Comparison of Kernel Functions in SVM Classification

Comparison of Kernel Functions in SVM Classification#

🌟 Motivation#

Support Vector Machines (SVMs) rely heavily on kernel functions to transform data into higher-dimensional spaces where it becomes easier to separate classes linearly. Different kernels provide different mappings and impact the classifier’s performance, complexity, and generalization.

This project explores:

  • How various kernel functions affect SVM classification.

  • The mathematical intuition behind kernel transformations.

📌 What You Will Do in This Project#

Implement or use an existing SVM classifier and compare its performance with multiple kernels on a standard classification dataset.

You will:

  • Train SVM models with different kernel functions:

    • Linear kernel

    • Polynomial kernel (with varying degrees)

    • Radial Basis Function (RBF) kernel

    • (Optional) Sigmoid or custom kernels

  • Analyze the mathematical effect of kernels on data transformation and decision boundaries.

  • Evaluate classification accuracy and computational aspects.

  • Discuss pros and cons of each kernel in practice.

🔍 Key Concepts You’ll Master#

  • Kernel trick and feature space transformations

  • SVM decision functions and margin maximization

  • Properties of linear, polynomial, RBF, and sigmoid kernels

🚧 Core Tasks (Implementation Details)#

  • Select a suitable dataset (e.g., UCI Iris or Breast Cancer).

  • Train SVM classifiers using scikit-learn’s SVC with specified kernels.

  • For polynomial kernels, vary the degree parameter and observe effects.

  • Measure and compare classification accuracy, training time, and model complexity.

  • Visualize decision boundaries for 2D feature subsets (if possible).

  • Provide mathematical explanation of each kernel’s transformation.

📝 Reporting: Analysis and Insights#

Your report (~2 pages) should include:

  • Theoretical overview of kernel functions and their effects.

  • Quantitative comparison of accuracy and computational cost.

  • Visualizations of decision boundaries.

  • Discussion of when to prefer each kernel based on data characteristics and task requirements.

✅ Summary Table#

Component

Description

Dataset

UCI Iris, Breast Cancer, or similar classification dataset

Goal

Compare SVM performance across different kernel functions

Key Concepts

Kernel trick, feature mapping, decision boundaries, overfitting risk

Core Tasks

Train SVM with linear, polynomial (vary degree), RBF, (optional sigmoid) kernels; evaluate accuracy and cost

Evaluation

Classification accuracy, training time, complexity analysis

Tools

scikit-learn, NumPy, matplotlib
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