import copy
from numbers import Real
import numpy as np
from scipy.sparse import issparse
from sklearn.base import ClusterMixin, TransformerMixin
from sklearn.cluster import AgglomerativeClustering
from sklearn.utils._param_validation import Interval
from sklearn.utils.validation import check_is_fitted
from .._lib.sklearn.tree import (
BaseDecisionTree,
DecisionTreeClassifier,
DecisionTreeRegressor,
_criterion,
)
from .._lib.sklearn.tree import _tree as _sklearn_tree
from .._lib.sklearn.tree._criterion import BaseCriterion
from .._lib.sklearn.tree._tree import BestFirstTreeBuilder, DepthFirstTreeBuilder
from . import _oblique_splitter
from ._neighbors import SimMatrixMixin
from ._oblique_splitter import ObliqueSplitter
from ._oblique_tree import ObliqueTree
from .manifold import _morf_splitter
from .manifold._morf_splitter import PatchSplitter
from .unsupervised import _unsup_criterion, _unsup_oblique_splitter, _unsup_splitter
from .unsupervised._unsup_criterion import UnsupervisedCriterion
from .unsupervised._unsup_oblique_splitter import UnsupervisedObliqueSplitter
from .unsupervised._unsup_oblique_tree import UnsupervisedObliqueTree
from .unsupervised._unsup_splitter import UnsupervisedSplitter
from .unsupervised._unsup_tree import (
UnsupervisedBestFirstTreeBuilder,
UnsupervisedDepthFirstTreeBuilder,
UnsupervisedTree,
)
DTYPE = _sklearn_tree.DTYPE
DOUBLE = _sklearn_tree.DOUBLE
CRITERIA_CLF = {
"gini": _criterion.Gini,
"log_loss": _criterion.Entropy,
"entropy": _criterion.Entropy,
}
CRITERIA_REG = {
"squared_error": _criterion.MSE,
"friedman_mse": _criterion.FriedmanMSE,
"absolute_error": _criterion.MAE,
"poisson": _criterion.Poisson,
}
OBLIQUE_DENSE_SPLITTERS = {
"best": _oblique_splitter.BestObliqueSplitter,
}
PATCH_DENSE_SPLITTERS = {
"best": _morf_splitter.BestPatchSplitter,
}
UNSUPERVISED_CRITERIA = {"twomeans": _unsup_criterion.TwoMeans, "fastbic": _unsup_criterion.FastBIC}
UNSUPERVISED_SPLITTERS = {
"best": _unsup_splitter.BestUnsupervisedSplitter,
}
UNSUPERVISED_OBLIQUE_SPLITTERS = {"best": _unsup_oblique_splitter.BestObliqueUnsupervisedSplitter}
[docs]class UnsupervisedDecisionTree(SimMatrixMixin, TransformerMixin, ClusterMixin, BaseDecisionTree):
"""Unsupervised decision tree.
Parameters
----------
criterion : {"twomeans", "fastbic"}, default="twomeans"
The function to measure the quality of a split. Supported criteria are
"twomeans" for the variance impurity and "fastbic" for the
BIC criterion. If ``UnsupervisedCriterion`` instance is passed in, then
the user must abide by the Cython internal API. See source code.
splitter : {"best", "random"}, default="best"
The strategy used to choose the split at each node. Supported
strategies are "best" to choose the best split and "random" to choose
the best random split. If ``UnsupervisedSplitter`` instance is passed in, then
the user must abide by the Cython internal API. See source code.
max_depth : int, default=None
The maximum depth of the tree. If None, then nodes are expanded until
all leaves are pure or until all leaves contain less than
min_samples_split samples.
min_samples_split : int or float, default=2
The minimum number of samples required to split an internal node:
- If int, then consider `min_samples_split` as the minimum number.
- If float, then `min_samples_split` is a fraction and
`ceil(min_samples_split * n_samples)` are the minimum
number of samples for each split.
min_samples_leaf : int or float, default=1
The minimum number of samples required to be at a leaf node.
A split point at any depth will only be considered if it leaves at
least ``min_samples_leaf`` training samples in each of the left and
right branches. This may have the effect of smoothing the model,
especially in regression.
- If int, then consider `min_samples_leaf` as the minimum number.
- If float, then `min_samples_leaf` is a fraction and
`ceil(min_samples_leaf * n_samples)` are the minimum
number of samples for each node.
min_weight_fraction_leaf : float, default=0.0
The minimum weighted fraction of the sum total of weights (of all
the input samples) required to be at a leaf node. Samples have
equal weight when sample_weight is not provided.
max_features : int, float or {"auto", "sqrt", "log2"}, default=None
The number of features to consider when looking for the best split:
- If int, then consider `max_features` features at each split.
- If float, then `max_features` is a fraction and
`max(1, int(max_features * n_features_in_))` features are considered at
each split.
- If "auto", then `max_features=sqrt(n_features)`.
- If "sqrt", then `max_features=sqrt(n_features)`.
- If "log2", then `max_features=log2(n_features)`.
- If None, then `max_features=n_features`.
max_leaf_nodes : int, default=None
Grow a tree with ``max_leaf_nodes`` in best-first fashion.
Best nodes are defined as relative reduction in impurity.
If None then unlimited number of leaf nodes.
random_state : int, RandomState instance or None, default=None
Controls the randomness of the estimator. The features are always
randomly permuted at each split, even if ``splitter`` is set to
``"best"``. When ``max_features < n_features``, the algorithm will
select ``max_features`` at random at each split before finding the best
split among them. But the best found split may vary across different
runs, even if ``max_features=n_features``. That is the case, if the
improvement of the criterion is identical for several splits and one
split has to be selected at random. To obtain a deterministic behaviour
during fitting, ``random_state`` has to be fixed to an integer.
See how scikit-learn defines ``random_state`` for details.
min_impurity_decrease : float, default=0.0
A node will be split if this split induces a decrease of the impurity
greater than or equal to this value.
The weighted impurity decrease equation is the following::
N_t / N * (impurity - N_t_R / N_t * right_impurity
- N_t_L / N_t * left_impurity)
where ``N`` is the total number of samples, ``N_t`` is the number of
samples at the current node, ``N_t_L`` is the number of samples in the
left child, and ``N_t_R`` is the number of samples in the right child.
``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,
if ``sample_weight`` is passed.
clustering_func : callable
Scikit-learn compatible clustering function to take the affinity matrix
and return cluster labels. By default, :class:`sklearn.cluster.AgglomerativeClustering`.
clustering_func_args : dict
Clustering function class keyword arguments. Passed to `clustering_func`.
"""
def __init__(
self,
*,
criterion="twomeans",
splitter="best",
max_depth=None,
min_samples_split=5,
min_samples_leaf=1,
min_weight_fraction_leaf=0.0,
max_features=None,
max_leaf_nodes=None,
random_state=None,
min_impurity_decrease=0.0,
clustering_func=None,
clustering_func_args=None,
):
super().__init__(
criterion=criterion,
splitter=splitter,
max_depth=max_depth,
min_samples_split=min_samples_split,
min_samples_leaf=min_samples_leaf,
min_weight_fraction_leaf=min_weight_fraction_leaf,
max_features=max_features,
max_leaf_nodes=max_leaf_nodes,
random_state=random_state,
min_impurity_decrease=min_impurity_decrease,
)
self.clustering_func = clustering_func
self.clustering_func_args = clustering_func_args
def fit(self, X, y=None, sample_weight=None, check_input=True):
if check_input:
# TODO: allow X to be sparse
check_X_params = dict(dtype=DTYPE) # , accept_sparse="csc"
X = self._validate_data(X, validate_separately=(check_X_params))
if issparse(X):
X.sort_indices()
if X.indices.dtype != np.intc or X.indptr.dtype != np.intc:
raise ValueError("No support for np.int64 index based sparse matrices")
super()._fit(X=X, y=None, sample_weight=sample_weight, check_input=check_input)
# apply to the leaves
n_samples = X.shape[0]
sim_mat = self.compute_similarity_matrix(X)
# compute the labels and set it
if n_samples >= 2:
self.labels_ = self._assign_labels(sim_mat)
return self
def _build_tree(
self,
X,
y,
sample_weight,
feature_has_missing,
min_samples_leaf,
min_weight_leaf,
max_leaf_nodes,
min_samples_split,
max_depth,
random_state,
):
criterion = self.criterion
if not isinstance(criterion, UnsupervisedCriterion):
criterion = UNSUPERVISED_CRITERIA[self.criterion]()
else:
# Make a deepcopy in case the criterion has mutable attributes that
# might be shared and modified concurrently during parallel fitting
criterion = copy.deepcopy(criterion)
splitter = self.splitter
if not isinstance(self.splitter, UnsupervisedSplitter):
splitter = UNSUPERVISED_SPLITTERS[self.splitter](
criterion,
self.max_features_,
min_samples_leaf,
min_weight_leaf,
random_state,
)
self.tree_ = UnsupervisedTree(self.n_features_in_)
# Use BestFirst if max_leaf_nodes given; use DepthFirst otherwise
if max_leaf_nodes < 0:
builder = UnsupervisedDepthFirstTreeBuilder(
splitter,
min_samples_split,
min_samples_leaf,
min_weight_leaf,
max_depth,
self.min_impurity_decrease,
)
else:
builder = UnsupervisedBestFirstTreeBuilder(
splitter,
min_samples_split,
min_samples_leaf,
min_weight_leaf,
max_depth,
max_leaf_nodes,
self.min_impurity_decrease,
)
builder.build(self.tree_, X, sample_weight)
[docs] def predict(self, X, check_input=True):
"""Assign labels based on clustering the affinity matrix.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Array to cluster.
check_input : bool, optional
Whether to validate input, by default True.
