Grouping PCA scores according to clusters and variables

I need to group my PCA outputs according to the clusters and biomechanical variables. In other words I need to find the PC score in PC1 corresponding to Ankle-Frontal motion and so on.

How do I attempt this? I have clusters sepeperated and PC numbers/scores calculated for each variable. How to I compare each of these values?

Example:

Biomechanical variables have been explained here according to 4 PCs and 2 seperate clusters.

Answer 1

[Krishna]

Hello,

From what I understand, you've conducted a Principal Component Analysis (PCA) on a dataset that includes various biochemical variables. Now, you're considering carrying out another PCA specifically on the first principal component (PC1).

Once you've determined the principal component (PC1) for the entire dataset, which essentially represents the most significant combination of features from the original data (with the eigenvector for PC1 being a weighted mix of these crucial features), there's no further need to conduct an additional PCA on PC1. The concept of calculating "PC scores in PC1" doesn't hold practical value. However, if your aim is to get even more significant components from the principal components you've already extracted, then you might consider performing PCA on the set of principal components you have, such as PC1, PC2, PC3, etc.

Please keep in mind while PCA reduces dimensions, it also discards some information, which might sometimes include important features for clustering. Therefore, the choice of the number of principal components to keep is crucial.

To know more about principal component analysis please go through this documentation,

https://www.turing.com/kb/guide-to-principal-component-analysis

And to use PCA in MATLAB go through this documentation,

https://www.mathworks.com/help/stats/pca.html

Hope this helps.