# Authors: Alexandre Gramfort # Mathieu Blondel # Olivier Grisel # Andreas Mueller # Eric Martin # Giorgio Patrini # Eric Chang # License: BSD 3 clause from itertools import chain, combinations import numbers import warnings from itertools import combinations_with_replacement as combinations_w_r import numpy as np from scipy import sparse from scipy import stats from scipy import optimize from scipy.special import boxcox from ..base import BaseEstimator, TransformerMixin from ..utils import check_array from ..utils.extmath import row_norms from ..utils.extmath import _incremental_mean_and_var from ..utils.sparsefuncs_fast import (inplace_csr_row_normalize_l1, inplace_csr_row_normalize_l2) from ..utils.sparsefuncs import (inplace_column_scale, mean_variance_axis, incr_mean_variance_axis, min_max_axis) from ..utils.validation import (check_is_fitted, check_random_state, FLOAT_DTYPES, _deprecate_positional_args) from ._csr_polynomial_expansion import _csr_polynomial_expansion from ._encoders import OneHotEncoder BOUNDS_THRESHOLD = 1e-7 __all__ = [ 'Binarizer', 'KernelCenterer', 'MinMaxScaler', 'MaxAbsScaler', 'Normalizer', 'OneHotEncoder', 'RobustScaler', 'StandardScaler', 'QuantileTransformer', 'PowerTransformer', 'add_dummy_feature', 'binarize', 'normalize', 'scale', 'robust_scale', 'maxabs_scale', 'minmax_scale', 'quantile_transform', 'power_transform', ] def _handle_zeros_in_scale(scale, copy=True): ''' Makes sure that whenever scale is zero, we handle it correctly. This happens in most scalers when we have constant features.''' # if we are fitting on 1D arrays, scale might be a scalar if np.isscalar(scale): if scale == .0: scale = 1. return scale elif isinstance(scale, np.ndarray): if copy: # New array to avoid side-effects scale = scale.copy() scale[scale == 0.0] = 1.0 return scale @_deprecate_positional_args def scale(X, *, axis=0, with_mean=True, with_std=True, copy=True): """Standardize a dataset along any axis Center to the mean and component wise scale to unit variance. Read more in the :ref:`User Guide `. Parameters ---------- X : {array-like, sparse matrix} The data to center and scale. axis : int (0 by default) axis used to compute the means and standard deviations along. If 0, independently standardize each feature, otherwise (if 1) standardize each sample. with_mean : boolean, True by default If True, center the data before scaling. with_std : boolean, True by default If True, scale the data to unit variance (or equivalently, unit standard deviation). copy : boolean, optional, default True set to False to perform inplace row normalization and avoid a copy (if the input is already a numpy array or a scipy.sparse CSC matrix and if axis is 1). Notes ----- This implementation will refuse to center scipy.sparse matrices since it would make them non-sparse and would potentially crash the program with memory exhaustion problems. Instead the caller is expected to either set explicitly `with_mean=False` (in that case, only variance scaling will be performed on the features of the CSC matrix) or to call `X.toarray()` if he/she expects the materialized dense array to fit in memory. To avoid memory copy the caller should pass a CSC matrix. NaNs are treated as missing values: disregarded to compute the statistics, and maintained during the data transformation. We use a biased estimator for the standard deviation, equivalent to `numpy.std(x, ddof=0)`. Note that the choice of `ddof` is unlikely to affect model performance. For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. See also -------- StandardScaler: Performs scaling to unit variance using the``Transformer`` API (e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`). """ # noqa X = check_array(X, accept_sparse='csc', copy=copy, ensure_2d=False, estimator='the scale function', dtype=FLOAT_DTYPES, force_all_finite='allow-nan') if sparse.issparse(X): if with_mean: raise ValueError( "Cannot center sparse matrices: pass `with_mean=False` instead" " See docstring for motivation and alternatives.") if axis != 0: raise ValueError("Can only scale sparse matrix on axis=0, " " got axis=%d" % axis) if with_std: _, var = mean_variance_axis(X, axis=0) var = _handle_zeros_in_scale(var, copy=False) inplace_column_scale(X, 1 / np.sqrt(var)) else: X = np.asarray(X) if with_mean: mean_ = np.nanmean(X, axis) if with_std: scale_ = np.nanstd(X, axis) # Xr is a view on the original array that enables easy use of # broadcasting on the axis in which we are interested in Xr = np.rollaxis(X, axis) if with_mean: Xr -= mean_ mean_1 = np.nanmean(Xr, axis=0) # Verify that mean_1 is 'close to zero'. If X contains very # large values, mean_1 can also be very large, due to a lack of # precision of mean_. In this case, a pre-scaling of the # concerned feature is efficient, for instance by its mean or # maximum. if not np.allclose(mean_1, 0): warnings.warn("Numerical issues were encountered " "when centering the data " "and might not be solved. Dataset may " "contain too large values. You may need " "to prescale your features.") Xr -= mean_1 if with_std: scale_ = _handle_zeros_in_scale(scale_, copy=False) Xr /= scale_ if with_mean: mean_2 = np.nanmean(Xr, axis=0) # If mean_2 is not 'close to zero', it comes from the fact that # scale_ is very small so that mean_2 = mean_1/scale_ > 0, even # if mean_1 was close to zero. The problem is thus essentially # due to the lack of precision of mean_. A solution is then to # subtract the mean again: if not np.allclose(mean_2, 0): warnings.warn("Numerical issues were encountered " "when scaling the data " "and might not be solved. The standard " "deviation of the data is probably " "very close to 0. ") Xr -= mean_2 return X class MinMaxScaler(TransformerMixin, BaseEstimator): """Transform features by scaling each feature to a given range. This estimator scales and translates each feature individually such that it is in the given range on the training set, e.g. between zero and one. The transformation is given by:: X_std = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0)) X_scaled = X_std * (max - min) + min where min, max = feature_range. This transformation is often used as an alternative to zero mean, unit variance scaling. Read more in the :ref:`User Guide `. Parameters ---------- feature_range : tuple (min, max), default=(0, 1) Desired range of transformed data. copy : bool, default=True Set to False to perform inplace row normalization and avoid a copy (if the input is already a numpy array). Attributes ---------- min_ : ndarray of shape (n_features,) Per feature adjustment for minimum. Equivalent to ``min - X.min(axis=0) * self.scale_`` scale_ : ndarray of shape (n_features,) Per feature relative scaling of the data. Equivalent to ``(max - min) / (X.max(axis=0) - X.min(axis=0))`` .. versionadded:: 0.17 *scale_* attribute. data_min_ : ndarray of shape (n_features,) Per feature minimum seen in the data .. versionadded:: 0.17 *data_min_* data_max_ : ndarray of shape (n_features,) Per feature maximum seen in the data .. versionadded:: 0.17 *data_max_* data_range_ : ndarray of shape (n_features,) Per feature range ``(data_max_ - data_min_)`` seen in the data .. versionadded:: 0.17 *data_range_* n_samples_seen_ : int The number of samples processed by the estimator. It will be reset on new calls to fit, but increments across ``partial_fit`` calls. Examples -------- >>> from sklearn.preprocessing import MinMaxScaler >>> data = [[-1, 2], [-0.5, 6], [0, 10], [1, 18]] >>> scaler = MinMaxScaler() >>> print(scaler.fit(data)) MinMaxScaler() >>> print(scaler.data_max_) [ 1. 18.] >>> print(scaler.transform(data)) [[0. 0. ] [0.25 0.25] [0.5 0.5 ] [1. 1. ]] >>> print(scaler.transform([[2, 2]])) [[1.5 0. ]] See also -------- minmax_scale: Equivalent function without the estimator API. Notes ----- NaNs are treated as missing values: disregarded in fit, and maintained in transform. For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. """ @_deprecate_positional_args def __init__(self, feature_range=(0, 1), *, copy=True): self.feature_range = feature_range self.copy = copy def _reset(self): """Reset internal data-dependent state of the scaler, if necessary. __init__ parameters are not touched. """ # Checking one attribute is enough, becase they are all set together # in partial_fit if hasattr(self, 'scale_'): del self.scale_ del self.min_ del self.n_samples_seen_ del self.data_min_ del self.data_max_ del self.data_range_ def fit(self, X, y=None): """Compute the minimum and maximum to be used for later scaling. Parameters ---------- X : array-like of shape (n_samples, n_features) The data used to compute the per-feature minimum and maximum used for later scaling along the features axis. y : None Ignored. Returns ------- self : object Fitted scaler. """ # Reset internal state before fitting self._reset() return self.partial_fit(X, y) def partial_fit(self, X, y=None): """Online computation of min and max on X for later scaling. All of X is processed as a single batch. This is intended for cases when :meth:`fit` is not feasible due to very large number of `n_samples` or because X is read from a continuous stream. Parameters ---------- X : array-like of shape (n_samples, n_features) The data used to compute the mean and standard deviation used for later scaling along the features axis. y : None Ignored. Returns ------- self : object Transformer instance. """ feature_range = self.feature_range if feature_range[0] >= feature_range[1]: raise ValueError("Minimum of desired feature range must be smaller" " than maximum. Got %s." % str(feature_range)) if sparse.issparse(X): raise TypeError("MinMaxScaler does not support sparse input. " "Consider using MaxAbsScaler instead.") first_pass = not hasattr(self, 'n_samples_seen_') X = self._validate_data(X, reset=first_pass, estimator=self, dtype=FLOAT_DTYPES, force_all_finite="allow-nan") data_min = np.nanmin(X, axis=0) data_max = np.nanmax(X, axis=0) if first_pass: self.n_samples_seen_ = X.shape[0] else: data_min = np.minimum(self.data_min_, data_min) data_max = np.maximum(self.data_max_, data_max) self.n_samples_seen_ += X.shape[0] data_range = data_max - data_min self.scale_ = ((feature_range[1] - feature_range[0]) / _handle_zeros_in_scale(data_range)) self.min_ = feature_range[0] - data_min * self.scale_ self.data_min_ = data_min self.data_max_ = data_max self.data_range_ = data_range return self def transform(self, X): """Scale features of X according to feature_range. Parameters ---------- X : array-like of shape (n_samples, n_features) Input data that will be transformed. Returns ------- Xt : array-like of shape (n_samples, n_features) Transformed data. """ check_is_fitted(self) X = check_array(X, copy=self.copy, dtype=FLOAT_DTYPES, force_all_finite="allow-nan") X *= self.scale_ X += self.min_ return X def inverse_transform(self, X): """Undo the scaling of X according to