Categorical features correlation

Question

I have some categorical features in my data along with continuous ones. Is it a good or absolutely bad idea to hot encode category features to find correlation of it to labels along with other continuous creatures?

Answer 1

There is a way to calculate the correlation coefficient without one-hot encoding the category variable. Cramers V statistic is one method for calculating the correlation of categorical variables. It can be calculated as follows. The following link is helpful. Using pandas, calculate Cramér's coefficient matrix For variables with other continuous values, you can categorize by using cut of pandas.

import pandas as pd
import numpy as np
import scipy.stats as ss
import seaborn as sns

tips = sns.load_dataset("tips")

tips["total_bill_cut"] = pd.cut(tips["total_bill"],
                                np.arange(0, 55, 5),
                                include_lowest=True,
                                right=False)

def cramers_v(confusion_matrix):
    """ calculate Cramers V statistic for categorial-categorial association.
        uses correction from Bergsma and Wicher,
        Journal of the Korean Statistical Society 42 (2013): 323-328
    """
    chi2 = ss.chi2_contingency(confusion_matrix)[0]
    n = confusion_matrix.sum()
    phi2 = chi2 / n
    r, k = confusion_matrix.shape
    phi2corr = max(0, phi2 - ((k-1)*(r-1))/(n-1))
    rcorr = r - ((r-1)**2)/(n-1)
    kcorr = k - ((k-1)**2)/(n-1)
    return np.sqrt(phi2corr / min((kcorr-1), (rcorr-1)))

confusion_matrix = pd.crosstab(tips["day"], tips["time"]).as_matrix()
cramers_v(confusion_matrix)
# Out[10]: 0.93866193407222209

confusion_matrix = pd.crosstab(tips["total_bill_cut"], tips["time"]).as_matrix()
cramers_v(confusion_matrix)
# Out[24]: 0.16498707494988371

Answer 2

I was looking to do same thing in BigQuery. For numeric features you can use built in CORR(x,y) function. For categorical features, you can calculate it as: cardinality (cat1 x cat2) / max (cardinality(cat1), cardinality(cat2). Which translates to following SQL:

SELECT 
COUNT(DISTINCT(CONCAT(cat1, cat2))) / GREATEST (COUNT(DISTINCT(cat1)), COUNT(DISTINCT(cat2))) as cat1_2,
COUNT(DISTINCT(CONCAT(cat1, cat3))) / GREATEST (COUNT(DISTINCT(cat1)), COUNT(DISTINCT(cat3))) as cat1_3,
....
FROM ...

Higher number means lower correlation.

I used following python script to generate SQL:

import itertools

arr = range(1,10)

query = ',\n'.join(list('COUNT(DISTINCT(CONCAT({a}, {b}))) / GREATEST (COUNT(DISTINCT({a})), COUNT(DISTINCT({b}))) as cat{a}_{b}'.format(a=a,b=b) 
  for (a,b) in itertools.combinations(arr,2)))
query = 'SELECT \n ' + query + '\n FROM  `...`;'
print (query)

It should be straightforward to do same thing in numpy.