Returns
-------
labels : array-like of shape (n_samples,)
The assigned labels for each sample.
"""
X = self._validate_X_predict(X, check_input=check_input)
affinity_matrix = self.transform(X)
# compute the labels and set it
return self._assign_labels(affinity_matrix)
def _assign_labels(self, affinity_matrix):
"""Assign cluster labels given X.
Parameters
----------
X : ndarray of shape (n_samples, n_samples)
The affinity matrix.
Returns
-------
predict_labels : ndarray of shape (n_samples,)
The predicted cluster labels
"""
if self.clustering_func is None:
self.clustering_func_ = AgglomerativeClustering
else:
self.clustering_func_ = self.clustering_func
if self.clustering_func_args is None:
self.clustering_func_args_ = dict()
else:
self.clustering_func_args_ = self.clustering_func_args
cluster = self.clustering_func_(**self.clustering_func_args_)
# apply agglomerative clustering to obtain cluster labels
predict_labels = cluster.fit_predict(affinity_matrix)
return predict_labels
[docs]class UnsupervisedObliqueDecisionTree(UnsupervisedDecisionTree):
"""Unsupervised oblique decision tree.
Parameters
----------
criterion : {"twomeans", "fastbic"}, default="twomeans"
The function to measure the quality of a split. Supported criteria are
"twomeans" for the variance impurity and "fastbic" for the
BIC criterion. If ``UnsupervisedCriterion`` instance is passed in, then
the user must abide by the Cython internal API. See source code.
splitter : {"best", "random"}, default="best"
The strategy used to choose the split at each node. Supported
strategies are "best" to choose the best split and "random" to choose
the best random split. If ``UnsupervisedSplitter`` instance is passed in, then
the user must abide by the Cython internal API. See source code.
max_depth : int, default=None
The maximum depth of the tree. If None, then nodes are expanded until
all leaves are pure or until all leaves contain less than
min_samples_split samples.
min_samples_split : int or float, default=2
The minimum number of samples required to split an internal node:
- If int, then consider `min_samples_split` as the minimum number.
- If float, then `min_samples_split` is a fraction and
`ceil(min_samples_split * n_samples)` are the minimum
number of samples for each split.
min_samples_leaf : int or float, default=1
The minimum number of samples required to be at a leaf node.
A split point at any depth will only be considered if it leaves at
least ``min_samples_leaf`` training samples in each of the left and
right branches. This may have the effect of smoothing the model,
especially in regression.
- If int, then consider `min_samples_leaf` as the minimum number.
- If float, then `min_samples_leaf` is a fraction and
`ceil(min_samples_leaf * n_samples)` are the minimum
number of samples for each node.
min_weight_fraction_leaf : float, default=0.0
The minimum weighted fraction of the sum total of weights (of all
the input samples) required to be at a leaf node. Samples have
equal weight when sample_weight is not provided.
max_features : int, float or {"auto", "sqrt", "log2"}, default=None
The number of features to consider when looking for the best split:
- If int, then consider `max_features` features at each split.
- If float, then `max_features` is a fraction and
`max(1, int(max_features * n_features_in_))` features are considered at
each split.
- If "auto", then `max_features=sqrt(n_features)`.
- If "sqrt", then `max_features=sqrt(n_features)`.
- If "log2", then `max_features=log2(n_features)`.
- If None, then `max_features=n_features`.
max_leaf_nodes : int, default=None
Grow a tree with ``max_leaf_nodes`` in best-first fashion.
Best nodes are defined as relative reduction in impurity.
If None then unlimited number of leaf nodes.
random_state : int, RandomState instance or None, default=None
Controls the randomness of the estimator. The features are always
randomly permuted at each split, even if ``splitter`` is set to
``"best"``. When ``max_features < n_features``, the algorithm will
select ``max_features`` at random at each split before finding the best
split among them. But the best found split may vary across different
runs, even if ``max_features=n_features``. That is the case, if the
improvement of the criterion is identical for several splits and one
split has to be selected at random. To obtain a deterministic behaviour
during fitting, ``random_state`` has to be fixed to an integer.
See how scikit-learn defines ``random_state`` for details.
min_impurity_decrease : float, default=0.0
A node will be split if this split induces a decrease of the impurity
greater than or equal to this value.
The weighted impurity decrease equation is the following::
N_t / N * (impurity - N_t_R / N_t * right_impurity
- N_t_L / N_t * left_impurity)
where ``N`` is the total number of samples, ``N_t`` is the number of
samples at the current node, ``N_t_L`` is the number of samples in the
left child, and ``N_t_R`` is the number of samples in the right child.
``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,
if ``sample_weight`` is passed.
feature_combinations : float, default=1.5
The number of features to combine on average at each split
of the decision trees.
clustering_func : callable
Scikit-learn compatible clustering function to take the affinity matrix
and return cluster labels. By default, :class:`sklearn.cluster.AgglomerativeClustering`.
clustering_func_args : dict
Clustering function class keyword arguments. Passed to `clustering_func`.
"""
tree_type = "oblique"
def __init__(
self,
*,
criterion="twomeans",
splitter="best",
max_depth=None,
min_samples_split=5,
min_samples_leaf=1,
min_weight_fraction_leaf=0,
max_features=None,
max_leaf_nodes=None,
random_state=None,
min_impurity_decrease=0,
feature_combinations=1.5,
clustering_func=None,
clustering_func_args=None,
):
super().__init__(
criterion=criterion,
splitter=splitter,
max_depth=max_depth,
min_samples_split=min_samples_split,
min_samples_leaf=min_samples_leaf,
min_weight_fraction_leaf=min_weight_fraction_leaf,
max_features=max_features,
max_leaf_nodes=max_leaf_nodes,
random_state=random_state,
min_impurity_decrease=min_impurity_decrease,
clustering_func=clustering_func,
clustering_func_args=clustering_func_args,
)
self.feature_combinations = feature_combinations
def _build_tree(
self,
X,
y,
sample_weight,
feature_has_missing,
min_samples_leaf,
min_weight_leaf,
max_leaf_nodes,
min_samples_split,
max_depth,
random_state,
):
# TODO: add feature_combinations fix that was used in obliquedecisiontreeclassifier
criterion = self.criterion
if not isinstance(criterion, UnsupervisedCriterion):
criterion = UNSUPERVISED_CRITERIA[self.criterion]()
else:
# Make a deepcopy in case the criterion has mutable attributes that
# might be shared and modified concurrently during parallel fitting
criterion = copy.deepcopy(criterion)
splitter = self.splitter
if not isinstance(self.splitter, UnsupervisedObliqueSplitter):
splitter = UNSUPERVISED_OBLIQUE_SPLITTERS[self.splitter](
criterion,
self.max_features_,
min_samples_leaf,
min_weight_leaf,
random_state,
self.feature_combinations,
)
self.tree_ = UnsupervisedObliqueTree(self.n_features_in_)
# Use BestFirst if max_leaf_nodes given; use DepthFirst otherwise
if max_leaf_nodes < 0:
builder = UnsupervisedDepthFirstTreeBuilder(
splitter,
min_samples_split,
min_samples_leaf,
min_weight_leaf,
max_depth,
self.min_impurity_decrease,
)
else:
builder = UnsupervisedBestFirstTreeBuilder(
splitter,
min_samples_split,
min_samples_leaf,
min_weight_leaf,
max_depth,
max_leaf_nodes,
self.min_impurity_decrease,
)
builder.build(self.tree_, X, sample_weight)
[docs]class ObliqueDecisionTreeClassifier(SimMatrixMixin, DecisionTreeClassifier):
"""A decision tree classifier.
Read more in the :ref:`User Guide <sklearn:tree>`. The implementation follows
that of :footcite:`breiman2001random` and :footcite:`TomitaSPORF2020`.
Parameters
----------
criterion : {"gini", "entropy"}, default="gini"
The function to measure the quality of a split. Supported criteria are
"gini" for the Gini impurity and "entropy" for the information gain.
splitter : {"best", "random"}, default="best"
The strategy used to choose the split at each node. Supported
strategies are "best" to choose the best split and "random" to choose
the best random split.
max_depth : int, default=None
The maximum depth of the tree. If None, then nodes are expanded until
all leaves are pure or until all leaves contain less than
min_samples_split samples.
min_samples_split : int or float, default=2
The minimum number of samples required to split an internal node:
- If int, then consider `min_samples_split` as the minimum number.
