"""
=========================================
Understanding the decision tree structure
=========================================
The decision tree structure can be analysed to gain further insight on the
relation between the features and the target to predict. In this example, we
show how to retrieve:
- the binary tree structure;
- the depth of each node and whether or not it's a leaf;
- the nodes that were reached by a sample using the ``decision_path`` method;
- the leaf that was reached by a sample using the apply method;
- the rules that were used to predict a sample;
- the decision path shared by a group of samples.
"""
# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
import numpy as np
from matplotlib import pyplot as plt
from sklearn import tree
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from sklearn.tree import DecisionTreeClassifier
##############################################################################
# Train tree classifier
# ---------------------
# First, we fit a :class:`~sklearn.tree.DecisionTreeClassifier` using the
# :func:`~sklearn.datasets.load_iris` dataset.
iris = load_iris()
X = iris.data
y = iris.target
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)
clf = DecisionTreeClassifier(max_leaf_nodes=3, random_state=0)
clf.fit(X_train, y_train)
##############################################################################
# Tree structure
# --------------
#
# The decision classifier has an attribute called ``tree_`` which allows access
# to low level attributes such as ``node_count``, the total number of nodes,
# and ``max_depth``, the maximal depth of the tree. The
# ``tree_.compute_node_depths()`` method computes the depth of each node in the
# tree. `tree_` also stores the entire binary tree structure, represented as a
# number of parallel arrays. The i-th element of each array holds information
# about the node ``i``. Node 0 is the tree's root. Some of the arrays only
# apply to either leaves or split nodes. In this case the values of the nodes
# of the other type is arbitrary. For example, the arrays ``feature`` and
# ``threshold`` only apply to split nodes. The values for leaf nodes in these
# arrays are therefore arbitrary.
#
# Among these arrays, we have:
#
# - ``children_left[i]``: id of the left child of node ``i`` or -1 if leaf
# node
# - ``children_right[i]``: id of the right child of node ``i`` or -1 if leaf
# node
# - ``feature[i]``: feature used for splitting node ``i``
# - ``threshold[i]``: threshold value at node ``i``
# - ``n_node_samples[i]``: the number of training samples reaching node
# ``i``
# - ``impurity[i]``: the impurity at node ``i``
# - ``weighted_n_node_samples[i]``: the weighted number of training samples
# reaching node ``i``
# - ``value[i, j, k]``: the summary of the training samples that reached node i for
# output j and class k (for regression tree, class is set to 1). See below
# for more information about ``value``.
#
# Using the arrays, we can traverse the tree structure to compute various
# properties. Below, we will compute the depth of each node and whether or not
# it is a leaf.
n_nodes = clf.tree_.node_count
children_left = clf.tree_.children_left
children_right = clf.tree_.children_right
feature = clf.tree_.feature
threshold = clf.tree_.threshold
values = clf.tree_.value
node_depth = np.zeros(shape=n_nodes, dtype=np.int64)
is_leaves = np.zeros(shape=n_nodes, dtype=bool)
stack = [(0, 0)] # start with the root node id (0) and its depth (0)
while len(stack) > 0:
# `pop` ensures each node is only visited once
node_id, depth = stack.pop()
node_depth[node_id] = depth
# If the left and right child of a node is not the same we have a split
# node
is_split_node = children_left[node_id] != children_right[node_id]
# If a split node, append left and right children and depth to `stack`
# so we can loop through them
if is_split_node:
stack.append((children_left[node_id], depth + 1))
stack.append((children_right[node_id], depth + 1))
else:
is_leaves[node_id] = True
print(
"The binary tree structure has {n} nodes and has "
"the following tree structure:\n".format(n=n_nodes)
)
for i in range(n_nodes):
if is_leaves[i]:
print(
"{space}node={node} is a leaf node with value={value}.".format(
space=node_depth[i] * "\t", node=i, value=np.around(values[i], 3)
)
)
else:
print(
"{space}node={node} is a split node with value={value}: "
"go to node {left} if X[:, {feature}] <= {threshold} "
"else to node {right}.".format(
space=node_depth[i] * "\t",
node=i,
left=children_left[i],
feature=feature[i],
threshold=threshold[i],
right=children_right[i],
value=np.around(values[i], 3),
)
)
