I was puzzled by Daniel Lichtbau’s comments on PCA (Principal Component Analysis). He demonstrated that the PrincipalComponents function is not what it is called and it does the Principal Coordinate Analysis.

https://community.wolfram.com/groups/-/m/t/2943840

This is confusing and disturbing because I consider PCA or SVD as the most important method that connects Engineering, statistics and other diciplines.

I tried to use the PrincipalComponents function in the past and found that it did not provide the loading vector (V) so I use the SingularValueDecomposition function instead.

In summary, the SingularValueDecomposition function should be used for PCA and WL does not have a function for PCA now.

1. The PrincipalComponents should be renamed as Principal Coordinate Analysis (Daniel Lichtbau found)

2. Most importantly, it would be great if WL shows the "V" for PCA and other dimension reduction methods such as multidimensional scaling. Without the "V”, we don't know how the reduced vectors are derived (it is a black box and it is like "WL says just use it").

I found that applying the Normal function to the DimensionReducerfunction (e.g., dimredLSA//Normal) show detail information but I don’t believe I understand them.

Attachments:

PCA and related ...nb