Kernel SVM is the abbreviated version of the kernel support vector machine. Kernel methods are a class of algorithms for pattern analysis, and the most common one is the kernel SVM.

Kernel SVM, or Kernel Support Vector Machine, is a powerful extension of the traditional Support Vector Machine (SVM) algorithm used for classification and regression tasks in machine learning. In traditional SVM, data points are represented as vectors in a high-dimensional space, and the algorithm tries to find the optimal hyperplane that separates different classes. However, in cases where the data is not linearly separable, traditional SVM may not perform well.

Kernel SVM addresses this limitation by introducing the concept of a “kernel function.” A kernel function is a mathematical function that implicitly maps the input data into a higher-dimensional feature space where it becomes linearly separable. This allows the SVM algorithm to find a hyperplane in the transformed space that effectively separates the data into different classes.

Some commonly used kernel functions include:

Linear Kernel: $K (x, y) = x^{T} y$
Polynomial Kernel: $K (x, y) = (γ x^{T} y + r)^{d}$
Radial Basis Function (RBF) Kernel (Gaussian Kernel): $K (x, y) = e^{- γ ∣∣ x - y ∣∣ 2}$
Sigmoid Kernel: $K (x, y) = tanh (γ x^{T} y + r)$

Here, $γ$ , $d$ , and $r$ are hyperparameters that control the behavior of the kernel function.

Kernel SVM is particularly useful when dealing with non-linearly separable data, as it allows the algorithm to capture complex patterns and relationships present in the data. However, it’s important to note that kernel selection and tuning of hyperparameters are crucial steps in achieving good performance with Kernel SVM.