- If float, then `min_samples_split` is a fraction and
`ceil(min_samples_split * n_samples)` are the minimum
number of samples for each split.
min_samples_leaf : int or float, default=1
The minimum number of samples required to be at a leaf node.
A split point at any depth will only be considered if it leaves at
least ``min_samples_leaf`` training samples in each of the left and
right branches. This may have the effect of smoothing the model,
especially in regression.
- If int, then consider `min_samples_leaf` as the minimum number.
- If float, then `min_samples_leaf` is a fraction and
`ceil(min_samples_leaf * n_samples)` are the minimum
number of samples for each node.
min_weight_fraction_leaf : float, default=0.0
The minimum weighted fraction of the sum total of weights (of all
the input samples) required to be at a leaf node. Samples have
equal weight when sample_weight is not provided.
max_features : int, float or {"auto", "sqrt", "log2"}, default=None
The number of features to consider when looking for the best split:
- If int, then consider `max_features` features at each split.
- If float, then `max_features` is a fraction and
`int(max_features * n_features)` features are considered at each
split.
- If "auto", then `max_features=sqrt(n_features)`.
- If "sqrt", then `max_features=sqrt(n_features)`.
- If "log2", then `max_features=log2(n_features)`.
- If None, then `max_features=n_features`.
Note: the search for a split does not stop until at least one
valid partition of the node samples is found, even if it requires to
effectively inspect more than ``max_features`` features.
Note: Compared to axis-aligned Random Forests, one can set
max_features to a number greater then ``n_features``.
random_state : int, RandomState instance or None, default=None
Controls the randomness of the estimator. The features are always
randomly permuted at each split, even if ``splitter`` is set to
``"best"``. When ``max_features < n_features``, the algorithm will
select ``max_features`` at random at each split before finding the best
split among them. But the best found split may vary across different
runs, even if ``max_features=n_features``. That is the case, if the
improvement of the criterion is identical for several splits and one
split has to be selected at random. To obtain a deterministic behaviour
during fitting, ``random_state`` has to be fixed to an integer.
See :term:`Glossary <random_state>` for details.
max_leaf_nodes : int, default=None
Grow a tree with ``max_leaf_nodes`` in best-first fashion.
Best nodes are defined as relative reduction in impurity.
If None then unlimited number of leaf nodes.
min_impurity_decrease : float, default=0.0
A node will be split if this split induces a decrease of the impurity
greater than or equal to this value.
The weighted impurity decrease equation is the following::
N_t / N * (impurity - N_t_R / N_t * right_impurity
- N_t_L / N_t * left_impurity)
where ``N`` is the total number of samples, ``N_t`` is the number of
samples at the current node, ``N_t_L`` is the number of samples in the
left child, and ``N_t_R`` is the number of samples in the right child.
``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,
if ``sample_weight`` is passed.
class_weight : dict, list of dict or "balanced", default=None
Weights associated with classes in the form ``{class_label: weight}``.
If None, all classes are supposed to have weight one. For
multi-output problems, a list of dicts can be provided in the same
order as the columns of y.
Note that for multioutput (including multilabel) weights should be
defined for each class of every column in its own dict. For example,
for four-class multilabel classification weights should be
[{0: 1, 1: 1}, {0: 1, 1: 5}, {0: 1, 1: 1}, {0: 1, 1: 1}] instead of
[{1:1}, {2:5}, {3:1}, {4:1}].
The "balanced" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as ``n_samples / (n_classes * np.bincount(y))``
For multi-output, the weights of each column of y will be multiplied.
Note that these weights will be multiplied with sample_weight (passed
through the fit method) if sample_weight is specified.
feature_combinations : float, default=None
The number of features to combine on average at each split
of the decision trees. If ``None``, then will default to the minimum of
``(1.5, n_features)``. This controls the number of non-zeros is the
projection matrix. Setting the value to 1.0 is equivalent to a
traditional decision-tree. ``feature_combinations * max_features``
gives the number of expected non-zeros in the projection matrix of shape
``(max_features, n_features)``. Thus this value must always be less than
``n_features`` in order to be valid.
Attributes
----------
classes_ : ndarray of shape (n_classes,) or list of ndarray
The classes labels (single output problem),
or a list of arrays of class labels (multi-output problem).
feature_importances_ : ndarray of shape (n_features,)
The impurity-based feature importances.
The higher, the more important the feature.
The importance of a feature is computed as the (normalized)
total reduction of the criterion brought by that feature. It is also
known as the Gini importance [4]_.
Warning: impurity-based feature importances can be misleading for
high cardinality features (many unique values). See
:func:`sklearn.inspection.permutation_importance` as an alternative.
max_features_ : int
The inferred value of max_features.
n_classes_ : int or list of int
The number of classes (for single output problems),
or a list containing the number of classes for each
output (for multi-output problems).
n_features_in_ : int
Number of features seen during :term:`fit`.
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
n_outputs_ : int
The number of outputs when ``fit`` is performed.
tree_ : Tree instance
The underlying Tree object. Please refer to
``help(sklearn.tree._tree.Tree)`` for
attributes of Tree object.
feature_combinations_ : float
The number of feature combinations on average taken to fit the tree.
See Also
--------
sklearn.tree.DecisionTreeClassifier : An axis-aligned decision tree classifier.
Notes
-----
Compared to ``DecisionTreeClassifier``, oblique trees can sample
more features then ``n_features``, where ``n_features`` is the number
of columns in ``X``. This is controlled via the ``max_features``
parameter. In fact, sampling more times results in better
trees with the caveat that there is an increased computation. It is
always recommended to sample more if one is willing to spend the
computational resources.
The default values for the parameters controlling the size of the trees
(e.g. ``max_depth``, ``min_samples_leaf``, etc.) lead to fully grown and
unpruned trees which can potentially be very large on some data sets. To
reduce memory consumption, the complexity and size of the trees should be
controlled by setting those parameter values.
The :meth:`predict` method operates using the :func:`numpy.argmax`
function on the outputs of :meth:`predict_proba`. This means that in
case the highest predicted probabilities are tied, the classifier will
predict the tied class with the lowest index in :term:`classes_`.
References
----------
.. [1] https://en.wikipedia.org/wiki/Decision_tree_learning
.. [2] L. Breiman, J. Friedman, R. Olshen, and C. Stone, "Classification
and Regression Trees", Wadsworth, Belmont, CA, 1984.
.. [3] T. Hastie, R. Tibshirani and J. Friedman. "Elements of Statistical
Learning", Springer, 2009.
.. [4] L. Breiman, and A. Cutler, "Random Forests",
https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm
Examples
--------
>>> from sklearn.datasets import load_iris
>>> from sklearn.model_selection import cross_val_score
>>> from sktree.tree import ObliqueDecisionTreeClassifier
>>> clf = ObliqueDecisionTreeClassifier(random_state=0)
>>> iris = load_iris()
>>> cross_val_score(clf, iris.data, iris.target, cv=10)
... # doctest: +SKIP
...
array([ 1. , 0.93..., 0.86..., 0.93..., 0.93...,
0.93..., 0.93..., 1. , 0.93..., 1. ])
"""
tree_type = "oblique"
_parameter_constraints = {
**DecisionTreeClassifier._parameter_constraints,
"feature_combinations": [
Interval(Real, 1.0, None, closed="left"),
None,
],
}
def __init__(
self,
*,
criterion="gini",
splitter="best",
max_depth=None,
min_samples_split=2,
min_samples_leaf=1,
min_weight_fraction_leaf=0.0,
max_features=None,
random_state=None,
max_leaf_nodes=None,
min_impurity_decrease=0.0,
class_weight=None,
feature_combinations=None,
):
super().__init__(
criterion=criterion,
splitter=splitter,
max_depth=max_depth,
min_samples_split=min_samples_split,
min_samples_leaf=min_samples_leaf,
min_weight_fraction_leaf=min_weight_fraction_leaf,
max_features=max_features,
max_leaf_nodes=max_leaf_nodes,
class_weight=class_weight,
random_state=random_state,
min_impurity_decrease=min_impurity_decrease,
)
self.feature_combinations = feature_combinations
def _build_tree(
self,
X,
y,
sample_weight,
feature_has_missing,
min_samples_leaf,
min_weight_leaf,
max_leaf_nodes,
min_samples_split,
max_depth,
random_state,
):
"""Build the actual tree.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Internally, it will be converted to
``dtype=np.float32`` and if a sparse matrix is provided
to a sparse ``csc_matrix``.
y : array-like of shape (n_samples,) or (n_samples, n_outputs)
The target values (class labels) as integers or strings.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights. If None, then samples are equally weighted. Splits
that would create child nodes with net zero or negative weight are
ignored while searching for a split in each node. Splits are also
ignored if they would result in any single class carrying a
negative weight in either child node.
min_samples_leaf : int or float
The minimum number of samples required to be at a leaf node.
min_weight_leaf : float, default=0.0
The minimum weighted fraction of the sum total of weights.
max_leaf_nodes : int, default=None
Grow a tree with ``max_leaf_nodes`` in best-first fashion.
min_samples_split : int or float, default=2
The minimum number of samples required to split an internal node.
max_depth : int, default=None
The maximum depth of the tree. If None, then nodes are expanded until
all leaves are pure or until all leaves contain less than
min_samples_split samples.
random_state : int, RandomState instance or None, default=None
Controls the randomness of the estimator.
