A Simple Explanation of Partial Least Squares

Partial Least Squares (PLS) is a widely used technique in chemometrics, especially in the case where the number of independent variables is significantly larger than the number of data points. There are many articles on PLS [HTF01, GK86] but the mathematical details of PLS do not always come out clearly in these treatments. This paper is an attempt to describe PLS in precise and simple mathematical terms.