The aim of the SVM algorithm is to find a hyperplane in an p -dimensional space, where p is the number of features that distinctly classifies the data points.
In a p -dimensional space, a hyperplane is what we call an affine subspace of dimension of p-1 . As an example, in two dimension, a hyperplane is simply as straight line while in three dimensions it is a two-dimensional subspace, or stated simply, a plane.
In two dimensions, with the variables x_1 and x_2 , the hyperplane is defined as b+w_1x_1+w_2x_2=0, where b is the intercept and w_1 and w_2 define the elements of a vector orthogonal to the line b+w_1x_1+w_2x_2=0 . In two dimensions we define the vectors \boldsymbol{x} =[x1,x2] and \boldsymbol{w}=[w1,w2] . We can then rewrite the above equation as \boldsymbol{w}^T\boldsymbol{x}+b=0.