938 lines
35 KiB
Python
938 lines
35 KiB
Python
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"""
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This file contains preprocessing tools based on polynomials.
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"""
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import collections
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from numbers import Integral
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from itertools import chain, combinations
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from itertools import combinations_with_replacement as combinations_w_r
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import numpy as np
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from scipy import sparse
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from scipy.interpolate import BSpline
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from scipy.special import comb
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from ..base import BaseEstimator, TransformerMixin
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from ..utils import check_array
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from ..utils.validation import check_is_fitted, FLOAT_DTYPES, _check_sample_weight
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from ..utils.validation import _check_feature_names_in
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from ..utils._param_validation import Interval, StrOptions
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from ..utils.stats import _weighted_percentile
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from ._csr_polynomial_expansion import _csr_polynomial_expansion
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__all__ = [
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"PolynomialFeatures",
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"SplineTransformer",
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]
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class PolynomialFeatures(TransformerMixin, BaseEstimator):
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"""Generate polynomial and interaction features.
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Generate a new feature matrix consisting of all polynomial combinations
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of the features with degree less than or equal to the specified degree.
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For example, if an input sample is two dimensional and of the form
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[a, b], the degree-2 polynomial features are [1, a, b, a^2, ab, b^2].
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Read more in the :ref:`User Guide <polynomial_features>`.
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Parameters
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----------
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degree : int or tuple (min_degree, max_degree), default=2
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If a single int is given, it specifies the maximal degree of the
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polynomial features. If a tuple `(min_degree, max_degree)` is passed,
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then `min_degree` is the minimum and `max_degree` is the maximum
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polynomial degree of the generated features. Note that `min_degree=0`
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and `min_degree=1` are equivalent as outputting the degree zero term is
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determined by `include_bias`.
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interaction_only : bool, default=False
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If `True`, only interaction features are produced: features that are
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products of at most `degree` *distinct* input features, i.e. terms with
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power of 2 or higher of the same input feature are excluded:
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- included: `x[0]`, `x[1]`, `x[0] * x[1]`, etc.
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- excluded: `x[0] ** 2`, `x[0] ** 2 * x[1]`, etc.
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include_bias : bool, default=True
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If `True` (default), then include a bias column, the feature in which
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all polynomial powers are zero (i.e. a column of ones - acts as an
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intercept term in a linear model).
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order : {'C', 'F'}, default='C'
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Order of output array in the dense case. `'F'` order is faster to
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compute, but may slow down subsequent estimators.
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.. versionadded:: 0.21
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Attributes
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----------
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powers_ : ndarray of shape (`n_output_features_`, `n_features_in_`)
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`powers_[i, j]` is the exponent of the jth input in the ith output.
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n_features_in_ : int
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Number of features seen during :term:`fit`.
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.. versionadded:: 0.24
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feature_names_in_ : ndarray of shape (`n_features_in_`,)
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Names of features seen during :term:`fit`. Defined only when `X`
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has feature names that are all strings.
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.. versionadded:: 1.0
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n_output_features_ : int
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The total number of polynomial output features. The number of output
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features is computed by iterating over all suitably sized combinations
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of input features.
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See Also
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--------
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SplineTransformer : Transformer that generates univariate B-spline bases
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for features.
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Notes
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-----
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Be aware that the number of features in the output array scales
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polynomially in the number of features of the input array, and
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exponentially in the degree. High degrees can cause overfitting.
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See :ref:`examples/linear_model/plot_polynomial_interpolation.py
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<sphx_glr_auto_examples_linear_model_plot_polynomial_interpolation.py>`
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Examples
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--------
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>>> import numpy as np
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>>> from sklearn.preprocessing import PolynomialFeatures
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>>> X = np.arange(6).reshape(3, 2)
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>>> X
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array([[0, 1],
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[2, 3],
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[4, 5]])
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>>> poly = PolynomialFeatures(2)
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>>> poly.fit_transform(X)
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array([[ 1., 0., 1., 0., 0., 1.],
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[ 1., 2., 3., 4., 6., 9.],
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[ 1., 4., 5., 16., 20., 25.]])
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>>> poly = PolynomialFeatures(interaction_only=True)
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>>> poly.fit_transform(X)
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array([[ 1., 0., 1., 0.],
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[ 1., 2., 3., 6.],
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[ 1., 4., 5., 20.]])
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"""
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_parameter_constraints: dict = {
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"degree": [Interval(Integral, 0, None, closed="left"), "array-like"],
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"interaction_only": ["boolean"],
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"include_bias": ["boolean"],
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"order": [StrOptions({"C", "F"})],
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}
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def __init__(
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self, degree=2, *, interaction_only=False, include_bias=True, order="C"
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):
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self.degree = degree
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self.interaction_only = interaction_only
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self.include_bias = include_bias
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self.order = order
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@staticmethod
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def _combinations(
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n_features, min_degree, max_degree, interaction_only, include_bias
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):
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comb = combinations if interaction_only else combinations_w_r
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start = max(1, min_degree)
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iter = chain.from_iterable(
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comb(range(n_features), i) for i in range(start, max_degree + 1)
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)
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if include_bias:
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iter = chain(comb(range(n_features), 0), iter)
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return iter
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@staticmethod
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def _num_combinations(
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n_features, min_degree, max_degree, interaction_only, include_bias
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):
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"""Calculate number of terms in polynomial expansion
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This should be equivalent to counting the number of terms returned by
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_combinations(...) but much faster.
