can easily see how we can draw our hyperplane we can do the same for this data set where it's easy to draw the hyperplane or line but for a machine will use a function to transform our data from two-dimensional to three dimensional feature space now the only problem with transformation into higher dimensional feature space is that it's computationally expensive we can use a kernel trick to reduce the computational costs a function that takes as inputs vectors in the original space and returns the dot product of the vectors