(Solved): 3. PCA (20 points): Consider the following two plots. These are plots of training data points X ...

3. PCA (20 points): Consider the following two plots. These are plots of training data points $$X$$ in $${\mathbb{R}}^2$$ belonging to 2 classes. Figure 2: Dataset-1 Figure 3: Dataset-2 Answer the following questions for each dataset. (a) (10 points) Draw all two principal components in the picture (you can take a screenshot). You are expected to draw the rough directions of the principal components instead of accurate computations. Hint: There are 2 principal components for each dataset. (b) (10 points) After projecting all the points onto one of the principal components, is it possible to correctly classify all the points by just a threshold function? If yes, which principal component should we project onto and why? If no, please explain your reasoning. Hint: Classifying with respect to a threshold function means you just need a threshold to classify them. For example, if $$x<0.64$$ then predict label-1 else predict label-0 end if Here $$0.64$$ is considered as the threshold.