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"""
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if interaction_only:
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combinations = sum(
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[
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comb(n_features, i, exact=True)
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for i in range(max(1, min_degree), min(max_degree, n_features) + 1)
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]
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)
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else:
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combinations = comb(n_features + max_degree, max_degree, exact=True) - 1
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if min_degree > 0:
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d = min_degree - 1
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combinations -= comb(n_features + d, d, exact=True) - 1
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if include_bias:
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combinations += 1
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return combinations
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@property
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def powers_(self):
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"""Exponent for each of the inputs in the output."""
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check_is_fitted(self)
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combinations = self._combinations(
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n_features=self.n_features_in_,
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min_degree=self._min_degree,
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max_degree=self._max_degree,
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interaction_only=self.interaction_only,
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include_bias=self.include_bias,
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)
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return np.vstack(
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[np.bincount(c, minlength=self.n_features_in_) for c in combinations]
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)
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def get_feature_names_out(self, input_features=None):
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"""Get output feature names for transformation.
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Parameters
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----------
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input_features : array-like of str or None, default=None
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Input features.
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- If `input_features is None`, then `feature_names_in_` is
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used as feature names in. If `feature_names_in_` is not defined,
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then the following input feature names are generated:
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`["x0", "x1", ..., "x(n_features_in_ - 1)"]`.
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- If `input_features` is an array-like, then `input_features` must
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match `feature_names_in_` if `feature_names_in_` is defined.
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Returns
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-------
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feature_names_out : ndarray of str objects
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Transformed feature names.
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"""
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powers = self.powers_
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input_features = _check_feature_names_in(self, input_features)
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feature_names = []
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for row in powers:
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inds = np.where(row)[0]
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if len(inds):
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name = " ".join(
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"%s^%d" % (input_features[ind], exp)
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if exp != 1
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else input_features[ind]
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for ind, exp in zip(inds, row[inds])
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)
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else:
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name = "1"
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feature_names.append(name)
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return np.asarray(feature_names, dtype=object)
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def fit(self, X, y=None):
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"""
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Compute number of output features.
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Parameters
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----------
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X : {array-like, sparse matrix} of shape (n_samples, n_features)
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The data.
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y : Ignored
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Not used, present here for API consistency by convention.
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Returns
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-------
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self : object
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Fitted transformer.
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"""
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self._validate_params()
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_, n_features = self._validate_data(X, accept_sparse=True).shape
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if isinstance(self.degree, Integral):
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if self.degree == 0 and not self.include_bias:
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raise ValueError(
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"Setting degree to zero and include_bias to False would result in"
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" an empty output array."
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)
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self._min_degree = 0
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self._max_degree = self.degree
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elif (
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isinstance(self.degree, collections.abc.Iterable) and len(self.degree) == 2
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):
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self._min_degree, self._max_degree = self.degree
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if not (
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isinstance(self._min_degree, Integral)
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and isinstance(self._max_degree, Integral)
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and self._min_degree >= 0
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and self._min_degree <= self._max_degree
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):
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raise ValueError(
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"degree=(min_degree, max_degree) must "
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"be non-negative integers that fulfil "
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"min_degree <= max_degree, got "
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f"{self.degree}."
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)
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elif self._max_degree == 0 and not self.include_bias:
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raise ValueError(
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"Setting both min_degree and max_degree to zero and include_bias to"
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" False would result in an empty output array."
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)
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else:
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raise ValueError(
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"degree must be a non-negative int or tuple "
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"(min_degree, max_degree), got "
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f"{self.degree}."
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)
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self.n_output_features_ = self._num_combinations(
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n_features=n_features,
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min_degree=self._min_degree,
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max_degree=self._max_degree,
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interaction_only=self.interaction_only,
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include_bias=self.include_bias,
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)
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# We also record the number of output features for
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# _max_degree = 0
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self._n_out_full = self._num_combinations(
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n_features=n_features,
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min_degree=0,
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max_degree=self._max_degree,
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interaction_only=self.interaction_only,
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include_bias=self.include_bias,
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)
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return self
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def transform(self, X):
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"""Transform data to polynomial features.
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Parameters
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----------
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X : {array-like, sparse matrix} of shape (n_samples, n_features)
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The data to transform, row by row.
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Prefer CSR over CSC for sparse input (for speed), but CSC is
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required if the degree is 4 or higher. If the degree is less than
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4 and the input format is CSC, it will be converted to CSR, have
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its polynomial features generated, then converted back to CSC.
