Support Vector Machines (SVMs) are a class of supervised learning algorithms used for classification and regression analysis. SVMs are based on the idea of finding a hyperplane that best separates data into different classes.
In binary classification, the hyperplane is a line that separates the two classes in the feature space. SVMs find the hyperplane that maximizes the margin between the two classes, which is the distance between the hyperplane and the closest data points from each class. The points closest to the hyperplane are called support vectors.
SVMs can handle both linear and nonlinearly separable data by transforming the input data into a higher-dimensional space through a technique called kernel trick. In the higher-dimensional space, the hyperplane can be linearly separable even if the original data is not.
SVMs have several advantages, including their ability to handle high-dimensional data, their effectiveness in handling small datasets, and their ability to generalize well to new data. SVMs have been successfully used in various applications, including image classification, text classification, and bioinformatics.