feature_range. Parameters ---------- X : array-like of shape (n_samples, n_features) Input data that will be transformed. It cannot be sparse. Returns ------- Xt : array-like of shape (n_samples, n_features) Transformed data. """ check_is_fitted(self) X = check_array(X, copy=self.copy, dtype=FLOAT_DTYPES, force_all_finite="allow-nan") X -= self.min_ X /= self.scale_ return X def _more_tags(self): return {'allow_nan': True} @_deprecate_positional_args def minmax_scale(X, feature_range=(0, 1), *, axis=0, copy=True): """Transform features by scaling each feature to a given range. This estimator scales and translates each feature individually such that it is in the given range on the training set, i.e. between zero and one. The transformation is given by (when ``axis=0``):: X_std = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0)) X_scaled = X_std * (max - min) + min where min, max = feature_range. The transformation is calculated as (when ``axis=0``):: X_scaled = scale * X + min - X.min(axis=0) * scale where scale = (max - min) / (X.max(axis=0) - X.min(axis=0)) This transformation is often used as an alternative to zero mean, unit variance scaling. Read more in the :ref:`User Guide `. .. versionadded:: 0.17 *minmax_scale* function interface to :class:`sklearn.preprocessing.MinMaxScaler`. Parameters ---------- X : array-like of shape (n_samples, n_features) The data. feature_range : tuple (min, max), default=(0, 1) Desired range of transformed data. axis : int, default=0 Axis used to scale along. If 0, independently scale each feature, otherwise (if 1) scale each sample. copy : bool, default=True Set to False to perform inplace scaling and avoid a copy (if the input is already a numpy array). See also -------- MinMaxScaler: Performs scaling to a given range using the``Transformer`` API (e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`). Notes ----- For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. """ # noqa # Unlike the scaler object, this function allows 1d input. # If copy is required, it will be done inside the scaler object. X = check_array(X, copy=False, ensure_2d=False, dtype=FLOAT_DTYPES, force_all_finite='allow-nan') original_ndim = X.ndim if original_ndim == 1: X = X.reshape(X.shape[0], 1) s = MinMaxScaler(feature_range=feature_range, copy=copy) if axis == 0: X = s.fit_transform(X) else: X = s.fit_transform(X.T).T if original_ndim == 1: X = X.ravel() return X class StandardScaler(TransformerMixin, BaseEstimator): """Standardize features by removing the mean and scaling to unit variance The standard score of a sample `x` is calculated as: z = (x - u) / s where `u` is the mean of the training samples or zero if `with_mean=False`, and `s` is the standard deviation of the training samples or one if `with_std=False`. Centering and scaling happen independently on each feature by computing the relevant statistics on the samples in the training set. Mean and standard deviation are then stored to be used on later data using :meth:`transform`. Standardization of a dataset is a common requirement for many machine learning estimators: they might behave badly if the individual features do not more or less look like standard normally distributed data (e.g. Gaussian with 0 mean and unit variance). For instance many elements used in the objective function of a learning algorithm (such as the RBF kernel of Support Vector Machines or the L1 and L2 regularizers of linear models) assume that all features are centered around 0 and have variance in the same order. If a feature has a variance that is orders of magnitude larger that others, it might dominate the objective function and make the estimator unable to learn from other features correctly as expected. This scaler can also be applied to sparse CSR or CSC matrices by passing `with_mean=False` to avoid breaking the sparsity structure of the data. Read more in the :ref:`User Guide `. Parameters ---------- copy : boolean, optional, default True If False, try to avoid a copy and do inplace scaling instead. This is not guaranteed to always work inplace; e.g. if the data is not a NumPy array or scipy.sparse CSR matrix, a copy may still be returned. with_mean : boolean, True by default If True, center the data before scaling. This does not work (and will raise an exception) when attempted on sparse matrices, because centering them entails building a dense matrix which in common use cases is likely to be too large to fit in memory. with_std : boolean, True by default If True, scale the data to unit variance (or equivalently, unit standard deviation). Attributes ---------- scale_ : ndarray or None, shape (n_features,) Per feature relative scaling of the data. This is calculated using `np.sqrt(var_)`. Equal to ``None`` when ``with_std=False``. .. versionadded:: 0.17 *scale_* mean_ : ndarray or None, shape (n_features,) The mean value for each feature in the training set. Equal to ``None`` when ``with_mean=False``. var_ : ndarray or None, shape (n_features,) The variance for each feature in the training set. Used to compute `scale_`. Equal to ``None`` when ``with_std=False``. n_samples_seen_ : int or array, shape (n_features,) The number of samples processed by the estimator for each feature. If there are not missing samples, the ``n_samples_seen`` will be an integer, otherwise it will be an array. Will be reset on new calls to fit, but increments across ``partial_fit`` calls. Examples -------- >>> from sklearn.preprocessing import StandardScaler >>> data = [[0, 0], [0, 0], [1, 1], [1, 1]] >>> scaler = StandardScaler() >>> print(scaler.fit(data)) StandardScaler() >>> print(scaler.mean_) [0.5 0.5] >>> print(scaler.transform(data)) [[-1. -1.] [-1. -1.] [ 1. 1.] [ 1. 1.]] >>> print(scaler.transform([[2, 2]])) [[3. 3.]] See also -------- scale: Equivalent function without the estimator API. :class:`sklearn.decomposition.PCA` Further removes the linear correlation across features with 'whiten=True'. Notes ----- NaNs are treated as missing values: disregarded in fit, and maintained in transform. We use a biased estimator for the standard deviation, equivalent to `numpy.std(x, ddof=0)`. Note that the choice of `ddof` is unlikely to affect model performance. For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. """ # noqa @_deprecate_positional_args def __init__(self, *, copy=True, with_mean=True, with_std=True): self.with_mean = with_mean self.with_std = with_std self.copy = copy def _reset(self): """Reset internal data-dependent state of the scaler, if necessary. __init__ parameters are not touched. """ # Checking one attribute is enough, becase they are all set together # in partial_fit if hasattr(self, 'scale_'): del self.scale_ del self.n_samples_seen_ del self.mean_ del self.var_ def fit(self, X, y=None): """Compute the mean and std to be used for later scaling. Parameters ---------- X : {array-like, sparse matrix}, shape [n_samples, n_features] The data used to compute the mean and standard deviation used for later scaling along the features axis. y Ignored """ # Reset internal state before fitting self._reset() return self.partial_fit(X, y) def partial_fit(self, X, y=None): """ Online computation of mean and std on X for later scaling. All of X is processed as a single batch. This is intended for cases when :meth:`fit` is not feasible due to very large number of `n_samples` or because X is read from a continuous stream. The algorithm for incremental mean and std is given in Equation 1.5a,b in Chan, Tony F., Gene H. Golub, and Randall J. LeVeque. "Algorithms for computing the sample variance: Analysis and recommendations." The American Statistician 37.3 (1983): 242-247: Parameters ---------- X : {array-like, sparse matrix}, shape [n_samples, n_features] The data used to compute the mean and standard deviation used for later scaling along the features axis. y : None Ignored. Returns ------- self : object Transformer instance. """ X = self._validate_data(X, accept_sparse=('csr', 'csc'), estimator=self, dtype=FLOAT_DTYPES, force_all_finite='allow-nan') # Even in the case of `with_mean=False`, we update the mean anyway # This is needed for the incremental computation of the var # See incr_mean_variance_axis and _incremental_mean_variance_axis # if n_samples_seen_ is an integer (i.e. no missing values), we need to # transform it to a NumPy array of shape (n_features,) required by # incr_mean_variance_axis and _incremental_variance_axis if (hasattr(self, 'n_samples_seen_') and isinstance(self.n_samples_seen_, numbers.Integral)): self.n_samples_seen_ = np.repeat( self.n_samples_seen_, X.shape[1]).astype(np.int64, copy=False) if sparse.issparse(X): if self.with_mean: raise ValueError( "Cannot center sparse matrices: pass `with_mean=False` " "instead. See docstring for motivation and alternatives.") sparse_constructor = (sparse.csr_matrix if X.format == 'csr' else sparse.csc_matrix) counts_nan = sparse_constructor( (np.isnan(X.data), X.indices, X.indptr), shape=X.shape).sum(axis=0).A.ravel() if not hasattr(self, 'n_samples_seen_'): self.n_samples_seen_ = ( X.shape[0] - counts_nan).astype(np.int64, copy=False) if self.with_std: # First pass if not hasattr(self, 'scale_'): self.mean_, self.var_ = mean_variance_axis(X, axis=0) # Next passes else: self.mean_, self.var_, self.n_samples_seen_ = \ incr_mean_variance_axis(X, axis=0, last_mean=self.mean_, last_var=self.var_, last_n=self.n_samples_seen_) else: self.mean_ = None self.var_ = None if hasattr(self, 'scale_'): self.n_samples_seen_ += X.shape[0] - counts_nan else: if not hasattr(self, 'n_samples_seen_'): self.n_samples_seen_ = np.zeros(X.shape[1], dtype=np.int64) # First pass if not hasattr(self, 'scale_'): self.mean_ = .0 if self.with_std: self.var_ = .0 else: self.var_ = None if not self.with_mean and not self.with_std: self.mean_ = None self.var_ = None self.n_samples_seen_ += X.shape[0] - np.isnan(X).sum(axis=0) else: self.mean_, self.var_, self.n_samples_seen_ = \ _incremental_mean_and_var(X, self.mean_, self.var_, self.n_samples_seen_) # for backward-compatibility, reduce n_samples_seen_ to an integer # if the number of samples is the same for each feature (i.e. no # missing values) if np.ptp(self.n_samples_seen_) == 0: self.n_samples_seen_ = self.n_samples_seen_[0] if self.with_std: self.scale_ = _handle_zeros_in_scale(np.sqrt(self.var_)) else: self.scale_ = None return self def transform(self, X, copy=None): """Perform standardization by centering and scaling Parameters ---------- X : array-like, shape [n_samples, n_features] The data used to scale along the features axis. copy : bool, optional (default: None) Copy the input X or not. """ check_is_fitted(self) copy = copy if copy is not None else self.copy X = self._validate_data(X, reset=False, accept_sparse='csr', copy=copy, estimator=self, dtype=FLOAT_DTYPES, force_all_finite='allow-nan') if sparse.issparse(X): if self.with_mean: raise