Do you know / used data reduction techniques other than PCA? What do you think of step-wise regression? What kind of step-wise techniques are you familiar with?

Do you know / used data reduction techniques other than PCA? What do you think of step-wise regression? What kind of step-wise techniques are you familiar with?

Data reduction techniques other than Principal component analysis (PCA):

-Partial least squares: like PCR (principal component regression) but chooses the principal components in a supervised way. Gives higher weights to variables that are most strongly related to the response

step-wise regression?
- the choice of predictive variables are carried out using a systematic procedure
- Usually, it takes the form of a sequence of F-tests, t-tests, adjusted R-squared, AIC, BIC
- at any given step, the model is fit using unconstrained least squares
- can get stuck in local optima
- Better: Lasso

step-wise techniques:
- Forward-selection: begin with no variables, adding them when they improve a chosen model comparison criterion
- Backward-selection: begin with all the variables, removing them when it improves a chosen model comparison criterion

Better than reduced data:
-Example 1: If all the components have a high variance: which components to discard with a guarantee that there will be no significant loss of the information?
-Example 2 (classification):
- One has 2 classes; the within class variance is very high as compared to between class variance
- PCA might discard the very information that separates the two classes

Better than a sample:
- When number of variables is high relative to the number of observations

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