Principle component analysis is a powerful technique when you have linear data sets.  Of course when entering the problem of I don’t know if my data is linear or not needs explorationref.

Partial Least Squares (PLS) is a powerful technique for a variety of problems.  Partial least squares regression (PLS regression) is a statistical method that bears some relation to principal components regression; instead of finding hyperplanes of maximum variance between the response and independent variables, it finds a linear regression model by projecting the predicted variablesand the observable variables to a new space. Because both the X and Y data are projected to new spaces, the PLS family of methods are known as bilinear factor models.

Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where linearly independent variables are highly correlated.[1] It has been used in many fields including econometrics, chemistry, and engineering