PCAs, how to interpret the scale of the axis

Question

[pisiposo84]

Hi there,

I have performed two PCA analysis on two different data sets, consisting of the analysis of different proprieties of the same samples.

I got what I was expecting, some samples are cluster together and away from others. However I also noticed that the scale of the PCA axis is quite different, on the left the range is much smaller compare to the PCA on the right, for both the x and y axis. How should I interpret this? Can I say that for the measurement Y there are more variations (and bigger fold change) among the different sample? Or this is due to the scale, data points, something else of the original data used for the PCA?

Thank you.

[Joe]

Why would you expect that the scales would be the same? They're different variables accounting for a different amount of the variance in that data set. The magnitude of the variance itself between 2 variables isn't really comparable.

Answer 1

[Jean-Karim Heriche]

The scale of a principal component is irrelevant. One way of seeing this is that a PC is an eigenvector and any multiple of an eigenvector is an eigenvector. Eigenvectors are usually scaled to have unit norm to reduce ambiguity (up to multiplication by -1).

Answer 2

[hakimelakhrass]

I always center and scale my data before doing PCA. That is the way I was taught. Maybe you can redo it and see what happens. Because if it is due to scale then the variation does not really exist.

[pisiposo84]

Hi,

I tried scaling and centering the data, however the picture does not really change. The ranges are a bit closer but, for the PCA on the right the range is still 20-50 units wider for both x and y axis.

[hakimelakhrass]

I did notice the two different datasets parts. Sorry about that. Indeed the scale irrelevant

Answer 3

[pisiposo84]

This is a direct comparision scailing vs no-scailing (both centered data) on a similar data set as above