Getting decision tree like rules for my cluster(s)

Question

After performing clustering and detailed cluster analysis, I am confident that my clusters make sense.

Now, for each cluster, I would like to generate rules in the form of decision tree output. With this, I intend to achieve two things:

1. Most significant variables
2. Most significant combinations of variables which lead to the cluster

I do not want to perform decision tree classification with K clusters as K classes and instead obtain rules for the population which is already segmented. Is there a way I can do this?

Answer 1

I do not want to perform decision tree classification with K clusters as K classes

You should.

A tree is a representation of rules in which you follow a path which begins in the root node and ends in every leaf node.

If the tree separates between x<=30 and x>30, then the rules are:

If x<=30 then
    Follow path A
Else:
    Follow Path B

Answer 2

This almost sounds like a combination of supervised learning and unsupervised learning. Consider finding significant features that predict a target variable like this (fee in your own data).

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
# matplotlib inline

df = pd.read_csv("https://rodeo-tutorials.s3.amazonaws.com/data/credit-data-trainingset.csv")
df.head()

from sklearn.ensemble import RandomForestClassifier

features = np.array(['revolving_utilization_of_unsecured_lines',
                     'age', 'number_of_time30-59_days_past_due_not_worse',
                     'debt_ratio', 'monthly_income','number_of_open_credit_lines_and_loans', 
                     'number_of_times90_days_late', 'number_real_estate_loans_or_lines',
                     'number_of_time60-89_days_past_due_not_worse', 'number_of_dependents'])
clf = RandomForestClassifier()
clf.fit(df[features], df['serious_dlqin2yrs'])

# from the calculated importances, order them from most to least important
# and make a barplot so we can visualize what is/isn't important
importances = clf.feature_importances_
sorted_idx = np.argsort(importances)


padding = np.arange(len(features)) + 0.5
plt.barh(padding, importances[sorted_idx], align='center')
plt.yticks(padding, features[sorted_idx])
plt.xlabel("Relative Importance")
plt.title("Variable Importance")
plt.show()

When you have your best features selected, consider applying KMeans, AffinityPropagation, Mean Shift, SpectralClustering, AgglomerativeClustering, or DBSCAN. See the link below for more details.

Comparing Python Clustering Algorithms | The hdbscan Clustering Library