# %%
# What is the values array used here?
# -----------------------------------
# The `tree_.value` array is a 3D array of shape
# [``n_nodes``, ``n_classes``, ``n_outputs``] which provides the proportion of samples
# reaching a node for each class and for each output.
# Each node has a ``value`` array which is the proportion of weighted samples reaching
# this node for each output and class with respect to the parent node.
#
# One could convert this to the absolute weighted number of samples reaching a node,
# by multiplying this number by `tree_.weighted_n_node_samples[node_idx]` for the
# given node. Note sample weights are not used in this example, so the weighted
# number of samples is the number of samples reaching the node because each sample
# has a weight of 1 by default.
#
# For example, in the above tree built on the iris dataset, the root node has
# ``value = [0.33, 0.304, 0.366]`` indicating there are 33% of class 0 samples,
# 30.4% of class 1 samples, and 36.6% of class 2 samples at the root node. One can
# convert this to the absolute number of samples by multiplying by the number of
# samples reaching the root node, which is `tree_.weighted_n_node_samples[0]`.
# Then the root node has ``value = [37, 34, 41]``, indicating there are 37 samples
# of class 0, 34 samples of class 1, and 41 samples of class 2 at the root node.
#
# Traversing the tree, the samples are split and as a result, the ``value`` array
# reaching each node changes. The left child of the root node has ``value = [1., 0, 0]``
# (or ``value = [37, 0, 0]`` when converted to the absolute number of samples)
# because all 37 samples in the left child node are from class 0.
#
# Note: In this example, `n_outputs=1`, but the tree classifier can also handle
# multi-output problems. The `value` array at each node would just be a 2D
# array instead.
##############################################################################
# We can compare the above output to the plot of the decision tree.
# Here, we show the proportions of samples of each class that reach each
# node corresponding to the actual elements of `tree_.value` array.
tree.plot_tree(clf, proportion=True)
plt.show()
##############################################################################
# Decision path
# -------------
#
# We can also retrieve the decision path of samples of interest. The
# ``decision_path`` method outputs an indicator matrix that allows us to
# retrieve the nodes the samples of interest traverse through. A non zero
# element in the indicator matrix at position ``(i, j)`` indicates that
# the sample ``i`` goes through the node ``j``. Or, for one sample ``i``, the
# positions of the non zero elements in row ``i`` of the indicator matrix
# designate the ids of the nodes that sample goes through.
#
# The leaf ids reached by samples of interest can be obtained with the
# ``apply`` method. This returns an array of the node ids of the leaves
# reached by each sample of interest. Using the leaf ids and the
# ``decision_path`` we can obtain the splitting conditions that were used to
# predict a sample or a group of samples. First, let's do it for one sample.
# Note that ``node_index`` is a sparse matrix.
node_indicator = clf.decision_path(X_test)
leaf_id = clf.apply(X_test)
sample_id = 0
# obtain ids of the nodes `sample_id` goes through, i.e., row `sample_id`
node_index = node_indicator.indices[
node_indicator.indptr[sample_id] : node_indicator.indptr[sample_id + 1]
]
print("Rules used to predict sample {id}:\n".format(id=sample_id))
for node_id in node_index:
# continue to the next node if it is a leaf node
if leaf_id[sample_id] == node_id:
continue
# check if value of the split feature for sample 0 is below threshold
if X_test[sample_id, feature[node_id]] <= threshold[node_id]:
threshold_sign = "<="
else:
threshold_sign = ">"
print(
"decision node {node} : (X_test[{sample}, {feature}] = {value}) "
"{inequality} {threshold})".format(
node=node_id,
sample=sample_id,
feature=feature[node_id],
value=X_test[sample_id, feature[node_id]],
inequality=threshold_sign,
threshold=threshold[node_id],
)
)
##############################################################################
# For a group of samples, we can determine the common nodes the samples go
# through.
sample_ids = [0, 1]
# boolean array indicating the nodes both samples go through
common_nodes = node_indicator.toarray()[sample_ids].sum(axis=0) == len(sample_ids)
# obtain node ids using position in array
common_node_id = np.arange(n_nodes)[common_nodes]
print(
"\nThe following samples {samples} share the node(s) {nodes} in the tree.".format(
samples=sample_ids, nodes=common_node_id
)
)
print("This is {prop}% of all nodes.".format(prop=100 * len(common_node_id) / n_nodes))