"""
_, n_features = X.shape
if self.feature_combinations is None:
self.feature_combinations_ = min(n_features, 1.5)
elif self.feature_combinations > n_features:
raise RuntimeError(
f"Feature combinations {self.feature_combinations} should not be "
f"greater than the possible number of features {n_features}"
)
else:
self.feature_combinations_ = self.feature_combinations
# Build tree
criterion = self.criterion
if not isinstance(criterion, BaseCriterion):
criterion = CRITERIA_CLF[self.criterion](self.n_outputs_, self.n_classes_)
else:
# Make a deepcopy in case the criterion has mutable attributes that
# might be shared and modified concurrently during parallel fitting
criterion = copy.deepcopy(criterion)
splitter = self.splitter
if issparse(X):
raise ValueError(
"Sparse input is not supported for oblique trees. "
"Please convert your data to a dense array."
)
else:
OBLIQUE_SPLITTERS = OBLIQUE_DENSE_SPLITTERS
if not isinstance(self.splitter, ObliqueSplitter):
splitter = OBLIQUE_SPLITTERS[self.splitter](
criterion,
self.max_features_,
min_samples_leaf,
min_weight_leaf,
random_state,
self.feature_combinations_,
)
self.tree_ = ObliqueTree(self.n_features_in_, self.n_classes_, self.n_outputs_)
# Use BestFirst if max_leaf_nodes given; use DepthFirst otherwise
if max_leaf_nodes < 0:
builder = DepthFirstTreeBuilder(
splitter,
min_samples_split,
min_samples_leaf,
min_weight_leaf,
max_depth,
self.min_impurity_decrease,
)
else:
builder = BestFirstTreeBuilder(
splitter,
min_samples_split,
min_samples_leaf,
min_weight_leaf,
max_depth,
max_leaf_nodes,
self.min_impurity_decrease,
)
builder.build(self.tree_, X, y, sample_weight)
if self.n_outputs_ == 1:
self.n_classes_ = self.n_classes_[0]
self.classes_ = self.classes_[0]
[docs]class ObliqueDecisionTreeRegressor(SimMatrixMixin, DecisionTreeRegressor):
"""An oblique decision tree Regressor.
Read more in the :ref:`User Guide <sklearn:tree>`. The implementation follows
that of :footcite:`breiman2001random` and :footcite:`TomitaSPORF2020`.
Parameters
----------
criterion : {"squared_error", "friedman_mse", "absolute_error", \
"poisson"}, default="squared_error"
The function to measure the quality of a split. Supported criteria
are "squared_error" for the mean squared error, which is equal to
variance reduction as feature selection criterion and minimizes the L2
loss using the mean of each terminal node, "friedman_mse", which uses
mean squared error with Friedman's improvement score for potential
splits, "absolute_error" for the mean absolute error, which minimizes
the L1 loss using the median of each terminal node, and "poisson" which
uses reduction in Poisson deviance to find splits.
splitter : {"best", "random"}, default="best"
The strategy used to choose the split at each node. Supported
strategies are "best" to choose the best split and "random" to choose
the best random split.
max_depth : int, default=None
The maximum depth of the tree. If None, then nodes are expanded until
all leaves are pure or until all leaves contain less than
min_samples_split samples.
min_samples_split : int or float, default=2
The minimum number of samples required to split an internal node:
- If int, then consider `min_samples_split` as the minimum number.
- If float, then `min_samples_split` is a fraction and
`ceil(min_samples_split * n_samples)` are the minimum
number of samples for each split.
min_samples_leaf : int or float, default=1
The minimum number of samples required to be at a leaf node.
A split point at any depth will only be considered if it leaves at
least ``min_samples_leaf`` training samples in each of the left and
right branches. This may have the effect of smoothing the model,
especially in regression.
- If int, then consider `min_samples_leaf` as the minimum number.
- If float, then `min_samples_leaf` is a fraction and
`ceil(min_samples_leaf * n_samples)` are the minimum
number of samples for each node.
min_weight_fraction_leaf : float, default=0.0
The minimum weighted fraction of the sum total of weights (of all
the input samples) required to be at a leaf node. Samples have
equal weight when sample_weight is not provided.
max_features : int, float or {"auto", "sqrt", "log2"}, default=None
The number of features to consider when looking for the best split:
- If int, then consider `max_features` features at each split.
- If float, then `max_features` is a fraction and
`int(max_features * n_features)` features are considered at each
split.
- If "auto", then `max_features=sqrt(n_features)`.
- If "sqrt", then `max_features=sqrt(n_features)`.
- If "log2", then `max_features=log2(n_features)`.
- If None, then `max_features=n_features`.
Note: the search for a split does not stop until at least one
valid partition of the node samples is found, even if it requires to
effectively inspect more than ``max_features`` features.
Note: Compared to axis-aligned Random Forests, one can set
max_features to a number greater then ``n_features``.
random_state : int, RandomState instance or None, default=None
Controls the randomness of the estimator. The features are always
randomly permuted at each split, even if ``splitter`` is set to
``"best"``. When ``max_features < n_features``, the algorithm will
select ``max_features`` at random at each split before finding the best
split among them. But the best found split may vary across different
runs, even if ``max_features=n_features``. That is the case, if the
improvement of the criterion is identical for several splits and one
split has to be selected at random. To obtain a deterministic behaviour
during fitting, ``random_state`` has to be fixed to an integer.
See :term:`Glossary <random_state>` for details.
max_leaf_nodes : int, default=None
Grow a tree with ``max_leaf_nodes`` in best-first fashion.
Best nodes are defined as relative reduction in impurity.
If None then unlimited number of leaf nodes.
min_impurity_decrease : float, default=0.0
A node will be split if this split induces a decrease of the impurity
greater than or equal to this value.
The weighted impurity decrease equation is the following::
N_t / N * (impurity - N_t_R / N_t * right_impurity
- N_t_L / N_t * left_impurity)
where ``N`` is the total number of samples, ``N_t`` is the number of
samples at the current node, ``N_t_L`` is the number of samples in the
left child, and ``N_t_R`` is the number of samples in the right child.
``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,
if ``sample_weight`` is passed.
feature_combinations : float, default=None
The number of features to combine on average at each split
of the decision trees. If ``None``, then will default to the minimum of
``(1.5, n_features)``. This controls the number of non-zeros is the
projection matrix. Setting the value to 1.0 is equivalent to a
traditional decision-tree. ``feature_combinations * max_features``
gives the number of expected non-zeros in the projection matrix of shape
``(max_features, n_features)``. Thus this value must always be less than
``n_features`` in order to be valid.
Attributes
----------
feature_importances_ : ndarray of shape (n_features,)
The impurity-based feature importances.
The higher, the more important the feature.
The importance of a feature is computed as the (normalized)
total reduction of the criterion brought by that feature. It is also
known as the Gini importance [4]_.
Warning: impurity-based feature importances can be misleading for
high cardinality features (many unique values). See
:func:`sklearn.inspection.permutation_importance` as an alternative.
max_features_ : int
The inferred value of max_features.
n_features_in_ : int
Number of features seen during :term:`fit`.
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
n_outputs_ : int
The number of outputs when ``fit`` is performed.
tree_ : Tree instance
The underlying Tree object. Please refer to
``help(sklearn.tree._tree.Tree)`` for
attributes of Tree object.
feature_combinations_ : float
The number of feature combinations on average taken to fit the tree.
See Also
--------
sklearn.tree.DecisionTreeRegressor : An axis-aligned decision tree regressor.
ObliqueDecisionTreeClassifier : An oblique decision tree classifier.
Notes
-----
Compared to ``DecisionTreeClassifier``, oblique trees can sample
more features then ``n_features``, where ``n_features`` is the number
of columns in ``X``. This is controlled via the ``max_features``
parameter. In fact, sampling more times results in better
trees with the caveat that there is an increased computation. It is
always recommended to sample more if one is willing to spend the
computational resources.
The default values for the parameters controlling the size of the trees
(e.g. ``max_depth``, ``min_samples_leaf``, etc.) lead to fully grown and
unpruned trees which can potentially be very large on some data sets. To
reduce memory consumption, the complexity and size of the trees should be
controlled by setting those parameter values.
References
----------
.. [1] https://en.wikipedia.org/wiki/Decision_tree_learning
.. [2] L. Breiman, J. Friedman, R. Olshen, and C. Stone, "Classification
and Regression Trees", Wadsworth, Belmont, CA, 1984.
.. [3] T. Hastie, R. Tibshirani and J. Friedman. "Elements of Statistical
Learning", Springer, 2009.
