0:00:00.150,0:00:02.650
And the answer is yes in all cases.
0:00:02.650,0:00:07.130
Now the clear cut case is the left one, which is the one we already discussed.
0:00:07.130,0:00:11.690
But we have data on a circle that could still be a main axis and
0:00:11.690,0:00:14.090
a secondary axis.
0:00:14.090,0:00:18.300
And PCA will actually give you a deterministic result, typically the
0:00:18.300,0:00:21.210
first X in this direction, second this direction.
0:00:21.210,0:00:22.540
The third one is surprising.
0:00:22.540,0:00:23.940
When we, remember regression,
0:00:23.940,0:00:27.480
it's impossible to build a regression that goes vertically because you
0:00:27.480,0:00:32.710
can't really divide this data set here as a function y equals f of x.
0:00:32.710,0:00:36.690
But regression treats the variables very asymmetrically.
0:00:36.690,0:00:38.740
One is the input, one is the output.
0:00:38.740,0:00:41.170
In PCA, all we get is vectors.
0:00:41.170,0:00:47.420
So I can easily imagine a coordinate system where the x axis falls vertically,
0:00:47.420,0:00:51.480
and the y axis goes to the left, and that's the answer for PCA in this case.