a) In each of the following plots, a training dataset of data points X in R^2 labeled either + or - is given, where the original features are the coordinates (x,y). You can assume that the data is origin-centered. For each of the two training sets below, answer the following questions:

1. Draw a simple simple recreation of each of the two datasets below (no need for exact precision) and draw all the principal components (eyeball it).
2. For each dataset, can we correctly classify the labels by using a halfspace after projecting onto one of the principle components? If so, which principal component should we project onto? If not, explain in 1-2 sentences why it is not possible.

b). Is it possible to have a data set in R^2 that is linearly separable by a halfspace in R^2 but is not linearly separate after projecting onto either of the two principal components?

y Figure 1: Dataset 1