scaling, PCA, and clustering with non-gaussian data?

Question

I’m feeling a bit unsure about what I’m working on as I have never dealt with this sort of data before, so I could use some feedback.

I have a large dataset that I have clustered. My approach was (1) scaling (between 0 & 1), (2) PCA, and then (3) K-means clustering. I also applied HDBSCAN as an experiment. The results seem reasonable, but I would like to understand more about the data, whether what I have done is acceptable, and whether there are other things that I should consider.

The variables look like the following, although this is fake data and I really have ~25 variables:

I am used to dealing with gaussian and occasionally slightly skewed data. These data are heavily zero inflated, extremely skewed, and some (e.g. #3) are Bernoulli distributed. My questions:

1. What do I need to keep in mind when dealing with this sort of data?
2. What are the implications for the data types when applying feature scaling? PCA?
3. What are the implications for choosing a distance metric when clustering?
4. Any other caveats?

Answer 1

PCA can still be applied to non-gaussian data, but you should normalize it (min/max scaling) first: normalization serves exactly the purpose of dealing with non-gaussian distributed data (link).

As for the distance used in K-measn, I would advise you to read this article: if you scroll all the way to the end, there's a table comparison the several different distance measures, and their advantages/ disadvantages. I'm not familiar with all, but in that table it is stated that Chord distance can work with non-normalized data, so maybe it is good for non-gaussian distributions (altough I'd check that information: like I said, I'm not familiar with chord distance so I can't vouch for that).

Hope it helped!