ValueError( "Cannot center sparse matrices: pass `with_mean=False` " "instead. See docstring for motivation and alternatives.") if self.scale_ is not None: inplace_column_scale(X, 1 / self.scale_) else: if self.with_mean: X -= self.mean_ if self.with_std: X /= self.scale_ return X def inverse_transform(self, X, copy=None): """Scale back the data to the original representation Parameters ---------- X : array-like, shape [n_samples, n_features] The data used to scale along the features axis. copy : bool, optional (default: None) Copy the input X or not. Returns ------- X_tr : array-like, shape [n_samples, n_features] Transformed array. """ check_is_fitted(self) copy = copy if copy is not None else self.copy if sparse.issparse(X): if self.with_mean: raise ValueError( "Cannot uncenter sparse matrices: pass `with_mean=False` " "instead See docstring for motivation and alternatives.") if not sparse.isspmatrix_csr(X): X = X.tocsr() copy = False if copy: X = X.copy() if self.scale_ is not None: inplace_column_scale(X, self.scale_) else: X = np.asarray(X) if copy: X = X.copy() if self.with_std: X *= self.scale_ if self.with_mean: X += self.mean_ return X def _more_tags(self): return {'allow_nan': True} class MaxAbsScaler(TransformerMixin, BaseEstimator): """Scale each feature by its maximum absolute value. This estimator scales and translates each feature individually such that the maximal absolute value of each feature in the training set will be 1.0. It does not shift/center the data, and thus does not destroy any sparsity. This scaler can also be applied to sparse CSR or CSC matrices. .. versionadded:: 0.17 Parameters ---------- copy : boolean, optional, default is True Set to False to perform inplace scaling and avoid a copy (if the input is already a numpy array). Attributes ---------- scale_ : ndarray, shape (n_features,) Per feature relative scaling of the data. .. versionadded:: 0.17 *scale_* attribute. max_abs_ : ndarray, shape (n_features,) Per feature maximum absolute value. n_samples_seen_ : int The number of samples processed by the estimator. Will be reset on new calls to fit, but increments across ``partial_fit`` calls. Examples -------- >>> from sklearn.preprocessing import MaxAbsScaler >>> X = [[ 1., -1., 2.], ... [ 2., 0., 0.], ... [ 0., 1., -1.]] >>> transformer = MaxAbsScaler().fit(X) >>> transformer MaxAbsScaler() >>> transformer.transform(X) array([[ 0.5, -1. , 1. ], [ 1. , 0. , 0. ], [ 0. , 1. , -0.5]]) See also -------- maxabs_scale: Equivalent function without the estimator API. Notes ----- NaNs are treated as missing values: disregarded in fit, and maintained in transform. For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. """ @_deprecate_positional_args def __init__(self, *, copy=True): self.copy = copy def _reset(self): """Reset internal data-dependent state of the scaler, if necessary. __init__ parameters are not touched. """ # Checking one attribute is enough, becase they are all set together # in partial_fit if hasattr(self, 'scale_'): del self.scale_ del self.n_samples_seen_ del self.max_abs_ def fit(self, X, y=None): """Compute the maximum absolute value to be used for later scaling. Parameters ---------- X : {array-like, sparse matrix}, shape [n_samples, n_features] The data used to compute the per-feature minimum and maximum used for later scaling along the features axis. """ # Reset internal state before fitting self._reset() return self.partial_fit(X, y) def partial_fit(self, X, y=None): """ Online computation of max absolute value of X for later scaling. All of X is processed as a single batch. This is intended for cases when :meth:`fit` is not feasible due to very large number of `n_samples` or because X is read from a continuous stream. Parameters ---------- X : {array-like, sparse matrix}, shape [n_samples, n_features] The data used to compute the mean and standard deviation used for later scaling along the features axis. y : None Ignored. Returns ------- self : object Transformer instance. """ first_pass = not hasattr(self, 'n_samples_seen_') X = self._validate_data(X, reset=first_pass, accept_sparse=('csr', 'csc'), estimator=self, dtype=FLOAT_DTYPES, force_all_finite='allow-nan') if sparse.issparse(X): mins, maxs = min_max_axis(X, axis=0, ignore_nan=True) max_abs = np.maximum(np.abs(mins), np.abs(maxs)) else: max_abs = np.nanmax(np.abs(X), axis=0) if first_pass: self.n_samples_seen_ = X.shape[0] else: max_abs = np.maximum(self.max_abs_, max_abs) self.n_samples_seen_ += X.shape[0] self.max_abs_ = max_abs self.scale_ = _handle_zeros_in_scale(max_abs) return self def transform(self, X): """Scale the data Parameters ---------- X : {array-like, sparse matrix} The data that should be scaled. """ check_is_fitted(self) X = check_array(X, accept_sparse=('csr', 'csc'), copy=self.copy, estimator=self, dtype=FLOAT_DTYPES, force_all_finite='allow-nan') if sparse.issparse(X): inplace_column_scale(X, 1.0 / self.scale_) else: X /= self.scale_ return X def inverse_transform(self, X): """Scale back the data to the original representation Parameters ---------- X : {array-like, sparse matrix} The data that should be transformed back. """ check_is_fitted(self) X = check_array(X, accept_sparse=('csr', 'csc'), copy=self.copy, estimator=self, dtype=FLOAT_DTYPES, force_all_finite='allow-nan') if sparse.issparse(X): inplace_column_scale(X, self.scale_) else: X *= self.scale_ return X def _more_tags(self): return {'allow_nan': True} @_deprecate_positional_args def maxabs_scale(X, *, axis=0, copy=True): """Scale each feature to the [-1, 1] range without breaking the sparsity. This estimator scales each feature individually such that the maximal absolute value of each feature in the training set will be 1.0. This scaler can also be applied to sparse CSR or CSC matrices. Parameters ---------- X : array-like, shape (n_samples, n_features) The data. axis : int (0 by default) axis used to scale along. If 0, independently scale each feature, otherwise (if 1) scale each sample. copy : boolean, optional, default is True Set to False to perform inplace scaling and avoid a copy (if the input is already a numpy array). See also -------- MaxAbsScaler: Performs scaling to the [-1, 1] range using the``Transformer`` API (e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`). Notes ----- NaNs are treated as missing values: disregarded to compute the statistics, and maintained during the data transformation. For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. """ # noqa # Unlike the scaler object, this function allows 1d input. # If copy is required, it will be done inside the scaler object. X = check_array(X, accept_sparse=('csr', 'csc'), copy=False, ensure_2d=False, dtype=FLOAT_DTYPES, force_all_finite='allow-nan') original_ndim = X.ndim if original_ndim == 1: X = X.reshape(X.shape[0], 1) s = MaxAbsScaler(copy=copy) if axis == 0: X = s.fit_transform(X) else: X = s.fit_transform(X.T).T if original_ndim == 1: X = X.ravel() return X class RobustScaler(TransformerMixin, BaseEstimator): """Scale features using statistics that are robust to outliers. This Scaler removes the median and scales the data according to the quantile range (defaults to IQR: Interquartile Range). The IQR is the range between the 1st quartile (25th quantile) and the 3rd quartile (75th quantile). Centering and scaling happen independently on each feature by computing the relevant statistics on the samples in the training set. Median and interquartile range are then stored to be used on later data using the ``transform`` method. Standardization of a dataset is a common requirement for many machine learning estimators. Typically this is done by removing the mean and scaling to unit variance. However, outliers can often influence the sample mean / variance in a negative way. In such cases, the median and the interquartile range often give better results. .. versionadded:: 0.17 Read more in the :ref:`User Guide `. Parameters ---------- with_centering : boolean, True by default If True, center the data before scaling. This will cause ``transform`` to raise an exception when attempted on sparse matrices, because centering them entails building a dense matrix which in common use cases is likely to be too large to fit in memory. with_scaling : boolean, True by default If True, scale the data to interquartile range. quantile_range : tuple (q_min, q_max), 0.0 < q_min < q_max < 100.0 Default: (25.0, 75.0) = (1st quantile, 3rd quantile) = IQR Quantile range used to calculate ``scale_``. .. versionadded:: 0.18 copy : boolean, optional, default is True If False, try to avoid a copy and do inplace scaling instead. This is not guaranteed to always work inplace; e.g. if the data is not a NumPy array or scipy.sparse CSR matrix, a copy may still be returned. Attributes ---------- center_ : array of floats The median value for each feature in the training set. scale_ : array of floats The (scaled) interquartile range for each feature in the training set. .. versionadded:: 0.17 *scale_* attribute. Examples -------- >>> from sklearn.preprocessing import RobustScaler >>> X = [[ 1., -2., 2.], ... [ -2., 1., 3.], ... [ 4., 1., -2.]] >>> transformer = RobustScaler().fit(X) >>> transformer RobustScaler() >>> transformer.transform(X) array([[ 0. , -2. , 0. ], [-1. , 0. , 0.4], [ 1. , 0. , -1.6]]) See also -------- robust_scale: Equivalent function without the estimator API. :class:`sklearn.decomposition.PCA` Further removes the linear correlation across features with 'whiten=True'. Notes ----- For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. https://en.wikipedia.org/wiki/Median https://en.wikipedia.org/wiki/Interquartile_range """ @_deprecate_positional_args def __init__(self, *, with_centering=True, with_scaling=True, quantile_range=(25.0, 75.0), copy=True): self.with_centering = with_centering self.with_scaling = with_scaling self.quantile_range = quantile_range self.copy = copy def fit(self, X, y=None): """Compute the median and quantiles to be used for scaling. Parameters ---------- X : array-like, shape [n_samples, n_features] The data used to compute the median and quantiles used for later scaling along the features axis. """ # at fit, convert sparse matrices to csc for optimized computation of # the quantiles X = self._validate_data(X, accept_sparse='csc', estimator=self, dtype=FLOAT_DTYPES, force_all_finite='allow-nan') q_min, q_max = self.quantile_range if not 0 <= q_min <= q_max <= 100: raise ValueError("Invalid quantile range: %s" % str(self.quantile_range)) if self.with_centering: if sparse.issparse(X): raise ValueError( "Cannot center sparse matrices: use `with_centering=False`" " instead. See docstring for motivation and alternatives.") self.center_ = np.nanmedian(X, axis=0) else: self.center_ = None if self.with_scaling: quantiles = [] for feature_idx in range(X.shape[1]): if sparse.issparse(X): column_nnz_data = X.data[X.indptr[feature_idx]: X.indptr[feature_idx + 1]] column_data = np.zeros(shape=X.shape[0], dtype=X.dtype) column_data[:len(column_nnz_data)] = column_nnz_data else: column_data = X[:, feature_idx] quantiles.append(np.nanpercentile(column_data, self.quantile_range)) quantiles = np.transpose(quantiles) self.scale_ = quantiles[1] - quantiles[0] self.scale_ = _handle_zeros_in_scale(self.scale_, copy=False) else: self.scale_ = None return self def transform(self, X): """Center and scale the data. Parameters ---------- X : {array-like, sparse matrix} The data used to scale along the specified axis. """ check_is_fitted(self) X = check_array(X, accept_sparse=('csr', 'csc'), copy=self.copy, estimator=self, dtype=FLOAT_DTYPES, force_all_finite='allow-nan') if sparse.issparse(X): if self.with_scaling: inplace_column_scale(X, 1.0 / self.scale_) else: if self.with_centering: X -= self.center_ if self.with_scaling: X /= self.scale_ return X def inverse_transform(self, X): """Scale back the data to the original representation Parameters ---------- X : array-like The data used to scale along the specified axis. """ check_is_fitted(self) X = check_array(X, accept_sparse=('csr', 'csc'), copy=self.copy, estimator=self, dtype=FLOAT_DTYPES, force_all_finite='allow-nan') if sparse.issparse(X): if self.with_scaling: inplace_column_scale(X, self.scale_) else: if self.with_scaling: X *= self.scale_ if self.with_centering: X += self.center_ return X def _more_tags(self): return {'allow_nan': True} @_deprecate_positional_args def robust_scale(X, *, axis=0, with_centering=True, with_scaling=True, quantile_range=(25.0, 75.0), copy=True): """Standardize a dataset along any axis Center to the median and component wise scale according to the interquartile range. Read more in the :ref:`User Guide `. Parameters ---------- X : array-like The data to center and scale. axis : int (0 by default) axis used to compute the medians and IQR along. If 0, independently scale each feature, otherwise (if 1) scale each sample. with_centering : boolean, True by default If True, center the data before scaling. with_scaling : boolean, True by default If True, scale the data to unit variance (or equivalently, unit standard deviation). quantile_range : tuple (q_min, q_max), 0.0 < q_min < q_max < 100.0 Default: (25.0, 75.0) = (1st quantile, 3rd quantile) = IQR Quantile range used to calculate ``scale_``. .. versionadded:: 0.18 copy : boolean, optional, default is True set to False to perform inplace row normalization and avoid a copy (if the input is already a numpy array or a scipy.sparse CSR matrix and if axis is 1). Notes ----- This implementation will refuse to center scipy.sparse matrices since it would make them non-sparse and would potentially crash the program with memory exhaustion problems. Instead the caller is expected to either set explicitly `with_centering=False` (in that case, only variance scaling will be performed on the features of the CSR matrix) or to call `X.toarray()` if he/she expects the materialized dense array to fit in memory. To avoid memory copy the caller should pass a CSR matrix. For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. See also -------- RobustScaler: Performs centering and scaling using the ``Transformer`` API (e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`). """ X = check_array(X, accept_sparse=('csr', 'csc'), copy=False, ensure_2d=False, dtype=FLOAT_DTYPES, force_all_finite='allow-nan') original_ndim = X.ndim if original_ndim == 1: X = X.reshape(X.shape[0], 1) s = RobustScaler(with_centering=with_centering, with_scaling=with_scaling, quantile_range=quantile_range, copy=copy) if axis == 0: X = s.fit_transform(X) else: X = s.fit_transform(X.T).T if original_ndim == 1: X = X.ravel() return X class PolynomialFeatures(TransformerMixin, BaseEstimator): """Generate polynomial and interaction features. Generate a new feature matrix consisting of all polynomial combinations of the features with degree less than or equal to the specified degree. For example, if an input sample is two dimensional and of the form [a, b], the degree-2 polynomial features are [1, a, b, a^2, ab, b^2]. Parameters ---------- degree : integer The degree of the polynomial features. Default = 2. interaction_only : boolean, default = False If true, only interaction features are produced: features that are products of at most ``degree`` *distinct* input features (so not ``x[1] ** 2``, ``x[0] * x[2] ** 3``, etc.). include_bias : boolean If True (default), then include a bias column, the feature in which all polynomial powers are zero (i.e. a column of ones - acts as an intercept term in a linear model). order : str in {'C', 'F'}, default 'C' Order of output array in the dense case. 'F' order is faster to compute, but may slow down subsequent estimators. .. versionadded:: 0.21 Examples -------- >>> import numpy as np >>> from sklearn.preprocessing import PolynomialFeatures >>> X = np.arange(6).reshape(3, 2) >>> X array([[0, 1], [2, 3], [4, 5]]) >>> poly = PolynomialFeatures(2) >>> poly.fit_transform(X) array([[ 1., 0., 1., 0., 0., 1.], [ 1., 2., 3., 4., 6., 9.], [ 1., 4., 5., 16., 20., 25.]]) >>> poly = PolynomialFeatures(interaction_only=True) >>> poly.fit_transform(X) array([[ 1., 0., 1., 0.], [ 1., 2., 3., 6.], [ 1., 4., 5., 20.]]) Attributes ---------- powers_ : array, shape (n_output_features, n_input_features) powers_[i, j] is the exponent of the jth input in the ith output. n_input_features_ : int The total number of input features. n_output_features_ : int The total number of polynomial output features. The number of output features is computed by iterating over all suitably sized combinations of input features. Notes ----- Be aware that the number of features in the output array scales polynomially in the number of features of the input array, and exponentially in the degree. High degrees can cause overfitting. See :ref:`examples/linear_model/plot_polynomial_interpolation.py ` """ @_deprecate_positional_args def __init__(self, degree=2, *, interaction_only=False, include_bias=True, order='C'): self.degree = degree self.interaction_only = interaction_only self.include_bias = include_bias self.order = order @staticmethod def _combinations(n_features, degree, interaction_only, include_bias): comb = (combinations if interaction_only else combinations_w_r) start = int(not include_bias) return chain.from_iterable(comb(range(n_features), i) for i in range(start, degree + 1)) @property def powers_(self): check_is_fitted(self) combinations = self._combinations(self.n_input_features_, self.degree, self.interaction_only, self.include_bias) return np.vstack([np.bincount(c, minlength=self.n_input_features_) for c in combinations]) def get_feature_names(self, input_features=None): """ Return feature names for output features Parameters ---------- input_features : list of string, length n_features, optional String names for input features if available. By default, "x0", "x1", ... "xn_features" is used. Returns ------- output_feature_names : list of string, length n_output_features """ powers = self.powers_ if input_features is None: input_features = ['x%d' % i for i in range(powers.shape[1])] feature_names = [] for row in powers: inds = np.where(row)[0] if len(inds): name = " ".join("%s^%d" % (input_features[ind], exp) if exp != 1 else input_features[ind] for ind, exp in zip(inds, row[inds])) else: name = "1" feature_names.append(name) return feature_names def fit(self, X, y=None): """ Compute number of output features. Parameters ---------- X : array-like, shape (n_samples, n_features) The data. Returns ------- self : instance """ n_samples, n_features = self._validate_data( X, accept_sparse=True).shape combinations = self._combinations(n_features, self.degree, self.interaction_only, self.include_bias) self.n_input_features_ = n_features self.n_output_features_ = sum(1 for _ in combinations) return self def transform(self, X): """Transform data to polynomial features Parameters ---------- X : array-like or CSR/CSC sparse matrix, shape [n_samples, n_features] The data to transform, row by row. Prefer CSR over CSC for sparse input (for speed), but CSC is required if the degree is 4 or higher. If the degree is less than 4 and the input format is CSC, it will be converted to CSR, have its polynomial features generated, then converted back to CSC. If the degree is 2 or 3, the method described in "Leveraging Sparsity to Speed Up Polynomial Feature Expansions of CSR Matrices Using K-Simplex Numbers" by Andrew Nystrom and John Hughes is used, which is much faster than the method used on CSC input. For this reason, a CSC input will be converted to CSR, and the output will be converted back to CSC prior to being returned, hence the preference of CSR. Returns ------- XP : np.ndarray or CSR/CSC sparse matrix, shape [n_samples, NP] The matrix of features, where NP is the number of polynomial features generated from the combination of inputs. """ check_is_fitted(self) X = check_array(X, order='F', dtype=FLOAT_DTYPES, accept_sparse=('csr', 'csc')) n_samples, n_features = X.shape if n_features != self.n_input_features_: raise ValueError("X shape does not match training shape") if sparse.isspmatrix_csr(X): if self.degree > 3: return self.transform(X.tocsc()).tocsr() to_stack = [] if self.include_bias: to_stack.append(np.ones(shape=(n_samples, 1), dtype=X.dtype)) to_stack.append(X) for deg in range(2, self.degree+1): Xp_next = _csr_polynomial_expansion(X.data, X.indices, X.indptr, X.shape[1], self.interaction_only, deg) if Xp_next is None: break to_stack.append(Xp_next) XP = sparse.hstack(to_stack, format='csr') elif sparse.isspmatrix_csc(X) and self.degree < 4: return self.transform(X.tocsr()).tocsc() else: if sparse.isspmatrix(X): combinations = self._combinations(n_features, self.degree, self.interaction_only, self.include_bias) columns = [] for comb in combinations: if comb: out_col = 1 for col_idx in comb: 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: XP = np.empty((n_samples, self.n_output_features_), 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. if self.include_bias: XP[:, 0] = 1 current_col = 1 else: current_col = 0 # d = 0 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) # d >= 1 for _ in range(1, self.degree): 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 return XP @_deprecate_positional_args def normalize(X, norm='l2', *, axis=1, copy=True, return_norm=False): """Scale input vectors individually to unit norm (vector length). Read more in the :ref:`User Guide `. Parameters ---------- X : {array-like, sparse matrix}, shape [n_samples, n_features] The data to normalize, element by element. scipy.sparse matrices should be in CSR format to avoid an un-necessary copy. norm : 'l1', 'l2', or 'max', optional ('l2' by default) The norm to use to normalize each non zero sample (or each non-zero feature if axis