.. [4] L. Breiman, and A. Cutler, "Random Forests",
https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm
Examples
--------
>>> from sklearn.datasets import load_diabetes
>>> from sklearn.model_selection import cross_val_score
>>> from sklearn.tree import ObliqueDecisionTreeRegressor
>>> X, y = load_diabetes(return_X_y=True)
>>> regressor = ObliqueDecisionTreeRegressor(random_state=0)
>>> cross_val_score(regressor, X, y, cv=10)
... # doctest: +SKIP
...
array([-0.68908909, -0.35854406, 0.35223873, -0.03616902, -0.56008907,
0.32235221, 0.06945264, -1.1465216 , 0.34597007, -0.15308512])
"""
tree_type = "oblique"
_parameter_constraints = {
**DecisionTreeRegressor._parameter_constraints,
"feature_combinations": [
Interval(Real, 1.0, None, closed="left"),
None,
],
}
def __init__(
self,
*,
criterion="squared_error",
splitter="best",
max_depth=None,
min_samples_split=2,
min_samples_leaf=1,
min_weight_fraction_leaf=0.0,
max_features=None,
random_state=None,
max_leaf_nodes=None,
min_impurity_decrease=0.0,
feature_combinations=None,
):
super().__init__(
criterion=criterion,
splitter=splitter,
max_depth=max_depth,
min_samples_split=min_samples_split,
min_samples_leaf=min_samples_leaf,
min_weight_fraction_leaf=min_weight_fraction_leaf,
max_features=max_features,
max_leaf_nodes=max_leaf_nodes,
random_state=random_state,
min_impurity_decrease=min_impurity_decrease,
)
self.feature_combinations = feature_combinations
def _build_tree(
self,
X,
y,
sample_weight,
feature_has_missing,
min_samples_leaf,
min_weight_leaf,
max_leaf_nodes,
min_samples_split,
max_depth,
random_state,
):
"""Build the actual tree.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Internally, it will be converted to
``dtype=np.float32`` and if a sparse matrix is provided
to a sparse ``csc_matrix``.
y : array-like of shape (n_samples,) or (n_samples, n_outputs)
The target values (real numbers). Use ``dtype=np.float64`` and
``order='C'`` for maximum efficiency.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights. If None, then samples are equally weighted. Splits
that would create child nodes with net zero or negative weight are
ignored while searching for a split in each node.
min_samples_leaf : int or float
The minimum number of samples required to be at a leaf node.
min_weight_leaf : float, default=0.0
The minimum weighted fraction of the sum total of weights.
max_leaf_nodes : int, default=None
Grow a tree with ``max_leaf_nodes`` in best-first fashion.
min_samples_split : int or float, default=2
The minimum number of samples required to split an internal node.
max_depth : int, default=None
The maximum depth of the tree. If None, then nodes are expanded until
all leaves are pure or until all leaves contain less than
min_samples_split samples.
random_state : int, RandomState instance or None, default=None
Controls the randomness of the estimator.
"""
n_samples, n_features = X.shape
if self.feature_combinations is None:
self.feature_combinations_ = min(n_features, 1.5)
elif self.feature_combinations > n_features:
raise RuntimeError(
f"Feature combinations {self.feature_combinations} should not be "
f"greater than the possible number of features {n_features}"
)
else:
self.feature_combinations_ = self.feature_combinations
# Build tree
criterion = self.criterion
if not isinstance(criterion, BaseCriterion):
criterion = CRITERIA_REG[self.criterion](self.n_outputs_, n_samples)
else:
# Make a deepcopy in case the criterion has mutable attributes that
# might be shared and modified concurrently during parallel fitting
criterion = copy.deepcopy(criterion)
splitter = self.splitter
if issparse(X):
raise ValueError(
"Sparse input is not supported for oblique trees. "
"Please convert your data to a dense array."
)
else:
OBLIQUE_SPLITTERS = OBLIQUE_DENSE_SPLITTERS
if not isinstance(self.splitter, ObliqueSplitter):
splitter = OBLIQUE_SPLITTERS[self.splitter](
criterion,
self.max_features_,
min_samples_leaf,
min_weight_leaf,
random_state,
self.feature_combinations_,
)
self.tree_ = ObliqueTree(
self.n_features_in_,
np.array([1] * self.n_outputs_, dtype=np.intp),
self.n_outputs_,
)
# Use BestFirst if max_leaf_nodes given; use DepthFirst otherwise
if max_leaf_nodes < 0:
builder = DepthFirstTreeBuilder(
splitter,
min_samples_split,
min_samples_leaf,
min_weight_leaf,
max_depth,
self.min_impurity_decrease,
)
else:
builder = BestFirstTreeBuilder(
splitter,
min_samples_split,
min_samples_leaf,
min_weight_leaf,
max_depth,
max_leaf_nodes,
self.min_impurity_decrease,
)
builder.build(self.tree_, X, y, sample_weight)
[docs]class PatchObliqueDecisionTreeClassifier(SimMatrixMixin, DecisionTreeClassifier):
"""A oblique decision tree classifier that operates over patches of data.
A patch oblique decision tree is also known as a manifold oblique decision tree
(called MORF in :footcite:`Li2019manifold`), where the splitter is aware of
the structure in the data. For example, in an image, a patch would be contiguous
along the rows and columns of the image. In a multivariate time-series, a patch
would be contiguous over time, but possibly discontiguous over the sensors.
Parameters
----------
criterion : {"gini", "entropy"}, default="gini"
The function to measure the quality of a split. Supported criteria are
"gini" for the Gini impurity and "entropy" for the information gain.
splitter : {"best", "random"}, default="best"
The strategy used to choose the split at each node. Supported
strategies are "best" to choose the best split and "random" to choose
the best random split.
max_depth : int, default=None
The maximum depth of the tree. If None, then nodes are expanded until
all leaves are pure or until all leaves contain less than
min_samples_split samples.
min_samples_split : int or float, default=2
The minimum number of samples required to split an internal node:
- If int, then consider `min_samples_split` as the minimum number.
- If float, then `min_samples_split` is a fraction and
`ceil(min_samples_split * n_samples)` are the minimum
number of samples for each split.
min_samples_leaf : int or float, default=1
The minimum number of samples required to be at a leaf node.
A split point at any depth will only be considered if it leaves at
least ``min_samples_leaf`` training samples in each of the left and
right branches. This may have the effect of smoothing the model,
especially in regression.
- If int, then consider `min_samples_leaf` as the minimum number.
- If float, then `min_samples_leaf` is a fraction and
`ceil(min_samples_leaf * n_samples)` are the minimum
number of samples for each node.
min_weight_fraction_leaf : float, default=0.0
The minimum weighted fraction of the sum total of weights (of all
the input samples) required to be at a leaf node. Samples have
equal weight when sample_weight is not provided.
max_features : int, float or {"auto", "sqrt", "log2"}, default=None
The number of features to consider when looking for the best split:
- If int, then consider `max_features` features at each split.
- If float, then `max_features` is a fraction and
`int(max_features * n_features)` features are considered at each
split.
- If "auto", then `max_features=sqrt(n_features)`.
- If "sqrt", then `max_features=sqrt(n_features)`.
- If "log2", then `max_features=log2(n_features)`.
- If None, then `max_features=n_features`.
Note: the search for a split does not stop until at least one
valid partition of the node samples is found, even if it requires to
effectively inspect more than ``max_features`` features.
Note: Compared to axis-aligned Random Forests, one can set
max_features to a number greater then ``n_features``.
random_state : int, RandomState instance or None, default=None
Controls the randomness of the estimator. The features are always
randomly permuted at each split, even if ``splitter`` is set to
``"best"``. When ``max_features < n_features``, the algorithm will
select ``max_features`` at random at each split before finding the best
split among them. But the best found split may vary across different
runs, even if ``max_features=n_features``. That is the case, if the
improvement of the criterion is identical for several splits and one
split has to be selected at random. To obtain a deterministic behaviour
during fitting, ``random_state`` has to be fixed to an integer.
See :term:`Glossary <random_state>` for details.
max_leaf_nodes : int, default=None
Grow a tree with ``max_leaf_nodes`` in best-first fashion.
Best nodes are defined as relative reduction in impurity.
If None then unlimited number of leaf nodes.
min_impurity_decrease : float, default=0.0
A node will be split if this split induces a decrease of the impurity
greater than or equal to this value.
The weighted impurity decrease equation is the following::
N_t / N * (impurity - N_t_R / N_t * right_impurity
- N_t_L / N_t * left_impurity)
where ``N`` is the total number of samples, ``N_t`` is the number of
samples at the current node, ``N_t_L`` is the number of samples in the
left child, and ``N_t_R`` is the number of samples in the right child.
``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,
if ``sample_weight`` is passed.
class_weight : dict, list of dict or "balanced", default=None
Weights associated with classes in the form ``{class_label: weight}``.
If None, all classes are supposed to have weight one. For
multi-output problems, a list of dicts can be provided in the same
order as the columns of y.
Note that for multioutput (including multilabel) weights should be
defined for each class of every column in its own dict. For example,
for four-class multilabel classification weights should be
[{0: 1, 1: 1}, {0: 1, 1: 5}, {0: 1, 1: 1}, {0: 1, 1: 1}] instead of
[{1:1}, {2:5}, {3:1}, {4:1}].
