How can i physically interpret PCA output

Hi all,

I'm trying to derive some information about PCA (quite new for me, so, please be kind) applied on my dataset made of 4 Variables (A,B,C,D) and 400 Observations.

Once built the matrix mymat composed of 4 columns (V) and 400 rows (O), i trivially want to analyze how variables contribute to principal components.

Thus, on behalf of 2 lines of matlab code i write:

[coeff,score,latent,tsquared] = pca(mymat);

biplot(coeff(:,1:2),'scores',score(:,1:2),'Marker','o','varlabels',{'A','B','C','D'});

The result is plotted in the attached image.

Now, the question is the following. According a "physical" interpretation, A variable "should" be critical since it governs some important facts across my dataset. The plot, instead, seems to say that A variable does not contribute for the first nor second principal components since it lies in the center of axis.

Do I miss anything? Does PCA reveal that A variable is absolutely unuseful for my analysis?

Thanks in advance for your help!

Answer 1

[Shubh Sahu]

‘A’ vector in biplot is almost zero which means it does not contribute in Component 1 and component 2. Maybe it can contribute to other component apart from these two components. But it will be not useful because variance will increase as you take the higher order of component. From my point of view ‘A’ is not useful data for your analysis because remaining three variables (B, C, D) are highly corelated. For more insights and help, please refer these links-

https://www.mathworks.com/help/stats/pca.html?searchHighlight=pca&s_tid=doc_srchtitle#bth9ibe-4

https://www.mathworks.com/help/stats/biplot.html?searchHighlight=biplot&s_tid=doc_srchtitle#bt_y8xe-2