Support Vector 2 Kernels

Lecture 37:- Support Vector 2 Kernels

Support Vector Machines (SVM) and Support Vector Regression (SVR) are versatile algorithms that can handle both linearly separable and non-linearly separable data. This is achieved by using different types of kernel functions that transform the data into higher-dimensional spaces, where the data may become linearly separable.

Here are two common types of kernels used in SVM and SVR:

Linear Kernel: The linear kernel is the simplest and most commonly used kernel. It performs a linear transformation of the data into a higher-dimensional space. In the transformed space, the data points are separated by a hyperplane. The decision boundary for a linear kernel SVM or SVR is a straight line or hyperplane.

The linear kernel is suitable for problems where the data is linearly separable. It works well when the relationship between the features and the target variable is approximately linear.

The linear kernel function is defined as:

Radial Basis Function (RBF) Kernel: The RBF kernel is a popular non-linear kernel. It maps the data points into an infinite-dimensional space, where the data becomes separable by circles or spheres. The decision boundary for an SVM or SVR with the RBF kernel is a non-linear curve or surface.

The RBF kernel is effective when the data has complex non-linear relationships. It is capable of capturing intricate patterns and can handle data with irregular decision boundaries.

The RBF kernel function is defined as:

Here, gamma is a hyperparameter that controls the width of the RBF kernel. A smaller gamma results in a wider kernel and a smoother decision boundary, while a larger gamma leads to a narrower kernel and a more complex decision boundary.

Kernel functions provide the flexibility needed to handle various data distributions and relationships between variables. Other commonly used kernels include polynomial kernels, sigmoid kernels, and custom kernels tailored to specific data characteristics.

The choice of the kernel function and the hyperparameters (e.g., gamma in the RBF kernel) significantly impacts the performance of SVM and SVR models. Proper tuning of these hyperparameters, often through techniques like grid search or cross-validation, is crucial for achieving the best possible model performance.