is 0). axis : 0 or 1, optional (1 by default) axis used to normalize the data along. If 1, independently normalize each sample, otherwise (if 0) normalize each feature. copy : boolean, optional, default True set to False to perform inplace row normalization and avoid a copy (if the input is already a numpy array or a scipy.sparse CSR matrix and if axis is 1). return_norm : boolean, default False whether to return the computed norms Returns ------- X : {array-like, sparse matrix}, shape [n_samples, n_features] Normalized input X. norms : array, shape [n_samples] if axis=1 else [n_features] An array of norms along given axis for X. When X is sparse, a NotImplementedError will be raised for norm 'l1' or 'l2'. See also -------- Normalizer: Performs normalization using the ``Transformer`` API (e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`). Notes ----- For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. """ if norm not in ('l1', 'l2', 'max'): raise ValueError("'%s' is not a supported norm" % norm) if axis == 0: sparse_format = 'csc' elif axis == 1: sparse_format = 'csr' else: raise ValueError("'%d' is not a supported axis" % axis) X = check_array(X, accept_sparse=sparse_format, copy=copy, estimator='the normalize function', dtype=FLOAT_DTYPES) if axis == 0: X = X.T if sparse.issparse(X): if return_norm and norm in ('l1', 'l2'): raise NotImplementedError("return_norm=True is not implemented " "for sparse matrices with norm 'l1' " "or norm 'l2'") if norm == 'l1': inplace_csr_row_normalize_l1(X) elif norm == 'l2': inplace_csr_row_normalize_l2(X) elif norm == 'max': mins, maxes = min_max_axis(X, 1) norms = np.maximum(abs(mins), maxes) norms_elementwise = norms.repeat(np.diff(X.indptr)) mask = norms_elementwise != 0 X.data[mask] /= norms_elementwise[mask] else: if norm == 'l1': norms = np.abs(X).sum(axis=1) elif norm == 'l2': norms = row_norms(X) elif norm == 'max': norms = np.max(abs(X), axis=1) norms = _handle_zeros_in_scale(norms, copy=False) X /= norms[:, np.newaxis] if axis == 0: X = X.T if return_norm: return X, norms else: return X class Normalizer(TransformerMixin, BaseEstimator): """Normalize samples individually to unit norm. Each sample (i.e. each row of the data matrix) with at least one non zero component is rescaled independently of other samples so that its norm (l1, l2 or inf) equals one. This transformer is able to work both with dense numpy arrays and scipy.sparse matrix (use CSR format if you want to avoid the burden of a copy / conversion). Scaling inputs to unit norms is a common operation for text classification or clustering for instance. For instance the dot product of two l2-normalized TF-IDF vectors is the cosine similarity of the vectors and is the base similarity metric for the Vector Space Model commonly used by the Information Retrieval community. Read more in the :ref:`User Guide `. Parameters ---------- norm : 'l1', 'l2', or 'max', optional ('l2' by default) The norm to use to normalize each non zero sample. If norm='max' is used, values will be rescaled by the maximum of the absolute values. copy : boolean, optional, default True set to False to perform inplace row normalization and avoid a copy (if the input is already a numpy array or a scipy.sparse CSR matrix). Examples -------- >>> from sklearn.preprocessing import Normalizer >>> X = [[4, 1, 2, 2], ... [1, 3, 9, 3], ... [5, 7, 5, 1]] >>> transformer = Normalizer().fit(X) # fit does nothing. >>> transformer Normalizer() >>> transformer.transform(X) array([[0.8, 0.2, 0.4, 0.4], [0.1, 0.3, 0.9, 0.3], [0.5, 0.7, 0.5, 0.1]]) Notes ----- This estimator is stateless (besides constructor parameters), the fit method does nothing but is useful when used in a pipeline. For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. See also -------- normalize: Equivalent function without the estimator API. """ @_deprecate_positional_args def __init__(self, norm='l2', *, copy=True): self.norm = norm self.copy = copy def fit(self, X, y=None): """Do nothing and return the estimator unchanged This method is just there to implement the usual API and hence work in pipelines. Parameters ---------- X : array-like """ self._validate_data(X, accept_sparse='csr') return self def transform(self, X, copy=None): """Scale each non zero row of X to unit norm Parameters ---------- X : {array-like, sparse matrix}, shape [n_samples, n_features] The data to normalize, row by row. scipy.sparse matrices should be in CSR format to avoid an un-necessary copy. copy : bool, optional (default: None) Copy the input X or not. """ copy = copy if copy is not None else self.copy X = check_array(X, accept_sparse='csr') return normalize(X, norm=self.norm, axis=1, copy=copy) def _more_tags(self): return {'stateless': True} @_deprecate_positional_args def binarize(X, *, threshold=0.0, copy=True): """Boolean thresholding of array-like or scipy.sparse matrix Read more in the :ref:`User Guide `. Parameters ---------- X : {array-like, sparse matrix}, shape [n_samples, n_features] The data to binarize, element by element. scipy.sparse matrices should be in CSR or CSC format to avoid an un-necessary copy. threshold : float, optional (0.0 by default) Feature values below or equal to this are replaced by 0, above it by 1. Threshold may not be less than 0 for operations on sparse matrices. copy : boolean, optional, default True set to False to perform inplace binarization and avoid a copy (if the input is already a numpy array or a scipy.sparse CSR / CSC matrix and if axis is 1). See also -------- Binarizer: Performs binarization using the ``Transformer`` API (e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`). """ X = check_array(X, accept_sparse=['csr', 'csc'], copy=copy) if sparse.issparse(X): if threshold < 0: raise ValueError('Cannot binarize a sparse matrix with threshold ' '< 0') cond = X.data > threshold not_cond = np.logical_not(cond) X.data[cond] = 1 X.data[not_cond] = 0 X.eliminate_zeros() else: cond = X > threshold not_cond = np.logical_not(cond) X[cond] = 1 X[not_cond] = 0 return X class Binarizer(TransformerMixin, BaseEstimator): """Binarize data (set feature values to 0 or 1) according to a threshold Values greater than the threshold map to 1, while values less than or equal to the threshold map to 0. With the default threshold of 0, only positive values map to 1. Binarization is a common operation on text count data where the analyst can decide to only consider the presence or absence of a feature rather than a quantified number of occurrences for instance. It can also be used as a pre-processing step for estimators that consider boolean random variables (e.g. modelled using the Bernoulli distribution in a Bayesian setting). Read more in the :ref:`User Guide `. Parameters ---------- threshold : float, optional (0.0 by default) Feature values below or equal to this are replaced by 0, above it by 1. Threshold may not be less than 0 for operations on sparse matrices. copy : boolean, optional, default True set to False to perform inplace binarization and avoid a copy (if the input is already a numpy array or a scipy.sparse CSR matrix). Examples -------- >>> from sklearn.preprocessing import Binarizer >>> X = [[ 1., -1., 2.], ... [ 2., 0., 0.], ... [ 0., 1., -1.]] >>> transformer = Binarizer().fit(X) # fit does nothing. >>> transformer Binarizer() >>> transformer.transform(X) array([[1., 0., 1.], [1., 0., 0.], [0., 1., 0.]]) Notes ----- If the input is a sparse matrix, only the non-zero values are subject to update by the Binarizer class. This estimator is stateless (besides constructor parameters), the fit method does nothing but is useful when used in a pipeline. See also -------- binarize: Equivalent function without the estimator API. """ @_deprecate_positional_args def __init__(self, *, threshold=0.0, copy=True): self.threshold = threshold self.copy = copy def fit(self, X, y=None): """Do nothing and return the estimator unchanged This method is just there to implement the usual API and hence work in pipelines. Parameters ---------- X : array-like """ self._validate_data(X, accept_sparse='csr') return self def transform(self, X, copy=None): """Binarize each element of X Parameters ---------- X : {array-like, sparse matrix}, shape [n_samples, n_features] The data to binarize, element by element. scipy.sparse matrices should be in CSR format to avoid an un-necessary copy. copy : bool Copy the input X or not. """ copy = copy if copy is not None else self.copy return binarize(X, threshold=self.threshold, copy=copy) def _more_tags(self): return {'stateless': True} class KernelCenterer(TransformerMixin, BaseEstimator): """Center a kernel matrix Let K(x, z) be a kernel defined by phi(x)^T phi(z), where phi is a function mapping x to a Hilbert space. KernelCenterer centers (i.e., normalize to have zero mean) the data without explicitly computing phi(x). It is equivalent to centering phi(x) with sklearn.preprocessing.StandardScaler(with_std=False). Read more in the :ref:`User Guide `. Attributes ---------- K_fit_rows_ : array, shape (n_samples,) Average of each column of kernel matrix K_fit_all_ : float Average of kernel matrix Examples -------- >>> from sklearn.preprocessing import KernelCenterer >>> from sklearn.metrics.pairwise import pairwise_kernels >>> X = [[ 1., -2., 2.], ... [ -2., 1., 3.], ... [ 4., 1., -2.]] >>> K = pairwise_kernels(X, metric='linear') >>> K array([[ 9., 2., -2.], [ 2., 14., -13.], [ -2., -13., 21.]]) >>> transformer = KernelCenterer().fit(K) >>> transformer KernelCenterer() >>> transformer.transform(K) array([[ 5., 0., -5.], [ 0., 14., -14.], [ -5., -14., 19.]]) """ def __init__(self): # Needed for backported inspect.signature compatibility with PyPy pass def fit(self, K, y=None): """Fit KernelCenterer Parameters ---------- K : numpy array of shape [n_samples, n_samples] Kernel matrix. Returns ------- self : returns an instance of self. """ K = self._validate_data(K, dtype=FLOAT_DTYPES) if K.shape[0] != K.shape[1]: raise ValueError("Kernel matrix must be a square matrix." " Input is a {}x{} matrix." .format(K.shape[0], K.shape[1])) n_samples = K.shape[0] self.K_fit_rows_ = np.sum(K, axis=0) / n_samples self.K_fit_all_ = self.K_fit_rows_.sum() / n_samples return self def transform(self, K, copy=True): """Center kernel matrix. Parameters ---------- K : numpy array of shape [n_samples1, n_samples2] Kernel matrix. copy : boolean, optional, default True Set to False to perform inplace computation. Returns ------- K_new : numpy array of shape [n_samples1, n_samples2] """ check_is_fitted(self) K = check_array(K, copy=copy, dtype=FLOAT_DTYPES) K_pred_cols = (np.sum(K, axis=1) / self.K_fit_rows_.shape[0])[:, np.newaxis] K -= self.K_fit_rows_ K -= K_pred_cols K += self.K_fit_all_ return K @property def _pairwise(self): return True def add_dummy_feature(X, value=1.0): """Augment dataset with an additional dummy feature. This is useful for fitting an intercept term with implementations which cannot otherwise fit it directly. Parameters ---------- X : {array-like, sparse matrix}, shape [n_samples, n_features] Data. value : float Value to use for the dummy feature. Returns ------- X : {array, sparse matrix}, shape [n_samples, n_features + 1] Same data with dummy feature added as first column. Examples -------- >>> from sklearn.preprocessing import add_dummy_feature >>> add_dummy_feature([[0, 1], [1, 0]]) array([[1., 0., 1.], [1., 1., 0.]]) """ X = check_array(X, accept_sparse=['csc', 'csr', 'coo'], dtype=FLOAT_DTYPES) n_samples, n_features = X.shape shape = (n_samples, n_features + 1) if sparse.issparse(X): if sparse.isspmatrix_coo(X): # Shift columns to the right. col = X.col + 1 # Column indices of dummy feature are 0 everywhere. col = np.concatenate((np.zeros(n_samples), col)) # Row indices of dummy feature are 0, ..., n_samples-1. row = np.concatenate((np.arange(n_samples), X.row)) # Prepend the dummy feature n_samples times. data = np.concatenate((np.full(n_samples, value), X.data)) return sparse.coo_matrix((data, (row, col)), shape) elif sparse.isspmatrix_csc(X): # Shift index pointers since we need to add n_samples elements. indptr = X.indptr + n_samples # indptr[0] must be 0. indptr = np.concatenate((np.array([0]), indptr)) # Row indices of dummy feature are 0, ..., n_samples-1. indices = np.concatenate((np.arange(n_samples), X.indices)) # Prepend the dummy feature n_samples times. data = np.concatenate((np.full(n_samples, value), X.data)) return sparse.csc_matrix((data, indices, indptr), shape) else: klass = X.