Kernel Trick is a mathematical function which when applied on data points, can find the region of classification between two different classes. Based on the choice of function, be it linear or radial, which purely depends upon the distribution of data, one can build a classifier.

The Kernel Trick is a fundamental concept in Support Vector Machine (SVM) algorithms that allows SVMs to perform non-linear classification by implicitly mapping input data into higher-dimensional feature spaces. In simple terms, the Kernel Trick enables SVMs to efficiently handle non-linearly separable data without explicitly transforming the data into higher dimensions.

Here’s how it works:

Mapping to a higher-dimensional space: The Kernel Trick involves transforming the input data from its original feature space into a higher-dimensional space. This transformation is typically non-linear and is achieved by using a kernel function. The kernel function calculates the dot product of the transformed feature vectors in the higher-dimensional space without actually computing the transformation explicitly.
Non-linear decision boundaries: In the higher-dimensional space, the SVM constructs a hyperplane that best separates the data into different classes. Even though the decision boundary appears linear in the higher-dimensional space, it corresponds to a non-linear decision boundary in the original feature space. This allows SVMs to effectively classify non-linearly separable data.
Types of kernels: Commonly used kernels include linear, polynomial, radial basis function (RBF/Gaussian), and sigmoid kernels. Each kernel has its own characteristics and is suitable for different types of data and classification problems.

In summary, the Kernel Trick in SVM algorithms enables the classification of non-linearly separable data by implicitly mapping the data into higher-dimensional spaces using kernel functions, thereby allowing SVMs to construct non-linear decision boundaries efficiently.