The "balanced" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as ``n_samples / (n_classes * np.bincount(y))``
For multi-output, the weights of each column of y will be multiplied.
Note that these weights will be multiplied with sample_weight (passed
through the fit method) if sample_weight is specified.
min_patch_dims : array-like, optional
The minimum dimensions of a patch, by default 1 along all dimensions.
max_patch_dims : array-like, optional
The maximum dimensions of a patch, by default 1 along all dimensions.
dim_contiguous : array-like of bool, optional
Whether or not each patch is sampled contiguously along this dimension.
data_dims : array-like, optional
The presumed dimensions of the un-vectorized feature vector, by default
will be a 1D vector with (1, n_features) shape.
boundary : optional, str {'wrap'}
The boundary condition to use when sampling patches, by default None.
'wrap' corresponds to the boundary condition as is in numpy and scipy.
feature_weight : array-like of shape (n_samples,n_features,), default=None
Feature weights. If None, then features are equally weighted as is.
If provided, then the feature weights are used to weight the
patches that are generated. The feature weights are used
as follows: for every patch that is sampled, the feature weights over
the entire patch is summed and normalizes the patch.
Attributes
----------
classes_ : ndarray of shape (n_classes,) or list of ndarray
The classes labels (single output problem),
or a list of arrays of class labels (multi-output problem).
feature_importances_ : ndarray of shape (n_features,)
The impurity-based feature importances.
The higher, the more important the feature.
The importance of a feature is computed as the (normalized)
total reduction of the criterion brought by that feature. It is also
known as the Gini importance [4]_.
Warning: impurity-based feature importances can be misleading for
high cardinality features (many unique values). See
:func:`sklearn.inspection.permutation_importance` as an alternative.
max_features_ : int
The inferred value of max_features.
n_classes_ : int or list of int
The number of classes (for single output problems),
or a list containing the number of classes for each
output (for multi-output problems).
n_features_in_ : int
Number of features seen during :term:`fit`.
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
n_outputs_ : int
The number of outputs when ``fit`` is performed.
tree_ : Tree instance
The underlying Tree object. Please refer to
``help(sklearn.tree._tree.Tree)`` for
attributes of Tree object.
min_patch_dims_ : array-like
The minimum dimensions of a patch.
max_patch_dims_ : array-like
The maximum dimensions of a patch.
data_dims_ : array-like
The presumed dimensions of the un-vectorized feature vector.
Notes
-----
Patches can be 2D masks that are applied onto the data matrix. Following sklearn
API standards, ``X`` is always a ``(n_samples, n_features)`` array even if
X is comprised of images, or multivariate-time series. The ``data_width`` and
``data_height`` parameters are used to inform the ``PatchObliqueDecisionTreeClassifier``
of the original structure of the data. It is required that
``data_width * data_height = n_features``.
When users pass in ``X`` to :meth:`fit`, tt is presumed that all vectorization operations
are done C-contiguously (i.e. the last axis is contiguous).
Note that for a patch height and width of size 1, the tree is exactly the same as the
decision tree, albeit with less efficienc optimizations. Therefore, it is always
recommended to set the range of patch heights and widths based on the structure of your
expected input data.
References
----------
.. footbibliography::
"""
tree_type = "oblique"
_parameter_constraints = {
**DecisionTreeClassifier._parameter_constraints,
"min_patch_dims": ["array-like", None],
"max_patch_dims": ["array-like", None],
"data_dims": ["array-like", None],
"dim_contiguous": ["array-like", None],
"boundary": [str, None],
"feature_weight": ["array-like", None],
}
def __init__(
self,
*,
criterion="gini",
splitter="best",
max_depth=None,
min_samples_split=2,
min_samples_leaf=1,
min_weight_fraction_leaf=0.0,
max_features=None,
random_state=None,
max_leaf_nodes=None,
min_impurity_decrease=0.0,
class_weight=None,
min_patch_dims=None,
max_patch_dims=None,
dim_contiguous=None,
data_dims=None,
boundary=None,
feature_weight=None,
):
super().__init__(
criterion=criterion,
splitter=splitter,
max_depth=max_depth,
min_samples_split=min_samples_split,
min_samples_leaf=min_samples_leaf,
min_weight_fraction_leaf=min_weight_fraction_leaf,
max_features=max_features,
max_leaf_nodes=max_leaf_nodes,
class_weight=class_weight,
random_state=random_state,
min_impurity_decrease=min_impurity_decrease,
)
self.min_patch_dims = min_patch_dims
self.max_patch_dims = max_patch_dims
self.dim_contiguous = dim_contiguous
self.data_dims = data_dims
self.boundary = boundary
self.feature_weight = feature_weight
[docs] def fit(self, X, y, sample_weight=None, check_input=True):
"""Fit tree.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Internally, it will be converted to
``dtype=np.float32`` and if a sparse matrix is provided
to a sparse ``csc_matrix``.
y : array-like of shape (n_samples,) or (n_samples, n_outputs)
The target values (class labels) as integers or strings.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights. If None, then samples are equally weighted. Splits
that would create child nodes with net zero or negative weight are
ignored while searching for a split in each node. Splits are also
ignored if they would result in any single class carrying a
negative weight in either child node.
check_input : bool, optional
Whether or not to check input, by default True.
"""
if check_input:
# Need to validate separately here.
# We can't pass multi_output=True because that would allow y to be
# csr.
check_X_params = dict(dtype=DTYPE, accept_sparse="csc")
check_y_params = dict(ensure_2d=False, dtype=None)
X, y = self._validate_data(X, y, validate_separately=(check_X_params, check_y_params))
if self.feature_weight is not None:
self.feature_weight = self._validate_data(
self.feature_weight, ensure_2d=True, dtype=DTYPE
)
if self.feature_weight.shape != X.shape:
raise ValueError(
f"feature_weight has shape {self.feature_weight.shape} but X has "
f"shape {X.shape}"
)
if issparse(X):
X.sort_indices()
if X.indices.dtype != np.intc or X.indptr.dtype != np.intc:
raise ValueError("No support for np.int64 index based sparse matrices")
if self.data_dims is None:
self.data_dims_ = np.array((1, X.shape[1]))
else:
if np.prod(self.data_dims) != X.shape[1]:
raise RuntimeError(f"Data dimensions {self.data_dims} do not match {X.shape[1]}.")
self.data_dims_ = np.array(self.data_dims)
ndim = len(self.data_dims_)
# validate contiguous parameter
if self.dim_contiguous is None:
self.dim_contiguous_ = np.ones((ndim,), dtype=np.bool_)
else:
if len(self.dim_contiguous) != ndim:
raise ValueError(f"Contiguous dimensions should equal {ndim} dimensions.")
self.dim_contiguous_ = np.array(self.dim_contiguous).astype(np.bool_)
# validate data height/width
if self.min_patch_dims is None:
self.min_patch_dims_ = np.ones((ndim,), dtype=np.intp)
else:
self.min_patch_dims_ = np.array(self.min_patch_dims)
if self.max_patch_dims is None:
self.max_patch_dims_ = np.ones((ndim,), dtype=np.intp)
self.max_patch_dims_[-1] = X.shape[1]
else:
self.max_patch_dims_ = np.array(self.max_patch_dims)
if len(self.min_patch_dims_) != ndim:
raise ValueError(f"Minimum patch dimensions should equal {ndim} dimensions.")
if len(self.max_patch_dims_) != ndim:
raise ValueError(f"Maximum patch dimensions should equal {ndim} dimensions.")
# validate patch parameters
for idx in range(ndim):
if self.min_patch_dims_[idx] > self.max_patch_dims_[idx]:
raise RuntimeError(
f"The minimum patch width {self.min_patch_dims_[idx]} is "
f"greater than the maximum patch width {self.max_patch_dims_[idx]}"
)
if self.min_patch_dims_[idx] > self.data_dims_[idx]:
raise RuntimeError(
f"The minimum patch width {self.min_patch_dims_[idx]} is "
f"greater than the data width {self.data_dims_[idx]}"
)
if self.max_patch_dims_[idx] > self.data_dims_[idx]:
raise RuntimeError(
f"The maximum patch width {self.max_patch_dims_[idx]} is "
f"greater than the data width {self.data_dims_[idx]}"
)
return super().fit(X, y, sample_weight, check_input=False)
def _build_tree(
self,
X,
y,
sample_weight,
feature_has_missing,
min_samples_leaf,
min_weight_leaf,
max_leaf_nodes,
min_samples_split,
max_depth,
random_state,
):
"""Build the actual tree.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Internally, it will be converted to
``dtype=np.float32`` and if a sparse matrix is provided
to a sparse ``csc_matrix``.
y : array-like of shape (n_samples,) or (n_samples, n_outputs)
The target values (class labels) as integers or strings.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights. If None, then samples are equally weighted. Splits
that would create child nodes with net zero or negative weight are
ignored while searching for a split in each node. Splits are also
ignored if they would result in any single class carrying a
negative weight in either child node.
min_samples_leaf : int or float
The minimum number of samples required to be at a leaf node.
min_weight_leaf : float, default=0.0
The minimum weighted fraction of the sum total of weights.
max_leaf_nodes : int, default=None
Grow a tree with ``max_leaf_nodes`` in best-first fashion.
min_samples_split : int or float, default=2
The minimum number of samples required to split an internal node.
max_depth : int, default=None
The maximum depth of the tree. If None, then nodes are expanded until
all leaves are pure or until all leaves contain less than
min_samples_split samples.
random_state : int, RandomState instance or None, default=None
Controls the randomness of the estimator.