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If the degree is 2 or 3, the method described in "Leveraging
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Sparsity to Speed Up Polynomial Feature Expansions of CSR Matrices
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Using K-Simplex Numbers" by Andrew Nystrom and John Hughes is
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used, which is much faster than the method used on CSC input. For
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this reason, a CSC input will be converted to CSR, and the output
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will be converted back to CSC prior to being returned, hence the
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preference of CSR.
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Returns
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-------
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XP : {ndarray, sparse matrix} of shape (n_samples, NP)
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The matrix of features, where `NP` is the number of polynomial
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features generated from the combination of inputs. If a sparse
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matrix is provided, it will be converted into a sparse
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`csr_matrix`.
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"""
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check_is_fitted(self)
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X = self._validate_data(
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X, order="F", dtype=FLOAT_DTYPES, reset=False, accept_sparse=("csr", "csc")
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)
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n_samples, n_features = X.shape
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if sparse.isspmatrix_csr(X):
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if self._max_degree > 3:
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return self.transform(X.tocsc()).tocsr()
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to_stack = []
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if self.include_bias:
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to_stack.append(
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sparse.csc_matrix(np.ones(shape=(n_samples, 1), dtype=X.dtype))
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)
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if self._min_degree <= 1 and self._max_degree > 0:
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to_stack.append(X)
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for deg in range(max(2, self._min_degree), self._max_degree + 1):
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Xp_next = _csr_polynomial_expansion(
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X.data, X.indices, X.indptr, X.shape[1], self.interaction_only, deg
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)
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if Xp_next is None:
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break
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to_stack.append(Xp_next)
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if len(to_stack) == 0:
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# edge case: deal with empty matrix
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XP = sparse.csr_matrix((n_samples, 0), dtype=X.dtype)
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else:
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XP = sparse.hstack(to_stack, format="csr")
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elif sparse.isspmatrix_csc(X) and self._max_degree < 4:
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return self.transform(X.tocsr()).tocsc()
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elif sparse.isspmatrix(X):
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|
|
combinations = self._combinations(
|
||
|
|
n_features=n_features,
|
||
|
|
min_degree=self._min_degree,
|
||
|
|
max_degree=self._max_degree,
|
||
|
|
interaction_only=self.interaction_only,
|
||
|
|
include_bias=self.include_bias,
|
||
|
|
)
|
||
|
|
columns = []
|
||
|
|
for combi in combinations:
|
||
|
|
if combi:
|
||
|
|
out_col = 1
|
||
|
|
for col_idx in combi:
|
||
|
|
out_col = X[:, col_idx].multiply(out_col)
|
||
|
|
columns.append(out_col)
|
||
|
|
else:
|
||
|
|
bias = sparse.csc_matrix(np.ones((X.shape[0], 1)))
|
||
|
|
columns.append(bias)
|
||
|
|
XP = sparse.hstack(columns, dtype=X.dtype).tocsc()
|
||
|
|
else:
|
||
|
|
# Do as if _min_degree = 0 and cut down array after the
|
||
|
|
# computation, i.e. use _n_out_full instead of n_output_features_.
|
||
|
|
XP = np.empty(
|
||
|
|
shape=(n_samples, self._n_out_full), dtype=X.dtype, order=self.order
|
||
|
|
)
|
||
|
|
|
||
|
|
# What follows is a faster implementation of:
|
||
|
|
# for i, comb in enumerate(combinations):
|
||
|
|
# XP[:, i] = X[:, comb].prod(1)
|
||
|
|
# This implementation uses two optimisations.
|
||
|
|
# First one is broadcasting,
|
||
|
|
# multiply ([X1, ..., Xn], X1) -> [X1 X1, ..., Xn X1]
|
||
|
|
# multiply ([X2, ..., Xn], X2) -> [X2 X2, ..., Xn X2]
|
||
|
|
# ...
|
||
|
|
# multiply ([X[:, start:end], X[:, start]) -> ...
|
||
|
|
# Second optimisation happens for degrees >= 3.
|
||
|
|
# Xi^3 is computed reusing previous computation:
|
||
|
|
# Xi^3 = Xi^2 * Xi.
|
||
|
|
|
||
|
|
# degree 0 term
|
||
|
|
if self.include_bias:
|
||
|
|
XP[:, 0] = 1
|
||
|
|
current_col = 1
|
||
|
|
else:
|
||
|
|
current_col = 0
|
||
|
|
|
||
|
|
if self._max_degree == 0:
|
||
|
|
return XP
|
||
|
|
|
||
|
|
# degree 1 term
|
||
|
|
XP[:, current_col : current_col + n_features] = X
|
||
|
|
index = list(range(current_col, current_col + n_features))
|
||
|
|
current_col += n_features
|
||
|
|
index.append(current_col)
|
||
|
|
|
||
|
|
# loop over degree >= 2 terms
|
||
|
|
for _ in range(2, self._max_degree + 1):
|
||
|
|
new_index = []
|
||
|
|
end = index[-1]
|
||
|
|
for feature_idx in range(n_features):
|
||
|
|
start = index[feature_idx]
|
||
|
|
new_index.append(current_col)
|
||
|
|
if self.interaction_only:
|
||
|
|
start += index[feature_idx + 1] - index[feature_idx]
|
||
|
|
next_col = current_col + end - start
|
||
|
|
if next_col <= current_col:
