Support Vector Machines (SVM): Optimal Decision Boundaries

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🧠 Support Vector Machines (SVM): Optimal Decision Boundaries

Support Vector Machines (SVM) are a powerful supervised learning algorithm used for classification and regression tasks. They excel at finding the optimal decision boundary that separates data points belonging to different classes.

What is SVM?

SVM is a machine learning model that transforms data into a higher-dimensional space to find a hyperplane that best separates classes. The goal is to maximize the margin—the distance between the hyperplane and the nearest data points from each class, called support vectors.

Key Concepts

1. Hyperplane
   The decision boundary that separates data points of different classes. In a 2D space, it is a line; in 3D, it becomes a plane, and in higher dimensions, it is a hyperplane.

2. Support Vectors
   The data points closest to the hyperplane, which are critical in defining the decision boundary.

3. Margin
   The distance between the hyperplane and the nearest support vectors. SVM aims to maximize this margin to ensure a robust decision boundary.

Types of SVM

• Linear SVM
  Suitable for linearly separable data where a straight-line hyperplane can differentiate classes.

• Non-Linear SVM
  For complex datasets, SVM uses kernel functions (e.g., polynomial, radial basis function) to transform data into a higher-dimensional space where a linear hyperplane can be applied.

Advantages of SVM

• Works well with high-dimensional data.

• Effective when the number of dimensions exceeds the number of samples.

• Robust against overfitting, especially in high-dimensional spaces.

Limitations of SVM

• Computationally intensive for large datasets.

• Performance depends heavily on the choice of kernel and hyperparameters.

Applications of SVM

• Image Recognition: Classifying objects in images.

• Text Classification: Categorizing emails, news, and documents.

• Medical Diagnosis: Identifying diseases from patient data.

SVM's ability to define optimal decision boundaries makes it a versatile and effective tool for solving complex classification problems in various domains.

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