What is a good heuristic to detect if a column in a pandas.DataFrame is categorical?

Here are a couple of approaches:

1. Find the ratio of number of unique values to the total number of unique values. Something like the following

   likely_cat = {}
   for var in df.columns:
       likely_cat[var] = 1.*df[var].nunique()/df[var].count() < 0.05 #or some other threshold
   

2. Check if the top n unique values account for more than a certain proportion of all values

   top_n = 10 
   likely_cat = {}
   for var in df.columns:
       likely_cat[var] = 1.*df[var].value_counts(normalize=True).head(top_n).sum() > 0.8 #or some other threshold
   

Approach 1) has generally worked better for me than Approach 2). But approach 2) is better if there is a ‘long-tailed distribution’, where a small number of categorical variables have high frequency while a large number of categorical variables have low frequency.