Practical Predictive Analytics

Simple illustration of a mapping function

To illustrate how a kernel mapping function can help in defining a linear boundary, look at the following plots and see how creating a new variable z will help differentiate among the new transformed points that are mapped by the polynomial function t2$Latitude^2*t2$High.Low.Temp^2 in two-dimensional space. However, a kernel mapping will take place in a higher dimension, and the results of the mapping reverse mapped back into the original space:

#generate a non-linear circle of point 
 
radius <- 2 
t2 <- data.frame(x=radius * cos(seq(0,6,length = 20)),y = radius * sin(seq(0, 6, length = 20))) 
names(t2) <- c("Latitude","High.Low.Temp") 
plot(t2$Latitude,t2$High.Low.Temp) # create a new variable and plot ...