|
||
|
|
break
|
||
|
|
# XP[:, start:end] are terms of degree d - 1
|
||
|
|
# that exclude feature #feature_idx.
|
||
|
|
np.multiply(
|
||
|
|
XP[:, start:end],
|
||
|
|
X[:, feature_idx : feature_idx + 1],
|
||
|
|
out=XP[:, current_col:next_col],
|
||
|
|
casting="no",
|
||
|
|
)
|
||
|
|
current_col = next_col
|
||
|
|
|
||
|
|
new_index.append(current_col)
|
||
|
|
index = new_index
|
||
|
|
|
||
|
|
if self._min_degree > 1:
|
||
|
|
n_XP, n_Xout = self._n_out_full, self.n_output_features_
|
||
|
|
if self.include_bias:
|
||
|
|
Xout = np.empty(
|
||
|
|
shape=(n_samples, n_Xout), dtype=XP.dtype, order=self.order
|
||
|
|
)
|
||
|
|
Xout[:, 0] = 1
|
||
|
|
Xout[:, 1:] = XP[:, n_XP - n_Xout + 1 :]
|
||
|
|
else:
|
||
|
|
Xout = XP[:, n_XP - n_Xout :].copy()
|
||
|
|
XP = Xout
|
||
|
|
return XP
|
||
|
|
|
||
|
|
|
||
|
|
# TODO:
|
||
|
|
# - sparse support (either scipy or own cython solution)?
|
||
|
|
class SplineTransformer(TransformerMixin, BaseEstimator):
|
||
|
|
"""Generate univariate B-spline bases for features.
|
||
|
|
|
||
|
|
Generate a new feature matrix consisting of
|
||
|
|
`n_splines=n_knots + degree - 1` (`n_knots - 1` for
|
||
|
|
`extrapolation="periodic"`) spline basis functions
|
||
|
|
(B-splines) of polynomial order=`degree` for each feature.
|
||
|
|
|
||
|
|
Read more in the :ref:`User Guide <spline_transformer>`.
|
||
|
|
|
||
|
|
.. versionadded:: 1.0
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
n_knots : int, default=5
|
||
|
|
Number of knots of the splines if `knots` equals one of
|
||
|
|
{'uniform', 'quantile'}. Must be larger or equal 2. Ignored if `knots`
|
||
|
|
is array-like.
|
||
|
|
|
||
|
|
degree : int, default=3
|
||
|
|
The polynomial degree of the spline basis. Must be a non-negative
|
||
|
|
integer.
|
||
|
|
|
||
|
|
knots : {'uniform', 'quantile'} or array-like of shape \
|
||
|
|
(n_knots, n_features), default='uniform'
|
||
|
|
Set knot positions such that first knot <= features <= last knot.
|
||
|
|
|
||
|
|
- If 'uniform', `n_knots` number of knots are distributed uniformly
|
||
|
|
from min to max values of the features.
|
||
|
|
- If 'quantile', they are distributed uniformly along the quantiles of
|
||
|
|
the features.
|
||
|
|
- If an array-like is given, it directly specifies the sorted knot
|
||
|
|
positions including the boundary knots. Note that, internally,
|
||
|
|
`degree` number of knots are added before the first knot, the same
|
||
|
|
after the last knot.
|
||
|
|
|
||
|
|
extrapolation : {'error', 'constant', 'linear', 'continue', 'periodic'}, \
|
||
|
|
default='constant'
|
||
|
|
If 'error', values outside the min and max values of the training
|
||
|
|
features raises a `ValueError`. If 'constant', the value of the
|
||
|
|
splines at minimum and maximum value of the features is used as
|
||
|
|
constant extrapolation. If 'linear', a linear extrapolation is used.
|
||
|
|
If 'continue', the splines are extrapolated as is, i.e. option
|
||
|
|
`extrapolate=True` in :class:`scipy.interpolate.BSpline`. If
|
||
|
|
'periodic', periodic splines with a periodicity equal to the distance
|
||
|
|
between the first and last knot are used. Periodic splines enforce
|
||
|
|
equal function values and derivatives at the first and last knot.
|
||
|
|
For example, this makes it possible to avoid introducing an arbitrary
|
||
|
|
jump between Dec 31st and Jan 1st in spline features derived from a
|
||
|
|
naturally periodic "day-of-year" input feature. In this case it is
|
||
|
|
recommended to manually set the knot values to control the period.
|
||
|
|
|
||
|
|
include_bias : bool, default=True
|
||
|
|
If True (default), then the last spline element inside the data range
|
||
|
|
of a feature is dropped. As B-splines sum to one over the spline basis
|
||
|
|
functions for each data point, they implicitly include a bias term,
|
||
|
|
i.e. a column of ones. It acts as an intercept term in a linear models.
