# Infer limits of unscaled values from their standardized values - Clustering

I am working on a clustering problem and I have some skewed variables.

So, I log transform them and use them in clustering.

However, instead of multivariate clustering, I do multiple univariate clustering (1D clustering of multiple variables seperately) using jenks approach.

My question is,

a) The pattern/cluster/cluster labels found based on standardized/log transformed values also apply to the original values? For ex: using log transformed values (and their correspondimg customer id), I can get their raw values. So, can I say that raw data from 100 to 102 belongs to cluster 0 and 800 to 804 belongs to cluster 1?

Meaning, the pattern found for normalized/standardized/transformed value are also applicable to raw values? Or is it like pattern found in log transformed values is kind of fake (amd not mecessarily apply to raw values)

my sample data looks like below. This is just dummy data to help understand the question (so transformation values may be incorrect) • How do you combine the univariate results into an overall cluster solution?
– whuber
May 31, 2022 at 16:11
• @whuber - based on some biz logic. May 31, 2022 at 22:04
• if variable 1 value belongs to Cluster 1 and variable 2 value belongs to Cluster 3 and variable 3 value belongs to cluster 4 then final_cluster_label = "High spenders" if variable 1 value belongs to Cluster 3 and variable 2 value belongs to Cluster 4 and variable 3 value belongs to cluster 1 then final_cluster_label = "Champions" May 31, 2022 at 22:06
• something like above...here by variable value, I meam log transformed values. May 31, 2022 at 22:07
• since number of variables is low, we write a if else logic.. we have 5 variables (5 1d clustering).. May 31, 2022 at 23:53

If I understand correctly, you're basically asking: "If I apply a log-transform to my data and run a clustering analysis on the transformed data, are the conclusions/patterns valid for the original data?"

Maybe someone can provide a formal theoretical/mathematical answer, but from a practical point of view, what you're describing is quite common and generally considered valid.

You should be a bit careful when you do this (especially in settings like regression - if you do regression on log-values, don't forget that the coefficients are for log-values and you have to do some transformation to get the raw value interpretation).

In your case, though, I think this kind of approach is perfectly fine. But you should think about the problem from a "common sense" standpoint and understand why your clustering might be better/different with the log-transformed values than with the original values, and whether that makes sense in your context (presumably, the log "squeezes" your skewed distribution, making sparse points closer together and therefore easier to cluster).

• Thanks. When log squeezes the raw data (so its able to find patterns because points are squeezed), how can that be applicable for their raw data (which can far from each other)? Jun 1, 2022 at 22:34
• for ex : if I say cluster 1's limit is from 800 to 804? Is that correct? (Though the cluster label was actually found using log values) Jun 1, 2022 at 22:35
• @TheGreat I'm not sure it's really correct to define the "limits" of a cluster (unless the algorithm somehow explicitly provides that, which I'm not sure really exists). I think you can only really say that points 1, 5, 12, 15 etc. belong to cluster 1. Jun 2, 2022 at 5:41
• Sorry, may I know which points are you referring as 1,5,12 and 15? because I don;t have such points in my sample above? Jun 2, 2022 at 6:15
• Additionally, can I know why not the limits be inferred? because, we agree that these points/customers belong to cluster 1. Now, I investigate each of these clusters (using their customer ids) and find out the variable (original variable - unstandardized) minimum value for ex: 10, and max limit for the same variable is 120. In this can't we consider that any customers with a variable value of this limit, would fall into cluster 1 Jun 2, 2022 at 6:20