__class__ return klass(add_dummy_feature(X.tocoo(), value)) else: return np.hstack((np.full((n_samples, 1), value), X)) class QuantileTransformer(TransformerMixin, BaseEstimator): """Transform features using quantiles information. This method transforms the features to follow a uniform or a normal distribution. Therefore, for a given feature, this transformation tends to spread out the most frequent values. It also reduces the impact of (marginal) outliers: this is therefore a robust preprocessing scheme. The transformation is applied on each feature independently. First an estimate of the cumulative distribution function of a feature is used to map the original values to a uniform distribution. The obtained values are then mapped to the desired output distribution using the associated quantile function. Features values of new/unseen data that fall below or above the fitted range will be mapped to the bounds of the output distribution. Note that this transform is non-linear. It may distort linear correlations between variables measured at the same scale but renders variables measured at different scales more directly comparable. Read more in the :ref:`User Guide `. .. versionadded:: 0.19 Parameters ---------- n_quantiles : int, optional (default=1000 or n_samples) Number of quantiles to be computed. It corresponds to the number of landmarks used to discretize the cumulative distribution function. If n_quantiles is larger than the number of samples, n_quantiles is set to the number of samples as a larger number of quantiles does not give a better approximation of the cumulative distribution function estimator. output_distribution : str, optional (default='uniform') Marginal distribution for the transformed data. The choices are 'uniform' (default) or 'normal'. ignore_implicit_zeros : bool, optional (default=False) Only applies to sparse matrices. If True, the sparse entries of the matrix are discarded to compute the quantile statistics. If False, these entries are treated as zeros. subsample : int, optional (default=1e5) Maximum number of samples used to estimate the quantiles for computational efficiency. Note that the subsampling procedure may differ for value-identical sparse and dense matrices. random_state : int, RandomState instance or None, optional (default=None) Determines random number generation for subsampling and smoothing noise. Please see ``subsample`` for more details. Pass an int for reproducible results across multiple function calls. See :term:`Glossary ` copy : boolean, optional, (default=True) Set to False to perform inplace transformation and avoid a copy (if the input is already a numpy array). Attributes ---------- n_quantiles_ : integer The actual number of quantiles used to discretize the cumulative distribution function. quantiles_ : ndarray, shape (n_quantiles, n_features) The values corresponding the quantiles of reference. references_ : ndarray, shape(n_quantiles, ) Quantiles of references. Examples -------- >>> import numpy as np >>> from sklearn.preprocessing import QuantileTransformer >>> rng = np.random.RandomState(0) >>> X = np.sort(rng.normal(loc=0.5, scale=0.25, size=(25, 1)), axis=0) >>> qt = QuantileTransformer(n_quantiles=10, random_state=0) >>> qt.fit_transform(X) array([...]) See also -------- quantile_transform : Equivalent function without the estimator API. PowerTransformer : Perform mapping to a normal distribution using a power transform. StandardScaler : Perform standardization that is faster, but less robust to outliers. RobustScaler : Perform robust standardization that removes the influence of outliers but does not put outliers and inliers on the same scale. Notes ----- NaNs are treated as missing values: disregarded in fit, and maintained in transform. For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. """ @_deprecate_positional_args def __init__(self, *, n_quantiles=1000, output_distribution='uniform', ignore_implicit_zeros=False, subsample=int(1e5), random_state=None, copy=True): self.n_quantiles = n_quantiles self.output_distribution = output_distribution self.ignore_implicit_zeros = ignore_implicit_zeros self.subsample = subsample self.random_state = random_state self.copy = copy def _dense_fit(self, X, random_state): """Compute percentiles for dense matrices. Parameters ---------- X : ndarray, shape (n_samples, n_features) The data used to scale along the features axis. """ if self.ignore_implicit_zeros: warnings.warn("'ignore_implicit_zeros' takes effect only with" " sparse matrix. This parameter has no effect.") n_samples, n_features = X.shape references = self.references_ * 100 self.quantiles_ = [] for col in X.T: if self.subsample < n_samples: subsample_idx = random_state.choice(n_samples, size=self.subsample, replace=False) col = col.take(subsample_idx, mode='clip') self.quantiles_.append(np.nanpercentile(col, references)) self.quantiles_ = np.transpose(self.quantiles_) # Due to floating-point precision error in `np.nanpercentile`, # make sure that quantiles are monotonically increasing. # Upstream issue in numpy: # https://github.com/numpy/numpy/issues/14685 self.quantiles_ = np.maximum.accumulate(self.quantiles_) def _sparse_fit(self, X, random_state): """Compute percentiles for sparse matrices. Parameters ---------- X : sparse matrix CSC, shape (n_samples, n_features) The data used to scale along the features axis. The sparse matrix needs to be nonnegative. """ n_samples, n_features = X.shape references = self.references_ * 100 self.quantiles_ = [] for feature_idx in range(n_features): column_nnz_data = X.data[X.indptr[feature_idx]: X.indptr[feature_idx + 1]] if len(column_nnz_data) > self.subsample: column_subsample = (self.subsample * len(column_nnz_data) // n_samples) if self.ignore_implicit_zeros: column_data = np.zeros(shape=column_subsample, dtype=X.dtype) else: column_data = np.zeros(shape=self.subsample, dtype=X.dtype) column_data[:column_subsample] = random_state.choice( column_nnz_data, size=column_subsample, replace=False) else: if self.ignore_implicit_zeros: column_data = np.zeros(shape=len(column_nnz_data), dtype=X.dtype) else: column_data = np.zeros(shape=n_samples, dtype=X.dtype) column_data[:len(column_nnz_data)] = column_nnz_data if not column_data.size: # if no nnz, an error will be raised for computing the # quantiles. Force the quantiles to be zeros. self.quantiles_.append([0] * len(references)) else: self.quantiles_.append( np.nanpercentile(column_data, references)) self.quantiles_ = np.transpose(self.quantiles_) # due to floating-point precision error in `np.nanpercentile`, # make sure the quantiles are monotonically increasing # Upstream issue in numpy: # https://github.com/numpy/numpy/issues/14685 self.quantiles_ = np.maximum.accumulate(self.quantiles_) def fit(self, X, y=None): """Compute the quantiles used for transforming. Parameters ---------- X : ndarray or sparse matrix, shape (n_samples, n_features) The data used to scale along the features axis. If a sparse matrix is provided, it will be converted into a sparse ``csc_matrix``. Additionally, the sparse matrix needs to be nonnegative if `ignore_implicit_zeros` is False. Returns ------- self : object """ if self.n_quantiles <= 0: raise ValueError("Invalid value for 'n_quantiles': %d. " "The number of quantiles must be at least one." % self.n_quantiles) if self.subsample <= 0: raise ValueError("Invalid value for 'subsample': %d. " "The number of subsamples must be at least one." % self.subsample) if self.n_quantiles > self.subsample: raise ValueError("The number of quantiles cannot be greater than" " the number of samples used. Got {} quantiles" " and {} samples.".format(self.n_quantiles, self.subsample)) X = self._check_inputs(X, in_fit=True, copy=False) n_samples = X.shape[0] if self.n_quantiles > n_samples: warnings.warn("n_quantiles (%s) is greater than the total number " "of samples (%s). n_quantiles is set to " "n_samples." % (self.n_quantiles, n_samples)) self.n_quantiles_ = max(1, min(self.n_quantiles, n_samples)) rng = check_random_state(self.random_state) # Create the quantiles of reference self.references_ = np.linspace(0, 1, self.n_quantiles_, endpoint=True) if sparse.issparse(X): self._sparse_fit(X, rng) else: self._dense_fit(X, rng) return self def _transform_col(self, X_col, quantiles, inverse): """Private function to transform a single feature""" output_distribution = self.output_distribution if not inverse: lower_bound_x = quantiles[0] upper_bound_x = quantiles[-1] lower_bound_y = 0 upper_bound_y = 1 else: lower_bound_x = 0 upper_bound_x = 1 lower_bound_y = quantiles[0] upper_bound_y = quantiles[-1] # for inverse transform, match a uniform distribution with np.errstate(invalid='ignore'): # hide NaN comparison warnings if output_distribution == 'normal': X_col = stats.norm.cdf(X_col) # else output distribution is already a uniform distribution # find index for lower and higher bounds with np.errstate(invalid='ignore'): # hide NaN comparison warnings if output_distribution == 'normal': lower_bounds_idx = (X_col - BOUNDS_THRESHOLD < lower_bound_x) upper_bounds_idx = (X_col + BOUNDS_THRESHOLD > upper_bound_x) if output_distribution == 'uniform': lower_bounds_idx = (X_col == lower_bound_x) upper_bounds_idx = (X_col == upper_bound_x) isfinite_mask = ~np.isnan(X_col) X_col_finite = X_col[isfinite_mask] if not inverse: # Interpolate in one direction and in the other and take the # mean. This is in case of repeated values in the features # and hence repeated quantiles # # If we don't do this, only one extreme of the duplicated is # used (the upper when we do ascending, and the # lower for descending). We take the mean of these two X_col[isfinite_mask] = .5 * ( np.interp(X_col_finite, quantiles, self.references_) - np.interp(-X_col_finite, -quantiles[::-1], -self.references_[::-1])) else: X_col[isfinite_mask] = np.interp(X_col_finite, self.references_, quantiles) X_col[upper_bounds_idx] = upper_bound_y X_col[lower_bounds_idx] = lower_bound_y # for forward transform, match the output distribution if not inverse: with np.errstate(invalid='ignore'): # hide NaN comparison warnings if output_distribution == 'normal': X_col = stats.norm.ppf(X_col) # find the value to clip the data to avoid mapping to # infinity. Clip such that the inverse transform will be # consistent clip_min = stats.norm.ppf(BOUNDS_THRESHOLD - np.spacing(1)) clip_max = stats.norm.ppf(1 - (BOUNDS_THRESHOLD - np.spacing(1))) X_col = np.clip(X_col, clip_min, clip_max) # else output distribution is uniform and the ppf is the # identity function so we let X_col unchanged return X_col def _check_inputs(self, X, in_fit, accept_sparse_negative=False, copy=False): """Check inputs before fit and transform""" # In theory reset should be equal to `in_fit`, but there are tests # checking the input number of feature and they expect a specific # string, which is not the same one raised by check_n_features. So we # don't check n_features_in_ here for now (it's done with adhoc code in # the estimator anyway). # TODO: set reset=in_fit when addressing reset in # predict/transform/etc. reset = True X = self._validate_data(X, reset=reset, accept_sparse='csc', copy=copy, dtype=FLOAT_DTYPES, force_all_finite='allow-nan') # we only accept positive sparse matrix when ignore_implicit_zeros is # false and that we call fit or transform. with np.errstate(invalid='ignore'): # hide NaN comparison warnings if (not accept_sparse_negative and not self.ignore_implicit_zeros and (sparse.issparse(X) and np.any(X.data < 0))): raise ValueError('QuantileTransformer only accepts' ' non-negative sparse matrices.') # check the output distribution if self.output_distribution not in ('normal', 'uniform'): raise ValueError("'output_distribution' has to be either 'normal'" " or 'uniform'. Got '{}' instead.".format( self.output_distribution)) return X def _check_is_fitted(self, X): """Check the inputs before transforming""" check_is_fitted(self) # check that the dimension of X are adequate with the fitted data if X.shape[1] != self.quantiles_.shape[1]: raise ValueError('X does not have the same number of features as' ' the previously fitted data. Got {} instead of' ' {}.'.format(X.shape[1], self.quantiles_.shape[1])) def _transform(self, X, inverse=False): """Forward and inverse transform. Parameters ---------- X : ndarray, shape (n_samples, n_features) The data used to scale along the features axis. inverse : bool, optional (default=False) If False, apply forward transform. If True, apply inverse transform. Returns ------- X : ndarray, shape (n_samples, n_features) Projected data """ if sparse.issparse(X): for feature_idx in range(X.shape[1]): column_slice = slice(X.indptr[feature_idx], X.indptr[feature_idx + 1]) X.data[column_slice] = self._transform_col( X.data[column_slice], self.quantiles_[:, feature_idx], inverse) else: for feature_idx in range(X.shape[1]): X[:, feature_idx] = self._transform_col( X[:, feature_idx], self.quantiles_[:, feature_idx], inverse) return X def transform(self, X): """Feature-wise transformation of the data. Parameters ---------- X : ndarray or sparse matrix, shape (n_samples, n_features) The data used to scale along the features axis. If a sparse matrix is provided, it will be converted into a sparse ``csc_matrix``. Additionally, the sparse matrix needs to be nonnegative if `ignore_implicit_zeros` is False. Returns ------- Xt : ndarray or sparse matrix, shape (n_samples, n_features) The projected data. """ X = self._check_inputs(X, in_fit=False, copy=self.copy) self._check_is_fitted(X) return self._transform(X, inverse=False) def inverse_transform(self, X): """Back-projection to the original space. Parameters ---------- X : ndarray or sparse matrix, shape (n_samples, n_features) The data used to scale along the features axis. If a sparse matrix is provided, it will be converted into a sparse ``csc_matrix``. Additionally, the sparse matrix needs to be nonnegative if `ignore_implicit_zeros` is False. Returns ------- Xt : ndarray or sparse matrix, shape (n_samples, n_features) The projected data. """ X = self._check_inputs(X, in_fit=False, accept_sparse_negative=True, copy=self.copy) self._check_is_fitted(X) return self._transform(X, inverse=True) def _more_tags(self): return {'allow_nan': True} @_deprecate_positional_args def quantile_transform(X, *, axis=0, n_quantiles=1000, output_distribution='uniform', ignore_implicit_zeros=False, subsample=int(1e5), random_state=None, copy=True): """Transform features using quantiles information. This method transforms the features to follow a uniform or a normal distribution. Therefore, for a given feature, this transformation tends to spread out the most frequent values. It also reduces the impact of (marginal) outliers: this is therefore a robust preprocessing scheme. The transformation is applied on each feature independently. First an estimate of the cumulative distribution function of a feature is used to map the original values to a uniform distribution. The obtained values are then mapped to the desired output distribution using the associated quantile function. Features values of new/unseen data that fall below or above the fitted range will be mapped to the bounds of the output distribution. Note that this transform is non-linear. It may distort linear correlations between variables measured at the same scale but renders variables measured at different scales more directly comparable. Read more in the :ref:`User Guide `. Parameters ---------- X : array-like, sparse matrix The data to transform. axis : int, (default=0) Axis used to compute the means and standard deviations along. If 0, transform each feature, otherwise (if 1) transform each sample. n_quantiles : int, optional (default=1000 or n_samples) Number of quantiles to be computed. It corresponds to the number of landmarks used to discretize the cumulative distribution function. If n_quantiles is larger than the number of samples, n_quantiles is set to the number of samples as a larger number of quantiles does not give a better approximation of the cumulative distribution function estimator. output_distribution : str, optional (default='uniform') Marginal distribution for the transformed data. The choices are 'uniform' (default) or 'normal'. ignore_implicit_zeros : bool, optional (default=False) Only applies to sparse matrices. If True, the sparse entries of the matrix are discarded to compute the quantile statistics. If False, these entries are treated as zeros. subsample : int, optional (default=1e5) Maximum number of samples used to estimate the quantiles for computational efficiency. Note that the subsampling procedure may differ for value-identical sparse and dense matrices. random_state : int, RandomState instance or None, optional (default=None) Determines random number generation for subsampling and smoothing noise. Please see ``subsample`` for more details. Pass an int for reproducible results across multiple function calls. See :term:`Glossary ` copy : boolean, optional, (default=True) Set to False to perform inplace transformation and avoid a copy (if the input is already a numpy array). If True, a copy of `X` is transformed, leaving the original `X` unchanged ..versionchanged:: 0.23 The default value of `copy` changed from False to True in 0.23. Returns ------- Xt : ndarray or sparse matrix, shape (n_samples, n_features) The transformed data. Examples -------- >>> import numpy as np >>> from sklearn.preprocessing import quantile_transform >>> rng = np.random.RandomState(0) >>> X = np.sort(rng.normal(loc=0.5, scale=0.25, size=(25, 1)), axis=0) >>> quantile_transform(X, n_quantiles=10, random_state=0, copy=True) array([...]) See also -------- QuantileTransformer : Performs quantile-based scaling using the ``Transformer`` API (e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`). power_transform : Maps data to a normal distribution using a power transformation. scale : Performs standardization that is faster, but less robust to outliers. robust_scale : Performs robust standardization that removes the influence of outliers but does not put outliers and inliers on the same scale. Notes ----- NaNs are treated as missing values: disregarded in fit, and maintained in transform. For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. """ n = QuantileTransformer(n_quantiles=n_quantiles, output_distribution=output_distribution, subsample=subsample, ignore_implicit_zeros=ignore_implicit_zeros, random_state=random_state, copy=copy) if axis == 0: return n.fit_transform(X) elif axis == 1: return n.fit_transform(X.T).T else: raise ValueError("axis should be either equal to 0 or 1. Got" " axis={}".format(axis)) class PowerTransformer(TransformerMixin, BaseEstimator): """Apply a power transform featurewise to make data more Gaussian-like. Power transforms are a family of parametric, monotonic transformations that are applied to make data more Gaussian-like. This is useful for modeling issues related to heteroscedasticity (non-constant variance), or other situations where normality is desired. Currently, PowerTransformer supports the Box-Cox transform and the Yeo-Johnson transform. The optimal parameter for stabilizing variance and minimizing skewness is estimated through maximum likelihood. Box-Cox requires input data to be strictly positive, while Yeo-Johnson supports both positive or negative data. By default, zero-mean, unit-variance normalization is applied to the transformed data. Read more in the :ref:`User Guide `. .. versionadded:: 0.20 Parameters ---------- method : str, (default='yeo-johnson') The power transform method. Available methods are: - 'yeo-johnson' [1]_, works with positive and negative values - 'box-cox' [2]_, only works with strictly positive values standardize : boolean, default=True Set to True to apply zero-mean, unit-variance normalization to the transformed output. copy : boolean, optional, default=True Set to False to perform inplace computation during transformation. Attributes ---------- lambdas_ : array of float, shape (n_features,) The parameters of the power transformation for the selected features. Examples -------- >>> import numpy as np >>> from sklearn.preprocessing import PowerTransformer >>> pt = PowerTransformer() >>> data = [[1, 2], [3, 2], [4, 5]] >>> print(pt.fit(data)) PowerTransformer() >>> print(pt.lambdas_) [ 1.386... -3.100...] >>> print(pt.transform(data)) [[-1.316... -0.707...] [ 0.209... -0.707...] [ 1.106... 