|
||
|
|
|
||
|
|
order : {'C', 'F'}, default='C'
|
||
|
|
Order of output array. 'F' order is faster to compute, but may slow
|
||
|
|
down subsequent estimators.
|
||
|
|
|
||
|
|
Attributes
|
||
|
|
----------
|
||
|
|
bsplines_ : list of shape (n_features,)
|
||
|
|
List of BSplines objects, one for each feature.
|
||
|
|
|
||
|
|
n_features_in_ : int
|
||
|
|
The total number of input features.
|
||
|
|
|
||
|
|
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.
|
||
|
|
|
||
|
|
.. versionadded:: 1.0
|
||
|
|
|
||
|
|
n_features_out_ : int
|
||
|
|
The total number of output features, which is computed as
|
||
|
|
`n_features * n_splines`, where `n_splines` is
|
||
|
|
the number of bases elements of the B-splines,
|
||
|
|
`n_knots + degree - 1` for non-periodic splines and
|
||
|
|
`n_knots - 1` for periodic ones.
|
||
|
|
If `include_bias=False`, then it is only
|
||
|
|
`n_features * (n_splines - 1)`.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
KBinsDiscretizer : Transformer that bins continuous data into intervals.
|
||
|
|
|
||
|
|
PolynomialFeatures : Transformer that generates polynomial and interaction
|
||
|
|
features.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
High degrees and a high number of knots can cause overfitting.
|
||
|
|
|
||
|
|
See :ref:`examples/linear_model/plot_polynomial_interpolation.py
|
||
|
|
<sphx_glr_auto_examples_linear_model_plot_polynomial_interpolation.py>`.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> from sklearn.preprocessing import SplineTransformer
|
||
|
|
>>> X = np.arange(6).reshape(6, 1)
|
||
|
|
>>> spline = SplineTransformer(degree=2, n_knots=3)
|
||
|
|
>>> spline.fit_transform(X)
|
||
|
|
array([[0.5 , 0.5 , 0. , 0. ],
|
||
|
|
[0.18, 0.74, 0.08, 0. ],
|
||
|
|
[0.02, 0.66, 0.32, 0. ],
|
||
|
|
[0. , 0.32, 0.66, 0.02],
|
||
|
|
[0. , 0.08, 0.74, 0.18],
|
||
|
|
[0. , 0. , 0.5 , 0.5 ]])
|
||
|
|
"""
|
||
|
|
|
||
|
|
_parameter_constraints: dict = {
|
||
|
|
"n_knots": [Interval(Integral, 2, None, closed="left")],
|
||
|
|
"degree": [Interval(Integral, 0, None, closed="left")],
|
||
|
|
"knots": [StrOptions({"uniform", "quantile"}), "array-like"],
|
||
|
|
"extrapolation": [
|
||
|
|
StrOptions({"error", "constant", "linear", "continue", "periodic"})
|
||
|
|
],
|
||
|
|
"include_bias": ["boolean"],
|
||
|
|
"order": [StrOptions({"C", "F"})],
|
||
|
|
}
|
||
|
|
|
||
|
|
def __init__(
|
||
|
|
self,
|
||
|
|
n_knots=5,
|
||
|
|
degree=3,
|
||
|
|
*,
|
||
|
|
knots="uniform",
|
||
|
|
extrapolation="constant",
|
||
|
|
include_bias=True,
|
||
|
|
order="C",
|
||
|
|
):
|
||
|
|
self.n_knots = n_knots
|
||
|
|
self.degree = degree
|
||
|
|
self.knots = knots
|
||
|
|
self.extrapolation = extrapolation
|
||
|
|
self.include_bias = include_bias
|
||
|
|
self.order = order
|
||
|
|
|
||
|
|
@staticmethod
|
||
|
|
def _get_base_knot_positions(X, n_knots=10, knots="uniform", sample_weight=None):
|
||
|
|
"""Calculate base knot positions.
|
||
|
|
|
||
|
|
Base knots such that first knot <= feature <= last knot. For the
|
||
|
|
B-spline construction with scipy.interpolate.BSpline, 2*degree knots
|
||
|
|
beyond the base interval are added.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
knots : ndarray of shape (n_knots, n_features), dtype=np.float64
|
||
|
|
Knot positions (points) of base interval.