"""
# Build tree
criterion = self.criterion
if not isinstance(criterion, BaseCriterion):
criterion = CRITERIA_CLF[self.criterion](self.n_outputs_, self.n_classes_)
else:
# Make a deepcopy in case the criterion has mutable attributes that
# might be shared and modified concurrently during parallel fitting
criterion = copy.deepcopy(criterion)
splitter = self.splitter
if issparse(X):
raise ValueError(
"Sparse input is not supported for oblique trees. "
"Please convert your data to a dense array."
)
else:
PATCH_SPLITTERS = PATCH_DENSE_SPLITTERS
if not isinstance(self.splitter, PatchSplitter):
splitter = PATCH_SPLITTERS[self.splitter](
criterion,
self.max_features_,
min_samples_leaf,
min_weight_leaf,
random_state,
self.min_patch_dims_,
self.max_patch_dims_,
self.dim_contiguous_,
self.data_dims_,
self.boundary,
self.feature_weight,
)
self.tree_ = ObliqueTree(self.n_features_in_, self.n_classes_, self.n_outputs_)
# Use BestFirst if max_leaf_nodes given; use DepthFirst otherwise
if max_leaf_nodes < 0:
builder = DepthFirstTreeBuilder(
splitter,
min_samples_split,
min_samples_leaf,
min_weight_leaf,
max_depth,
self.min_impurity_decrease,
)
else:
builder = BestFirstTreeBuilder(
splitter,
min_samples_split,
min_samples_leaf,
min_weight_leaf,
max_depth,
max_leaf_nodes,
self.min_impurity_decrease,
)
builder.build(self.tree_, X, y, sample_weight)
if self.n_outputs_ == 1:
self.n_classes_ = self.n_classes_[0]
self.classes_ = self.classes_[0]
def _more_tags(self):
# XXX: nans should be supportable in SPORF by just using RF-like splits on missing values
# However, for MORF it is not supported
allow_nan = False
return {"multilabel": True, "allow_nan": allow_nan}
[docs]class PatchObliqueDecisionTreeRegressor(SimMatrixMixin, DecisionTreeRegressor):
"""A oblique decision tree regressor that operates over patches of data.
A patch oblique decision tree is also known as a manifold oblique decision tree
(called MORF in :footcite:`Li2019manifold`), where the splitter is aware of
the structure in the data. For example, in an image, a patch would be contiguous
along the rows and columns of the image. In a multivariate time-series, a patch
would be contiguous over time, but possibly discontiguous over the sensors.
Parameters
----------
criterion : {"squared_error", "friedman_mse", "absolute_error", \
"poisson"}, default="squared_error"
The function to measure the quality of a split. Supported criteria
are "squared_error" for the mean squared error, which is equal to
variance reduction as feature selection criterion and minimizes the L2
loss using the mean of each terminal node, "friedman_mse", which uses
mean squared error with Friedman's improvement score for potential
splits, "absolute_error" for the mean absolute error, which minimizes
the L1 loss using the median of each terminal node, and "poisson" which
uses reduction in Poisson deviance to find splits.
splitter : {"best", "random"}, default="best"
The strategy used to choose the split at each node. Supported
strategies are "best" to choose the best split and "random" to choose
the best random split.
max_depth : int, default=None
The maximum depth of the tree. If None, then nodes are expanded until
all leaves are pure or until all leaves contain less than
min_samples_split samples.
min_samples_split : int or float, default=2
The minimum number of samples required to split an internal node:
- If int, then consider `min_samples_split` as the minimum number.
- If float, then `min_samples_split` is a fraction and
`ceil(min_samples_split * n_samples)` are the minimum
number of samples for each split.
min_samples_leaf : int or float, default=1
The minimum number of samples required to be at a leaf node.
A split point at any depth will only be considered if it leaves at
least ``min_samples_leaf`` training samples in each of the left and
right branches. This may have the effect of smoothing the model,
especially in regression.
- If int, then consider `min_samples_leaf` as the minimum number.
- If float, then `min_samples_leaf` is a fraction and
`ceil(min_samples_leaf * n_samples)` are the minimum
number of samples for each node.
min_weight_fraction_leaf : float, default=0.0
The minimum weighted fraction of the sum total of weights (of all
the input samples) required to be at a leaf node. Samples have
equal weight when sample_weight is not provided.
max_features : int, float or {"auto", "sqrt", "log2"}, default=None
The number of features to consider when looking for the best split:
- If int, then consider `max_features` features at each split.
- If float, then `max_features` is a fraction and
`int(max_features * n_features)` features are considered at each
split.
- If "auto", then `max_features=sqrt(n_features)`.
- If "sqrt", then `max_features=sqrt(n_features)`.
- If "log2", then `max_features=log2(n_features)`.
- If None, then `max_features=n_features`.
Note: the search for a split does not stop until at least one
valid partition of the node samples is found, even if it requires to
effectively inspect more than ``max_features`` features.
Note: Compared to axis-aligned Random Forests, one can set
max_features to a number greater then ``n_features``.
random_state : int, RandomState instance or None, default=None
Controls the randomness of the estimator. The features are always
randomly permuted at each split, even if ``splitter`` is set to
``"best"``. When ``max_features < n_features``, the algorithm will
select ``max_features`` at random at each split before finding the best
split among them. But the best found split may vary across different
runs, even if ``max_features=n_features``. That is the case, if the
improvement of the criterion is identical for several splits and one
split has to be selected at random. To obtain a deterministic behaviour
during fitting, ``random_state`` has to be fixed to an integer.
See :term:`Glossary <random_state>` for details.
max_leaf_nodes : int, default=None
Grow a tree with ``max_leaf_nodes`` in best-first fashion.
Best nodes are defined as relative reduction in impurity.
If None then unlimited number of leaf nodes.
min_impurity_decrease : float, default=0.0
A node will be split if this split induces a decrease of the impurity
greater than or equal to this value.
The weighted impurity decrease equation is the following::
N_t / N * (impurity - N_t_R / N_t * right_impurity
- N_t_L / N_t * left_impurity)
where ``N`` is the total number of samples, ``N_t`` is the number of
samples at the current node, ``N_t_L`` is the number of samples in the
left child, and ``N_t_R`` is the number of samples in the right child.
``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,
if ``sample_weight`` is passed.
min_patch_dims : array-like, optional
The minimum dimensions of a patch, by default 1 along all dimensions.
max_patch_dims : array-like, optional
The maximum dimensions of a patch, by default 1 along all dimensions.
dim_contiguous : array-like of bool, optional
Whether or not each patch is sampled contiguously along this dimension.
data_dims : array-like, optional
The presumed dimensions of the un-vectorized feature vector, by default
will be a 1D vector with (1, n_features) shape.
boundary : optional, str {'wrap'}
The boundary condition to use when sampling patches, by default None.
'wrap' corresponds to the boundary condition as is in numpy and scipy.
feature_weight : array-like of shape (n_samples,n_features,), default=None
Feature weights. If None, then features are equally weighted as is.
If provided, then the feature weights are used to weight the
patches that are generated. The feature weights are used
as follows: for every patch that is sampled, the feature weights over
the entire patch is summed and normalizes the patch.
Attributes
----------
feature_importances_ : ndarray of shape (n_features,)
The impurity-based feature importances.
The higher, the more important the feature.
The importance of a feature is computed as the (normalized)
total reduction of the criterion brought by that feature. It is also
known as the Gini importance [4]_.
Warning: impurity-based feature importances can be misleading for
high cardinality features (many unique values). See
:func:`sklearn.inspection.permutation_importance` as an alternative.
max_features_ : int
The inferred value of max_features.
n_features_in_ : int
Number of features seen during :term:`fit`.
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
n_outputs_ : int
The number of outputs when ``fit`` is performed.
tree_ : Tree instance
The underlying Tree object. Please refer to
``help(sklearn.tree._tree.Tree)`` for
attributes of Tree object.
min_patch_dims_ : array-like
The minimum dimensions of a patch.
max_patch_dims_ : array-like
The maximum dimensions of a patch.
data_dims_ : array-like
The presumed dimensions of the un-vectorized feature vector.
Notes
-----
Patches are 2D masks that are applied onto the data matrix. Following sklearn
API standards, ``X`` is always a ``(n_samples, n_features)`` array even if
X is comprised of images, or multivariate-time series. The ``data_width`` and
``data_height`` parameters are used to inform the ``PatchObliqueDecisionTreeRegressor``
of the original structure of the data. It is required that
``data_width * data_height = n_features``.
When users pass in ``X`` to :meth:`fit`, tt is presumed that all vectorization operations
are done C-contiguously (i.e. the last axis is contiguous).