1.414...]] See also -------- power_transform : Equivalent function without the estimator API. QuantileTransformer : Maps data to a standard normal distribution with the parameter `output_distribution='normal'`. Notes ----- NaNs are treated as missing values: disregarded in ``fit``, and maintained in ``transform``. For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. References ---------- .. [1] I.K. Yeo and R.A. Johnson, "A new family of power transformations to improve normality or symmetry." Biometrika, 87(4), pp.954-959, (2000). .. [2] G.E.P. Box and D.R. Cox, "An Analysis of Transformations", Journal of the Royal Statistical Society B, 26, 211-252 (1964). """ @_deprecate_positional_args def __init__(self, method='yeo-johnson', *, standardize=True, copy=True): self.method = method self.standardize = standardize self.copy = copy def fit(self, X, y=None): """Estimate the optimal parameter lambda for each feature. The optimal lambda parameter for minimizing skewness is estimated on each feature independently using maximum likelihood. Parameters ---------- X : array-like, shape (n_samples, n_features) The data used to estimate the optimal transformation parameters. y : Ignored Returns ------- self : object """ self._fit(X, y=y, force_transform=False) return self def fit_transform(self, X, y=None): return self._fit(X, y, force_transform=True) def _fit(self, X, y=None, force_transform=False): X = self._check_input(X, in_fit=True, check_positive=True, check_method=True) if not self.copy and not force_transform: # if call from fit() X = X.copy() # force copy so that fit does not change X inplace optim_function = {'box-cox': self._box_cox_optimize, 'yeo-johnson': self._yeo_johnson_optimize }[self.method] with np.errstate(invalid='ignore'): # hide NaN warnings self.lambdas_ = np.array([optim_function(col) for col in X.T]) if self.standardize or force_transform: transform_function = {'box-cox': boxcox, 'yeo-johnson': self._yeo_johnson_transform }[self.method] for i, lmbda in enumerate(self.lambdas_): with np.errstate(invalid='ignore'): # hide NaN warnings X[:, i] = transform_function(X[:, i], lmbda) if self.standardize: self._scaler = StandardScaler(copy=False) if force_transform: X = self._scaler.fit_transform(X) else: self._scaler.fit(X) return X def transform(self, X): """Apply the power transform to each feature using the fitted lambdas. Parameters ---------- X : array-like, shape (n_samples, n_features) The data to be transformed using a power transformation. Returns ------- X_trans : array-like, shape (n_samples, n_features) The transformed data. """ check_is_fitted(self) X = self._check_input(X, in_fit=False, check_positive=True, check_shape=True) transform_function = {'box-cox': boxcox, 'yeo-johnson': self._yeo_johnson_transform }[self.method] for i, lmbda in enumerate(self.lambdas_): with np.errstate(invalid='ignore'): # hide NaN warnings X[:, i] = transform_function(X[:, i], lmbda) if self.standardize: X = self._scaler.transform(X) return X def inverse_transform(self, X): """Apply the inverse power transformation using the fitted lambdas. The inverse of the Box-Cox transformation is given by:: if lambda_ == 0: X = exp(X_trans) else: X = (X_trans * lambda_ + 1) ** (1 / lambda_) The inverse of the Yeo-Johnson transformation is given by:: if X >= 0 and lambda_ == 0: X = exp(X_trans) - 1 elif X >= 0 and lambda_ != 0: X = (X_trans * lambda_ + 1) ** (1 / lambda_) - 1 elif X < 0 and lambda_ != 2: X = 1 - (-(2 - lambda_) * X_trans + 1) ** (1 / (2 - lambda_)) elif X < 0 and lambda_ == 2: X = 1 - exp(-X_trans) Parameters ---------- X : array-like, shape (n_samples, n_features) The transformed data. Returns ------- X : array-like, shape (n_samples, n_features) The original data """ check_is_fitted(self) X = self._check_input(X, in_fit=False, check_shape=True) if self.standardize: X = self._scaler.inverse_transform(X) inv_fun = {'box-cox': self._box_cox_inverse_tranform, 'yeo-johnson': self._yeo_johnson_inverse_transform }[self.method] for i, lmbda in enumerate(self.lambdas_): with np.errstate(invalid='ignore'): # hide NaN warnings X[:, i] = inv_fun(X[:, i], lmbda) return X def _box_cox_inverse_tranform(self, x, lmbda): """Return inverse-transformed input x following Box-Cox inverse transform with parameter lambda. """ if lmbda == 0: x_inv = np.exp(x) else: x_inv = (x * lmbda + 1) ** (1 / lmbda) return x_inv def _yeo_johnson_inverse_transform(self, x, lmbda): """Return inverse-transformed input x following Yeo-Johnson inverse transform with parameter lambda. """ x_inv = np.zeros_like(x) pos = x >= 0 # when x >= 0 if abs(lmbda) < np.spacing(1.): x_inv[pos] = np.exp(x[pos]) - 1 else: # lmbda != 0 x_inv[pos] = np.power(x[pos] * lmbda + 1, 1 / lmbda) - 1 # when x < 0 if abs(lmbda - 2) > np.spacing(1.): x_inv[~pos] = 1 - np.power(-(2 - lmbda) * x[~pos] + 1, 1 / (2 - lmbda)) else: # lmbda == 2 x_inv[~pos] = 1 - np.exp(-x[~pos]) return x_inv def _yeo_johnson_transform(self, x, lmbda): """Return transformed input x following Yeo-Johnson transform with parameter lambda. """ out = np.zeros_like(x) pos = x >= 0 # binary mask # when x >= 0 if abs(lmbda) < np.spacing(1.): out[pos] = np.log1p(x[pos]) else: # lmbda != 0 out[pos] = (np.power(x[pos] + 1, lmbda) - 1) / lmbda # when x < 0 if abs(lmbda - 2) > np.spacing(1.): out[~pos] = -(np.power(-x[~pos] + 1, 2 - lmbda) - 1) / (2 - lmbda) else: # lmbda == 2 out[~pos] = -np.log1p(-x[~pos]) return out def _box_cox_optimize(self, x): """Find and return optimal lambda parameter of the Box-Cox transform by MLE, for observed data x. We here use scipy builtins which uses the brent optimizer. """ # the computation of lambda is influenced by NaNs so we need to # get rid of them _, lmbda = stats.boxcox(x[~np.isnan(x)], lmbda=None) return lmbda def _yeo_johnson_optimize(self, x): """Find and return optimal lambda parameter of the Yeo-Johnson transform by MLE, for observed data x. Like for Box-Cox, MLE is done via the brent optimizer. """ def _neg_log_likelihood(lmbda): """Return the negative log likelihood of the observed data x as a function of lambda.""" x_trans = self._yeo_johnson_transform(x, lmbda) n_samples = x.shape[0] loglike = -n_samples / 2 * np.log(x_trans.var()) loglike += (lmbda - 1) * (np.sign(x) * np.log1p(np.abs(x))).sum() return -loglike # the computation of lambda is influenced by NaNs so we need to # get rid of them x = x[~np.isnan(x)] # choosing bracket -2, 2 like for boxcox return optimize.brent(_neg_log_likelihood, brack=(-2, 2)) def _check_input(self, X, in_fit, check_positive=False, check_shape=False, check_method=False): """Validate the input before fit and transform. Parameters ---------- X : array-like, shape (n_samples, n_features) check_positive : bool If True, check that all data is positive and non-zero (only if ``self.method=='box-cox'``). check_shape : bool If True, check that n_features matches the length of self.lambdas_ check_method : bool If True, check that the transformation method is valid. """ X = self._validate_data(X, ensure_2d=True, dtype=FLOAT_DTYPES, copy=self.copy, force_all_finite='allow-nan') with np.warnings.catch_warnings(): np.warnings.filterwarnings( 'ignore', r'All-NaN (slice|axis) encountered') if (check_positive and self.method == 'box-cox' and np.nanmin(X) <= 0): raise ValueError("The Box-Cox transformation can only be " "applied to strictly positive data") if check_shape and not X.shape[1] == len(self.lambdas_): raise ValueError("Input data has a different number of features " "than fitting data. Should have {n}, data has {m}" .format(n=len(self.lambdas_), m=X.shape[1])) valid_methods = ('box-cox', 'yeo-johnson') if check_method and self.method not in valid_methods: raise ValueError("'method' must be one of {}, " "got {} instead." .format(valid_methods, self.method)) return X def _more_tags(self): return {'allow_nan': True} @_deprecate_positional_args def power_transform(X, method='yeo-johnson', *, standardize=True, copy=True): """ Power transforms are a family of parametric, monotonic transformations that are applied to make data more Gaussian-like. This is useful for modeling issues related to heteroscedasticity (non-constant variance), or other situations where normality is desired. Currently, power_transform supports the Box-Cox transform and the Yeo-Johnson transform. The optimal parameter for stabilizing variance and minimizing skewness is estimated through maximum likelihood. Box-Cox requires input data to be strictly positive, while Yeo-Johnson supports both positive or negative data. By default, zero-mean, unit-variance normalization is applied to the transformed data. Read more in the :ref:`User Guide `. Parameters ---------- X : array-like, shape (n_samples, n_features) The data to be transformed using a power transformation. method : {'yeo-johnson', 'box-cox'}, default='yeo-johnson' The power transform method. Available methods are: - 'yeo-johnson' [1]_, works with positive and negative values - 'box-cox' [2]_, only works with strictly positive values .. versionchanged:: 0.23 The default value of the `method` parameter changed from 'box-cox' to 'yeo-johnson' in 0.23. standardize : boolean, default=True Set to True to apply zero-mean, unit-variance normalization to the transformed output. copy : boolean, optional, default=True Set to False to perform inplace computation during transformation. Returns ------- X_trans : array-like, shape (n_samples, n_features) The transformed data. Examples -------- >>> import numpy as np >>> from sklearn.preprocessing import power_transform >>> data = [[1, 2], [3, 2], [4, 5]] >>> print(power_transform(data, method='box-cox')) [[-1.332... -0.707...] [ 0.256... -0.707...] [ 1.076... 1.414...]] See also -------- PowerTransformer : Equivalent transformation with the ``Transformer`` API (e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`). quantile_transform : Maps data to a standard normal distribution with the parameter `output_distribution='normal'`. Notes ----- NaNs are treated as missing values: disregarded in ``fit``, and maintained in ``transform``. For a comparison of the different scalers, transformers, and normalizers, see :ref:`examples/preprocessing/plot_all_scaling.py `. References ---------- .. [1] I.K. Yeo and R.A. Johnson, "A new family of power transformations to improve normality or symmetry." Biometrika, 87(4), pp.954-959, (2000). .. [2] G.E.P. Box and D.R. Cox, "An Analysis of Transformations", Journal of the Royal Statistical Society B, 26, 211-252 (1964). """ pt = PowerTransformer(method=method, standardize=standardize, copy=copy) return pt.fit_transform(X)