Hyperplane

In machine learning, especially in the context of Support Vector Machines (SVMs), a hyperplane is used to separate data points belonging to different classes. For instance, in a 2-dimensional space (a plane), a hyperplane is a line; in a 3-dimensional space, it's a regular plane. The optimal hyperplane in SVMs maximizes the margin, which is the distance between the hyperplane and the nearest data points from each class (support vectors). The equation of a hyperplane is typically represented as w⋅x + b = 0, where 'w' is the normal vector to the hyperplane, 'x' is a point on the hyperplane, and 'b' is a bias term. Hyperplanes are fundamental for linear classification and regression tasks, providing a decision boundary to categorize or predict data based on its features.