|
||
|
|
"""
|
||
|
|
if knots == "quantile":
|
||
|
|
percentiles = 100 * np.linspace(
|
||
|
|
start=0, stop=1, num=n_knots, dtype=np.float64
|
||
|
|
)
|
||
|
|
|
||
|
|
if sample_weight is None:
|
||
|
|
knots = np.percentile(X, percentiles, axis=0)
|
||
|
|
else:
|
||
|
|
knots = np.array(
|
||
|
|
[
|
||
|
|
_weighted_percentile(X, sample_weight, percentile)
|
||
|
|
for percentile in percentiles
|
||
|
|
]
|
||
|
|
)
|
||
|
|
|
||
|
|
else:
|
||
|
|
# knots == 'uniform':
|
||
|
|
# Note that the variable `knots` has already been validated and
|
||
|
|
# `else` is therefore safe.
|
||
|
|
# Disregard observations with zero weight.
|
||
|
|
mask = slice(None, None, 1) if sample_weight is None else sample_weight > 0
|
||
|
|
x_min = np.amin(X[mask], axis=0)
|
||
|
|
x_max = np.amax(X[mask], axis=0)
|
||
|
|
|
||
|
|
knots = np.linspace(
|
||
|
|
start=x_min,
|
||
|
|
stop=x_max,
|
||
|
|
num=n_knots,
|
||
|
|
endpoint=True,
|
||
|
|
dtype=np.float64,
|
||
|
|
)
|
||
|
|
|
||
|
|
return knots
|
||
|
|
|
||
|
|
def get_feature_names_out(self, input_features=None):
|
||
|
|
"""Get output feature names for transformation.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
input_features : array-like of str or None, default=None
|
||
|
|
Input features.
|
||
|
|
|
||
|
|
- If `input_features` is `None`, then `feature_names_in_` is
|
||
|
|
used as feature names in. If `feature_names_in_` is not defined,
|
||
|
|
then the following input feature names are generated:
|
||
|
|
`["x0", "x1", ..., "x(n_features_in_ - 1)"]`.
|
||
|
|
- If `input_features` is an array-like, then `input_features` must
|
||
|
|
match `feature_names_in_` if `feature_names_in_` is defined.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
feature_names_out : ndarray of str objects
|
||
|
|
Transformed feature names.
|
||
|
|
"""
|
||
|
|
n_splines = self.bsplines_[0].c.shape[1]
|
||
|
|
|
||
|
|
input_features = _check_feature_names_in(self, input_features)
|
||
|
|
feature_names = []
|
||
|
|
for i in range(self.n_features_in_):
|
||
|
|
for j in range(n_splines - 1 + self.include_bias):
|
||
|
|
feature_names.append(f"{input_features[i]}_sp_{j}")
|
||
|
|
return np.asarray(feature_names, dtype=object)
|
||
|
|
|
||
|
|
def fit(self, X, y=None, sample_weight=None):
|
||
|
|
"""Compute knot positions of splines.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : array-like of shape (n_samples, n_features)
|
||
|
|
The data.
|
||
|
|
|
||
|
|
y : None
|
||
|
|
Ignored.
|
||
|
|
|
||
|
|
sample_weight : array-like of shape (n_samples,), default = None
|
||
|
|
Individual weights for each sample. Used to calculate quantiles if
|
||
|
|
`knots="quantile"`. For `knots="uniform"`, zero weighted
|
||
|
|
observations are ignored for finding the min and max of `X`.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
self : object
|
||
|
|
Fitted transformer.
|
||
|
|
"""
|
||
|
|
self._validate_params()
|
||
|
|
|
||
|
|
X = self._validate_data(
|
||
|
|
X,
|
||
|
|
reset=True,
|
||
|
|
accept_sparse=False,
|
||
|
|
ensure_min_samples=2,
|
||
|
|
ensure_2d=True,
|
||
|
|
)
|
||
|
|
if sample_weight is not None:
|
||
|
|
sample_weight = _check_sample_weight(sample_weight, X, dtype=X.dtype)
|
||
|
|
|
||
|
|
_, n_features = X.shape
|
||
|
|
|
||
|
|
if isinstance(self.knots, str):
|
||
|
|
base_knots = self._get_base_knot_positions(
|
||
|
|
X, n_knots=self.n_knots, knots=self.knots, sample_weight=sample_weight
|
||
|
|
)
|
||
|
|
else:
|
||
|
|
base_knots = check_array(self.knots, dtype=np.float64)
|
||
|
|
if base_knots.shape[0] < 2:
|
||
|
|
raise ValueError("Number of knots, knots.shape[0], must be >= 2.")
|
||
|
|
elif base_knots.shape[1] != n_features:
|
||
|
|
raise ValueError("knots.shape[1] == n_features is violated.")
|
||
|
|
elif not np.all(np.diff(base_knots, axis=0) > 0):
|
||
|
|
raise ValueError("knots must be sorted without duplicates.")
|
||
|
|
|
||
|
|
# number of knots for base interval
|
||
|
|
n_knots = base_knots.shape[0]
|
||
|
|
|
||
|
|
if self.extrapolation == "periodic" and n_knots <= self.degree:
|
||
|
|
raise ValueError(
|
||
|
|
"Periodic splines require degree < n_knots. Got n_knots="
|
||
|
|
f"{n_knots} and degree={self.degree}."