Note that for a patch height and width of size 1, the tree is exactly the same as the
decision tree, albeit with less efficienc optimizations. Therefore, it is always
recommended to set the range of patch heights and widths based on the structure of your
expected input data.
References
----------
.. footbibliography::
Examples
--------
>>> from sklearn.datasets import load_diabetes
>>> from sklearn.model_selection import cross_val_score
>>> X, y = load_diabetes(return_X_y=True)
>>> from sktree.tree import PatchObliqueDecisionTreeRegressor as RGS
>>> regressor = RGS(random_state=0)
>>> cross_val_score(regressor, X, y, cv=10)
... # doctest: +SKIP
...
array([-0.10163671, -0.78786738, 0.01490768, 0.32737289, -0.24816698,
0.41881754, 0.0588273 , -1.48722913, -0.07927208, -0.15600762])
"""
tree_type = "oblique"
_parameter_constraints = {
**DecisionTreeRegressor._parameter_constraints,
"min_patch_dims": ["array-like", None],
"max_patch_dims": ["array-like", None],
"data_dims": ["array-like", None],
"dim_contiguous": ["array-like", None],
"boundary": [str, None],
"feature_weight": ["array-like", None],
}
def __init__(
self,
*,
criterion="squared_error",
splitter="best",
max_depth=None,
min_samples_split=2,
min_samples_leaf=1,
min_weight_fraction_leaf=0.0,
max_features=None,
random_state=None,
max_leaf_nodes=None,
min_impurity_decrease=0.0,
min_patch_dims=None,
max_patch_dims=None,
dim_contiguous=None,
data_dims=None,
boundary=None,
feature_weight=None,
):
super().__init__(
criterion=criterion,
splitter=splitter,
max_depth=max_depth,
min_samples_split=min_samples_split,
min_samples_leaf=min_samples_leaf,
min_weight_fraction_leaf=min_weight_fraction_leaf,
max_features=max_features,
max_leaf_nodes=max_leaf_nodes,
random_state=random_state,
min_impurity_decrease=min_impurity_decrease,
)
self.min_patch_dims = min_patch_dims
self.max_patch_dims = max_patch_dims
self.dim_contiguous = dim_contiguous
self.data_dims = data_dims
self.boundary = boundary
self.feature_weight = feature_weight
[docs] def fit(self, X, y, sample_weight=None, check_input=True):
"""Fit tree.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Internally, it will be converted to
``dtype=np.float32`` and if a sparse matrix is provided
to a sparse ``csc_matrix``.
y : array-like of shape (n_samples,) or (n_samples, n_outputs)
The target values (real numbers). Use ``dtype=np.float64`` and
``order='C'`` for maximum efficiency.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights. If None, then samples are equally weighted. Splits
that would create child nodes with net zero or negative weight are
ignored while searching for a split in each node.
check_input : bool, optional
Whether or not to check input, by default True.
"""
if check_input:
# Need to validate separately here.
# We can't pass multi_output=True because that would allow y to be
# csr.
check_X_params = dict(dtype=DTYPE, accept_sparse="csc")
check_y_params = dict(ensure_2d=False, dtype=None)
X, y = self._validate_data(X, y, validate_separately=(check_X_params, check_y_params))
if self.feature_weight is not None:
self.feature_weight = self._validate_data(
self.feature_weight, ensure_2d=True, dtype=DTYPE
)
if self.feature_weight.shape != X.shape:
raise ValueError(
f"feature_weight has shape {self.feature_weight.shape} but X has "
f"shape {X.shape}"
)
if issparse(X):
X.sort_indices()
if X.indices.dtype != np.intc or X.indptr.dtype != np.intc:
raise ValueError("No support for np.int64 index based sparse matrices")
if self.data_dims is None:
self.data_dims_ = np.array((1, X.shape[1]))
else:
if np.prod(self.data_dims) != X.shape[1]:
raise RuntimeError(f"Data dimensions {self.data_dims} do not match {X.shape[1]}.")
self.data_dims_ = np.array(self.data_dims)
ndim = len(self.data_dims_)
# validate contiguous parameter
if self.dim_contiguous is None:
self.dim_contiguous_ = np.ones((ndim,), dtype=np.bool_)
else:
if len(self.dim_contiguous) != ndim:
raise ValueError(f"Contiguous dimensions should equal {ndim} dimensions.")
self.dim_contiguous_ = np.array(self.dim_contiguous).astype(np.bool_)
# validate data height/width
if self.min_patch_dims is None:
self.min_patch_dims_ = np.ones((ndim,), dtype=np.intp)
else:
self.min_patch_dims_ = np.array(self.min_patch_dims)
if self.max_patch_dims is None:
self.max_patch_dims_ = np.ones((ndim,), dtype=np.intp)
self.max_patch_dims_[-1] = X.shape[1]
else:
self.max_patch_dims_ = np.array(self.max_patch_dims)
if len(self.min_patch_dims_) != ndim:
raise ValueError(f"Minimum patch dimensions should equal {ndim} dimensions.")
if len(self.max_patch_dims_) != ndim:
raise ValueError(f"Maximum patch dimensions should equal {ndim} dimensions.")
# validate patch parameters
for idx in range(ndim):
if self.min_patch_dims_[idx] > self.max_patch_dims_[idx]:
raise RuntimeError(
f"The minimum patch width {self.min_patch_dims_[idx]} is "
f"greater than the maximum patch width {self.max_patch_dims_[idx]}"
)
if self.min_patch_dims_[idx] > self.data_dims_[idx]:
raise RuntimeError(
f"The minimum patch width {self.min_patch_dims_[idx]} is "
f"greater than the data width {self.data_dims_[idx]}"
)
if self.max_patch_dims_[idx] > self.data_dims_[idx]:
raise RuntimeError(
f"The maximum patch width {self.max_patch_dims_[idx]} is "
f"greater than the data width {self.data_dims_[idx]}"
)
return super().fit(X, y, sample_weight, check_input=False)
def _build_tree(
self,
X,
y,
sample_weight,
feature_has_missing,
min_samples_leaf,
min_weight_leaf,
max_leaf_nodes,
min_samples_split,
max_depth,
random_state,
):
"""Build the actual tree.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Internally, it will be converted to
``dtype=np.float32`` and if a sparse matrix is provided
to a sparse ``csc_matrix``.
y : array-like of shape (n_samples,) or (n_samples, n_outputs)
The target values (real numbers). Use ``dtype=np.float64`` and
``order='C'`` for maximum efficiency.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights. If None, then samples are equally weighted. Splits
that would create child nodes with net zero or negative weight are
ignored while searching for a split in each node.
min_samples_leaf : int or float
The minimum number of samples required to be at a leaf node.
min_weight_leaf : float, default=0.0
The minimum weighted fraction of the sum total of weights.
max_leaf_nodes : int, default=None
Grow a tree with ``max_leaf_nodes`` in best-first fashion.
min_samples_split : int or float, default=2
The minimum number of samples required to split an internal node.
max_depth : int, default=None
The maximum depth of the tree. If None, then nodes are expanded until
all leaves are pure or until all leaves contain less than
min_samples_split samples.
random_state : int, RandomState instance or None, default=None
Controls the randomness of the estimator.
"""
n_samples = X.shape[0]
# Build tree
criterion = self.criterion
if not isinstance(criterion, BaseCriterion):
criterion = CRITERIA_REG[self.criterion](self.n_outputs_, n_samples)
else:
# Make a deepcopy in case the criterion has mutable attributes that
# might be shared and modified concurrently during parallel fitting
criterion = copy.deepcopy(criterion)
splitter = self.splitter
if issparse(X):
raise ValueError(
"Sparse input is not supported for oblique trees. "
"Please convert your data to a dense array."
)
else:
PATCH_SPLITTERS = PATCH_DENSE_SPLITTERS
if not isinstance(self.splitter, PatchSplitter):
splitter = PATCH_SPLITTERS[self.splitter](
criterion,
self.max_features_,
min_samples_leaf,
min_weight_leaf,
random_state,
self.min_patch_dims_,
self.max_patch_dims_,
self.dim_contiguous_,
self.data_dims_,
self.boundary,
self.feature_weight,
)
self.tree_ = ObliqueTree(
self.n_features_in_,
np.array([1] * self.n_outputs_, dtype=np.intp),
self.n_outputs_,
)
# Use BestFirst if max_leaf_nodes given; use DepthFirst otherwise
if max_leaf_nodes < 0:
builder = DepthFirstTreeBuilder(
splitter,
min_samples_split,
min_samples_leaf,
min_weight_leaf,
max_depth,
self.min_impurity_decrease,
)
else:
builder = BestFirstTreeBuilder(
splitter,
min_samples_split,
min_samples_leaf,
min_weight_leaf,
max_depth,
max_leaf_nodes,
self.min_impurity_decrease,
)
builder.build(self.tree_, X, y, sample_weight)
def _more_tags(self):
# XXX: nans should be supportable in SPORF by just using RF-like splits on missing values
# However, for MORF it is not supported
allow_nan = False
return {"multilabel": True, "allow_nan": allow_nan}