What is a support vector machine (SVM) algorithm in C and how is it implemented?

Table of Contents

• Introduction
• Core Concepts of SVM
  • What is a Support Vector Machine?
  • Key Components of SVM
  • SVM Optimization Objective
• SVM Implementation in C
  • Simple Linear SVM Implementation
    • SVM Header File (svm.h)
    • SVM Implementation File (svm.c)
    • Main File (main.c)
• Conclusion

Introduction

A Support Vector Machine (SVM) is a supervised machine learning algorithm used for classification and regression tasks, but it is particularly known for its ability to solve classification problems. The SVM algorithm identifies the optimal hyperplane that divides data into different classes. For non-linear data, SVM can utilize kernel functions to map the data into higher dimensions, making it easier to separate with a hyperplane. In this guide, we'll explore the fundamentals of SVM and how to implement a simple SVM algorithm in C.

Core Concepts of SVM

What is a Support Vector Machine?

The SVM algorithm works by finding the hyperplane that maximizes the margin between two classes. This margin is defined by the support vectors—data points closest to the decision boundary. SVM is particularly useful for high-dimensional data and can handle both linear and non-linear separations using kernel tricks.

Key Components of SVM

• Hyperplane: The decision boundary that separates the data classes.
• Margin: The distance between the hyperplane and the nearest data points of each class.
• Support Vectors: Data points that are closest to the hyperplane and that directly affect its position and orientation.
• Kernel Function: A method for transforming non-linearly separable data into a higher-dimensional space to make it linearly separable.

SVM Optimization Objective

The SVM objective function can be formulated as:

min⁡12∥w∥2\min \frac12 \|w\|^2min21​∥w∥2

Subject to:

yi(wTxi+b)≥1∀iy_i(w^T x_i + b) \geq 1 \quad \forall iyi​(wTxi​+b)≥1∀i

Where www is the weight vector, xix_ixi​ is the input feature vector, yiy_iyi​ is the class label, and bbb is the bias term.

SVM Implementation in C

Simple Linear SVM Implementation

Below is a simple implementation of a linear SVM in C using gradient descent for optimization. We will not include kernels for simplicity, but this approach will work for linearly separable data.

SVM Header File (svm.h)

SVM Implementation File (svm.c)

Main File (main.c)

Conclusion

The Support Vector Machine (SVM) algorithm is a powerful tool for classification tasks, and its implementation in C involves manually optimizing the objective function using gradient descent. In this guide, we walked through a basic linear SVM implementation in C. This basic implementation can be expanded with kernel methods for non-linear classification, more advanced optimization techniques, and additional functionality for larger datasets.