|
||
|
|
)
|
||
|
|
|
||
|
|
# number of splines basis functions
|
||
|
|
if self.extrapolation != "periodic":
|
||
|
|
n_splines = n_knots + self.degree - 1
|
||
|
|
else:
|
||
|
|
# periodic splines have self.degree less degrees of freedom
|
||
|
|
n_splines = n_knots - 1
|
||
|
|
|
||
|
|
degree = self.degree
|
||
|
|
n_out = n_features * n_splines
|
||
|
|
# We have to add degree number of knots below, and degree number knots
|
||
|
|
# above the base knots in order to make the spline basis complete.
|
||
|
|
if self.extrapolation == "periodic":
|
||
|
|
# For periodic splines the spacing of the first / last degree knots
|
||
|
|
# needs to be a continuation of the spacing of the last / first
|
||
|
|
# base knots.
|
||
|
|
period = base_knots[-1] - base_knots[0]
|
||
|
|
knots = np.r_[
|
||
|
|
base_knots[-(degree + 1) : -1] - period,
|
||
|
|
base_knots,
|
||
|
|
base_knots[1 : (degree + 1)] + period,
|
||
|
|
]
|
||
|
|
|
||
|
|
else:
|
||
|
|
# Eilers & Marx in "Flexible smoothing with B-splines and
|
||
|
|
# penalties" https://doi.org/10.1214/ss/1038425655 advice
|
||
|
|
# against repeating first and last knot several times, which
|
||
|
|
# would have inferior behaviour at boundaries if combined with
|
||
|
|
# a penalty (hence P-Spline). We follow this advice even if our
|
||
|
|
# splines are unpenalized. Meaning we do not:
|
||
|
|
# knots = np.r_[
|
||
|
|
# np.tile(base_knots.min(axis=0), reps=[degree, 1]),
|
||
|
|
# base_knots,
|
||
|
|
# np.tile(base_knots.max(axis=0), reps=[degree, 1])
|
||
|
|
# ]
|
||
|
|
# Instead, we reuse the distance of the 2 fist/last knots.
|
||
|
|
dist_min = base_knots[1] - base_knots[0]
|
||
|
|
dist_max = base_knots[-1] - base_knots[-2]
|
||
|
|
|
||
|
|
knots = np.r_[
|
||
|
|
np.linspace(
|
||
|
|
base_knots[0] - degree * dist_min,
|
||
|
|
base_knots[0] - dist_min,
|
||
|
|
num=degree,
|
||
|
|
),
|
||
|
|
base_knots,
|
||
|
|
np.linspace(
|
||
|
|
base_knots[-1] + dist_max,
|
||
|
|
base_knots[-1] + degree * dist_max,
|
||
|
|
num=degree,
|
||
|
|
),
|
||
|
|
]
|
||
|
|
|
||
|
|
# With a diagonal coefficient matrix, we get back the spline basis
|
||
|
|
# elements, i.e. the design matrix of the spline.
|
||
|
|
# Note, BSpline appreciates C-contiguous float64 arrays as c=coef.
|
||
|
|
coef = np.eye(n_splines, dtype=np.float64)
|
||
|
|
if self.extrapolation == "periodic":
|
||
|
|
coef = np.concatenate((coef, coef[:degree, :]))
|
||
|
|
|
||
|
|
extrapolate = self.extrapolation in ["periodic", "continue"]
|
||
|
|
|
||
|
|
bsplines = [
|
||
|
|
BSpline.construct_fast(
|
||
|
|
knots[:, i], coef, self.degree, extrapolate=extrapolate
|
||
|
|
)
|
||
|
|
for i in range(n_features)
|
||
|
|
]
|
||
|
|
self.bsplines_ = bsplines
|
||
|
|
|
||
|
|
self.n_features_out_ = n_out - n_features * (1 - self.include_bias)
|
||
|
|
return self
|
||
|
|
|
||
|
|
def transform(self, X):
|
||
|
|
"""Transform each feature data to B-splines.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : array-like of shape (n_samples, n_features)
|
||
|
|
The data to transform.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
XBS : ndarray of shape (n_samples, n_features * n_splines)
|
||
|
|
The matrix of features, where n_splines is the number of bases
|
||
|
|
elements of the B-splines, n_knots + degree - 1.
|
||
|
|
"""
|
||
|
|
check_is_fitted(self)
|
||
|
|
|
||
|
|
X = self._validate_data(X, reset=False, accept_sparse=False, ensure_2d=True)
|
||
|
|
|
||
|
|
n_samples, n_features = X.shape
|
||
|
|
n_splines = self.bsplines_[0].c.shape[1]
|
||
|
|
degree = self.degree
|
||
|
|
|
||
|
|
# Note that scipy BSpline returns float64 arrays and converts input
|
||
|
|
# x=X[:, i] to c-contiguous float64.
|
||
|
|
n_out = self.n_features_out_ + n_features * (1 - self.include_bias)
|
||
|
|
if X.dtype in FLOAT_DTYPES:
|
||
|
|
dtype = X.dtype
|
||
|
|
else:
|
||
|
|
dtype = np.float64
|
||
|
|
XBS = np.zeros((n_samples, n_out), dtype=dtype, order=self.order)
|
||
|
|
|
||
|
|
for i in range(n_features):
|
||
|
|
spl = self.bsplines_[i]
|
||
|
|
|
||
|
|
if self.extrapolation in ("continue", "error", "periodic"):
|
||
|
|
if self.extrapolation == "periodic":
