I used PCA on 9-D data. I want to plot PCs direction

Hi , I extract 2 PC and know I want to plot direction of PCs but I don't know how.

I attached data and code

clc;
clear;
data=importdata('data.txt');
n_data=zscore(data);
[coeff,scores,latent] = pca(n_data,'Algorithm','eig');
p=scatter(scores(:,1),scores(:,2),'filled')

p = 
  Scatter with properties:

             Marker: 'o'
    MarkerEdgeColor: 'none'
    MarkerFaceColor: 'flat'
          LineWidth: 0.5000
              XData: [-2.6987 -2.9086 -2.6022 -2.7088 -2.5972 -2.6443 -2.4184 -2.6105 -2.6442 -2.6342 -2.7498 -2.8929 -3.0329 -2.9947 -2.7199 -2.6996 -2.6480 -2.6630 -2.5890 -2.4588 -2.3512 -2.6149 -2.6046 -2.6306 -2.7813 -2.9008 -2.8532 -2.5646 … ]
              YData: [-1.1820 -0.3770 -1.9835 -1.6290 -1.4321 -0.6428 -1.4788 -1.7337 -1.9207 -2.0610 -2.2508 -1.8076 0.1766 -0.5802 -1.0807 -1.6126 -1.1661 -1.0277 -2.4950 -1.5415 -1.4948 -1.3786 -0.6466 0.3495 0.0197 -0.0436 0.5450 0.6005 0.2341 … ]
           SizeData: 36
              CData: [0 0.4470 0.7410]

  Show all properties

        xlabel('Principal Component 1');
        ylabel('Principal Component 2');

[John D'Errico]

What exactly do you intend to plot in 9 dimensions? Does your monitor support 9 dimensional plots? Perhaps you have one of the new hyper-holographic monitors, but I thought Starfleet Command was not building them for at least a few hundred years into the future.

[the cyclist]

I am confused by what you mean by "direction of PCs".

Because you are plotting the scores variable, you are plotting in principal component space (not the original coordinate space). I would say that the x- and y- axes are the "direction of the PCs" in this plot. (The other 7 PCs are orthogonal to these.)

If this does not make sense, or does not capture what you mean, maybe you could explain some more. What are you trying to illustrate?

[farshad jahangiri]

@the cyclist Hi . I am confused about this. in some researches like this picture they showed direction of principal components. I want to show when covariance matrix changes, the PCs direction will be change.

I think we just can show this direction in not transformed data and in original axis, not transformed data (scores).

In this case How can I show the direction of PCs in original data and what data should be used instead of scores? I am confused because the scores have all 9 dimensions and can be shown in one dimension, but the original data cannot

Answer 1

[the cyclist]

Your comment was helpful. I think the biplot function may do what you need.

The biplot illustrates what the original axes look like in (two or three dimensions of) PC space.

I think that making a biplot of the inverse of coeff would illustrate what the PC vectors look like in the original space. (I am not certain of this last statement. I'd need to think about it more, and experiment a bit.)