-convex cluster structures, providing valuable insights into the inherent patterns within datasets.

Key Takeaways:

  • Spectral clustering is an effective technique for partitioning non-linearly separable data into clusters of arbitrary shapes
  • It overcomes the limitations of centroid-based methods like K-means by using eigenvectors and connectivity measures
  • Spectral clustering is useful for applications like image segmentation, speech separation, and social network analysis
  • While computationally expensive for large datasets, it offers a powerful solution for complex, non-convex cluster structures

Frequently Asked Questions

Q1. What is meant by spectral clustering?

A. Spectral clustering partitions data based on affinity, using eigenvalues and eigenvectors of similarity matrices to group data points into clusters, often effective for non-linearly separable data.

Q2. What is the difference between K-means and spectral clustering?

A. K-means partitions data based on centroids and distances, suitable for convex clusters, while spectral clustering uses eigenvectors to find more complex clusters in non-linear datasets.

Q3. What is the objective function of spectral clustering?

A. The objective function of spectral clustering aims to minimize the normalized cut or ratio cut, quantifying the dissimilarity between clusters while maximizing similarity within clusters using eigenvectors.

Q4. What are spectral methods for graph clustering?

A. Spectral methods for graph clustering use eigenvalues and eigenvectors of matrices derived from graph structures to partition nodes into clusters based on similarities, offering effective solutions for complex network structures.

The media shown in this article are not owned by Analytics Vidhya and is used at the Author’s discretion. 

blugathonSpectral Clustering
K
Keerthana

Free Courses

Generative AI 4.7

Generative AI - A Way of Life

Explore Generative AI for beginners: create text and images, use top AI tools, learn practical skills, and ethics.
Large Language Models 4.5

Getting Started with Large Language Models

Master Large Language Models (LLMs) with this course, offering clear guidance in NLP and model training made simple.
Prompt Engineering 4.6

Building LLM Applications using Prompt Engineering

This free course guides you on building LLM apps, mastering prompt engineering, and developing chatbots with enterprise data.
LlamaIndex 4.8

Improving Real World RAG Systems: Key Challenges & Practical Solutions

Explore practical solutions, advanced retrieval strategies, and agentic RAG systems to improve context, relevance, and accuracy in AI-driven applications.
RAG systems using LlamaIndex 4.7

Microsoft Excel: Formulas & Functions

Master MS Excel for data analysis with key formulas, functions, and LookUp tools in this comprehensive course.

Recommended Articles

Responses From Readers

Clear

y2MP3
y2MP3

This guide is fantastic for beginners! I love how clearly you explained the concepts behind spectral clustering. The visuals really helped me understand the process better. Can't wait to try it out on my own datasets!

123

Write for us

Write, captivate, and earn accolades and rewards for your work
  • Reach a Global Audience
  • Get Expert Feedback
  • Build Your Brand & Audience
  • Cash In on Your Knowledge
  • Join a Thriving Community
  • Level Up Your Data Science Game
imag

We use cookies essential for this site to function well. Please click to help us improve its usefulness with additional cookies. Learn about our use of cookies in our Privacy Policy & Cookies Policy.

Show details