Why does Feature Importance change with each iteration of a Decision Tree Classifier?

Question

After applying PCA to reduce the number of features, I am using a DecisionTreeClassifier for a ML problem

Additionally I want to compute the feature_importances_. However, with each iteration of the DecisionTreeClassifier, the feature_importances_ change.

Iteration #1

Iteration #2

Why would it change? I thought the initial split was made on a feature to "produce the purest subsets (weighted by their size)". Acting on the same training set, why would that change?

Thanks in advance for any help.

Answer 1

From sklearn.tree.DecisionTreeClassifier help:

The features are always randomly permuted at each split. Therefore, the best found split may vary, even with the same training data and max_features=n_features, if the improvement of the criterion is identical for several splits enumerated during the search of the best split. To obtain a deterministic behaviour during fitting, random_state has to be fixed.

Also, you might want to have a look at my critique on feature importance.