Are principal components similar to new features engineered from existing features? For instance, if a dataset is 2-dimensional (i.e., has 2 features x_1,x_2), PCA can reduce the dataset to 1 dimension by finding a new axis or principal component z, which exists on the original 2D plane. Would that principal component be equivalent to some new feature engineered using the original 2 features (e.g., z=x_1*x_2)?
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PCA takes a set of data and turns it into a new equivalent set of data where all of the features are orthogonal.
This allows you to eliminate individual dimensions (thereby throwing away data), starting from the dimensions that have the least variance.
By “features” of the new equivalent set of data, do you mean the principal components? Is it valid to think of principal components as features?
“Features” has the same meaning as the original dataset. They are the set of values for each example.