|
||
|
|
# With periodic extrapolation we map x to the segment
|
||
|
|
# [spl.t[k], spl.t[n]].
|
||
|
|
# This is equivalent to BSpline(.., extrapolate="periodic")
|
||
|
|
# for scipy>=1.0.0.
|
||
|
|
n = spl.t.size - spl.k - 1
|
||
|
|
# Assign to new array to avoid inplace operation
|
||
|
|
x = spl.t[spl.k] + (X[:, i] - spl.t[spl.k]) % (
|
||
|
|
spl.t[n] - spl.t[spl.k]
|
||
|
|
)
|
||
|
|
else:
|
||
|
|
x = X[:, i]
|
||
|
|
|
||
|
|
XBS[:, (i * n_splines) : ((i + 1) * n_splines)] = spl(x)
|
||
|
|
|
||
|
|
else:
|
||
|
|
xmin = spl.t[degree]
|
||
|
|
xmax = spl.t[-degree - 1]
|
||
|
|
mask = (xmin <= X[:, i]) & (X[:, i] <= xmax)
|
||
|
|
XBS[mask, (i * n_splines) : ((i + 1) * n_splines)] = spl(X[mask, i])
|
||
|
|
|
||
|
|
# Note for extrapolation:
|
||
|
|
# 'continue' is already returned as is by scipy BSplines
|
||
|
|
if self.extrapolation == "error":
|
||
|
|
# BSpline with extrapolate=False does not raise an error, but
|
||
|
|
# output np.nan.
|
||
|
|
if np.any(np.isnan(XBS[:, (i * n_splines) : ((i + 1) * n_splines)])):
|
||
|
|
raise ValueError(
|
||
|
|
"X contains values beyond the limits of the knots."
|
||
|
|
)
|
||
|
|
elif self.extrapolation == "constant":
|
||
|
|
# Set all values beyond xmin and xmax to the value of the
|
||
|
|
# spline basis functions at those two positions.
|
||
|
|
# Only the first degree and last degree number of splines
|
||
|
|
# have non-zero values at the boundaries.
|
||
|
|
|
||
|
|
# spline values at boundaries
|
||
|
|
f_min = spl(xmin)
|
||
|
|
f_max = spl(xmax)
|
||
|
|
mask = X[:, i] < xmin
|
||
|
|
if np.any(mask):
|
||
|
|
XBS[mask, (i * n_splines) : (i * n_splines + degree)] = f_min[
|
||
|
|
:degree
|
||
|
|
]
|
||
|
|
|
||
|
|
mask = X[:, i] > xmax
|
||
|
|
if np.any(mask):
|
||
|
|
XBS[
|
||
|
|
mask,
|
||
|
|
((i + 1) * n_splines - degree) : ((i + 1) * n_splines),
|
||
|
|
] = f_max[-degree:]
|
||
|
|
|
||
|
|
elif self.extrapolation == "linear":
|
||
|
|
# Continue the degree first and degree last spline bases
|
||
|
|
# linearly beyond the boundaries, with slope = derivative at
|
||
|
|
# the boundary.
|
||
|
|
# Note that all others have derivative = value = 0 at the
|
||
|
|
# boundaries.
|
||
|
|
|
||
|
|
# spline values at boundaries
|
||
|
|
f_min, f_max = spl(xmin), spl(xmax)
|
||
|
|
# spline derivatives = slopes at boundaries
|
||
|
|
fp_min, fp_max = spl(xmin, nu=1), spl(xmax, nu=1)
|
||
|
|
# Compute the linear continuation.
|
||
|
|
if degree <= 1:
|
||
|
|
# For degree=1, the derivative of 2nd spline is not zero at
|
||
|
|
# boundary. For degree=0 it is the same as 'constant'.
|
||
|
|
degree += 1
|
||
|
|
for j in range(degree):
|
||
|
|
mask = X[:, i] < xmin
|
||
|
|
if np.any(mask):
|
||
|
|
XBS[mask, i * n_splines + j] = (
|
||
|
|
f_min[j] + (X[mask, i] - xmin) * fp_min[j]
|
||
|
|
)
|
||
|
|
|
||
|
|
mask = X[:, i] > xmax
|
||
|
|
if np.any(mask):
|
||
|
|
k = n_splines - 1 - j
|
||
|
|
XBS[mask, i * n_splines + k] = (
|
||
|
|
f_max[k] + (X[mask, i] - xmax) * fp_max[k]
|
||
|
|
)
|
||
|
|
|
||
|
|
if self.include_bias:
|
||
|
|
return XBS
|
||
|
|
else:
|
||
|
|
# We throw away one spline basis per feature.
|
||
|
|
# We chose the last one.
|
||
|
|
indices = [j for j in range(XBS.shape[1]) if (j + 1) % n_splines != 0]
|
||
|
|
return XBS[:, indices]
|