I want to cluster. I have different features for that. Some features have a very small value range (from 0 to 0.8) and some have a very large value range (from 0 to 5 million). I want to use the logarithm. Do I have to apply this feature transformation to all features, including the small values (shift the values before by +1) or can I just choose the features I want to do the transformation on? Is there any literature or work on this?
Either can be good or bad. It's not necessary to apply the same transformation to all attributes; but if youe attributes differ that much, you likely have some major problem anyway.
It depends on what you want to achieve what is appropriate. Try to approach it from having to explain your choices later. Can you argue why you transform the data this way? What is the statistical meaning of this transform for your problem? Here you'll quickly realize that with mixed data you can't really argue much - your results are based on guessing, not in a sound model.