Partial Least Squares (PLS)

The idea behind Partial Least Squares is to decompose both the design matrix X and response matrix Y (we consider the general case of multiple responses here) like in principal component and then perform regression between their eigenvectors T and U. The idea behind partial least squares is that we want the decompositions of X and Y to be done by taking information from each other into account. So, the following algorithm comes into play.

REFERENCES

OpenAI. (2023). ChatGPT (August 3 Version) [Large language model]. https://chat.openai.com