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1. If I wanted to use PCA, is there a better approach than normalization? I am asking because you seem better at math than I (based on your comment history). 2
by dr_kiszonka 2y ago
1. If I wanted to use PCA, is there a better approach than normalization? I am asking because you seem better at math than I (based on your comment history).
2. Not that PCA is my favorite technique, but you can apply PCA to data that are expressed in the same units.
3. Do you oppose most clustering techniques since one can apply them to mixed units data?
- xeonmc 2y ago1. Yes, take the logarithm, especially if your data domain is a constitutive quantity (i.e. there exists an unequovical "absolute zero"). It converts multiplicative scale factors into translational offsets. If your data domain have negatives, consider whether if it's just an artifact of your relative measurement and try to re-offset your data based on reasoning. If your data is a positional quantity, consider if there exists a corresponding metric for which your data is an exponential measurement of (e.g. acidity <-> concentration), and re-shape your log base appropriately. 2. Almost yes, but you also need to make sure that there can exist a rotational symmetry in the measurement metrics, unless it is precisely the asymmetry which you are measuring (but then that would mean you have determined a priori that it's axis-aligned?) 3. Depends, I cannot say I am encyclopedically well-versed to give a judgement on the proportion of how many techniques are well-founded and how many are not. However, I can give you an example of one which is rigorous and spectacularly elegant -- see Michael F. Ashby's work.