Question 2. What does each view of the data show?
The same dataset, drawn eight ways. plotdata is the
single entry point; type picks the view, and the origin of
the cars colours the points throughout.
Answer. Hard to see much in panels that small. It does look as though Europe and Asia overlap, and that America is separated from the other two.
Answer. For most variables American cars cover a
wider range of values than European and Asian ones. Except for the first
and the last variable, their values are also higher: mpg is
lower for American cars, and acceleration slightly
lower.
Answer. The same observations, read along the lines instead of across the boxes.
Answer. For every variable but the last
(acceleration), small values are more frequent than large
ones.
Answer. The factorial plane shows three homogeneous groups. The leftmost one mixes the three origins; so does the middle one, though it is mostly American cars; the rightmost one contains American cars only.
Answer. Two groups this time – one mixing the three origins, one of American cars only. Note the difference in what is being asked: PCA looks for the axes of greatest variance and ignores the origin of the cars, while discriminant analysis looks for the axes that separate the three origins best. Being told the answer does not make the picture show more structure; here it shows less.
Answer. The same information as the factorial plane, which is no accident: on centred and scaled data, an SVD and a PCA are the same decomposition.
# Variable, and visibly so: t-SNE starts from a random embedding and optimises it. Two runs
# without 'seed' give two different pictures -- same groups, different positions and shapes.
plotdata (autompg, type = "tsne", labels = FALSE, perplexity = 50, seed = 0)
Answer. The same three groups as the factorial plane, but pulled apart: American cars only in two of them, the third holding the European and Asian cars together with the American ones that resemble them. This is what a non-linear embedding buys, at the price of distances between the groups that can no longer be read quantitatively.