.. currentmodule:: sklearn.preprocessing
The sklearn.preprocessing package provides several common
utility functions and transformer classes to change raw feature vectors
into a representation that is more suitable for the downstream estimators.
Standardization of datasets is a common requirement for many machine learning estimators implemented in the scikit: they might behave badly if the individual feature do not more or less look like standard normally distributed data: Gaussian with zero mean and unit variance.
In practice we often ignore the shape of the distribution and just transform the data to center it by removing the mean value of each feature, then scale it by dividing non-constant features by their standard deviation.
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 zero 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.
The function :func:`scale` provides a quick and easy way to perform this operation on a single array-like dataset:
>>> from sklearn import preprocessing
>>> import numpy as np
>>> X = np.array([[ 1., -1., 2.],
... [ 2., 0., 0.],
... [ 0., 1., -1.]])
>>> X_scaled = preprocessing.scale(X)
>>> X_scaled # doctest: +ELLIPSIS
array([[ 0. ..., -1.22..., 1.33...],
[ 1.22..., 0. ..., -0.26...],
[-1.22..., 1.22..., -1.06...]])
Scaled data has zero mean and unit variance:
>>> X_scaled.mean(axis=0) array([ 0., 0., 0.]) >>> X_scaled.std(axis=0) array([ 1., 1., 1.])
The preprocessing module further provides a utility class
:class:`StandardScaler` that implements the Transformer API to compute
the mean and standard deviation on a training set so as to be
able to later reapply the same transformation on the testing set.
This class is hence suitable for use in the early steps of a
:class:`sklearn.pipeline.Pipeline`:
>>> scaler = preprocessing.StandardScaler().fit(X)
>>> scaler
StandardScaler(copy=True, with_mean=True, with_std=True)
>>> scaler.mean_ # doctest: +ELLIPSIS
array([ 1. ..., 0. ..., 0.33...])
>>> scaler.std_ # doctest: +ELLIPSIS
array([ 0.81..., 0.81..., 1.24...])
>>> scaler.transform(X) # doctest: +ELLIPSIS
array([[ 0. ..., -1.22..., 1.33...],
[ 1.22..., 0. ..., -0.26...],
[-1.22..., 1.22..., -1.06...]])
The scaler instance can then be used on new data to transform it the same way it did on the training set:
>>> scaler.transform([[-1., 1., 0.]]) # doctest: +ELLIPSIS array([[-2.44..., 1.22..., -0.26...]])
It is possible to disable either centering or scaling by either
passing with_mean=False or with_std=False to the constructor
of :class:`StandardScaler`.
An alternative standardization is scaling features to lie between a given minimum and maximum value, often between zero and one. This can be achieved using :class:`MinMaxScaler`.
The motivation to use this scaling include robustness to very small standard deviations of features and preserving zero entries in sparse data.
Here is an example to scale a toy data matrix to the [0, 1] range:
>>> X_train = np.array([[ 1., -1., 2.],
... [ 2., 0., 0.],
... [ 0., 1., -1.]])
...
>>> min_max_scaler = preprocessing.MinMaxScaler()
>>> X_train_minmax = min_max_scaler.fit_transform(X_train)
>>> X_train_minmax
array([[ 0.5 , 0. , 1. ],
[ 1. , 0.5 , 0.33333333],
[ 0. , 1. , 0. ]])
The same instance of the transformer can then be applied to some new test data unseen during the fit call: the same scaling and shifting operations will be applied to be consistent with the transformation performed on the train data:
>>> X_test = np.array([[ -3., -1., 4.]]) >>> X_test_minmax = min_max_scaler.transform(X_test) >>> X_test_minmax array([[-1.5 , 0. , 1.66666667]])
It is possible to introspect the scaler attributes to find about the exact nature of the transformation learned on the training data:
>>> min_max_scaler.scale_ # doctest: +ELLIPSIS array([ 0.5 , 0.5 , 0.33...]) >>> min_max_scaler.min_ # doctest: +ELLIPSIS array([ 0. , 0.5 , 0.33...])
If :class:`MinMaxScaler` is given an explicit feature_range=(min, max) the
full formula is:
X_std = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0)) X_scaled = X_std / (max - min) + min
References:
Further discussion on the importance of centering and scaling data is available on this FAQ: Should I normalize/standardize/rescale the data?
Scaling vs Whitening
It is sometimes not enough to center and scale the features independently, since a downstream model can further make some assumption on the linear independence of the features.
To address this issue you can use :class:`sklearn.decomposition.PCA`
or :class:`sklearn.decomposition.RandomizedPCA` with whiten=True
to further remove the linear correlation across features.
Sparse input
:func:`scale` and :class:`StandardScaler` accept scipy.sparse matrices
as input only when with_mean=False is explicitly passed to the
constructor. Otherwise a ValueError will be raised as
silently centering would break the sparsity and would often crash the
execution by allocating excessive amounts of memory unintentionally.
If the centered data is expected to be small enough, explicitly convert
the input to an array using the toarray method of sparse matrices
instead.
For sparse input the data is converted to the Compressed Sparse Rows
representation (see scipy.sparse.csr_matrix).
To avoid unnecessary memory copies, it is recommended to choose the CSR
representation upstream.
Scaling target variables in regression
:func:`scale` and :class:`StandardScaler` work out-of-the-box with 1d arrays. This is very useful for scaling the target / response variables used for regression.
If you have a kernel matrix of a kernel K that computes a dot product in a feature space defined by function phi, a :class:`KernelCenterer` can transform the kernel matrix so that it contains inner products in the feature space defined by phi followed by removal of the mean in that space.
Normalization is the process of scaling individual samples to have unit norm. This process can be useful if you plan to use a quadratic form such as the dot-product or any other kernel to quantify the similarity of any pair of samples.
This assumption is the base of the Vector Space Model often used in text classification and clustering contexts.
The function :func:`normalize` provides a quick and easy way to perform this
operation on a single array-like dataset, either using the l1 or l2
norms:
>>> X = [[ 1., -1., 2.],
... [ 2., 0., 0.],
... [ 0., 1., -1.]]
>>> X_normalized = preprocessing.normalize(X, norm='l2')
>>> X_normalized # doctest: +ELLIPSIS
array([[ 0.40..., -0.40..., 0.81...],
[ 1. ..., 0. ..., 0. ...],
[ 0. ..., 0.70..., -0.70...]])
The preprocessing module further provides a utility class
:class:`Normalizer` that implements the same operation using the
Transformer API (even though the fit method is useless in this case:
the class is stateless as this operation treats samples independently).
This class is hence suitable for use in the early steps of a :class:`sklearn.pipeline.Pipeline`:
>>> normalizer = preprocessing.Normalizer().fit(X) # fit does nothing >>> normalizer Normalizer(copy=True, norm='l2')
The normalizer instance can then be used on sample vectors as any transformer:
>>> normalizer.transform(X) # doctest: +ELLIPSIS
array([[ 0.40..., -0.40..., 0.81...],
[ 1. ..., 0. ..., 0. ...],
[ 0. ..., 0.70..., -0.70...]])
>>> normalizer.transform([[-1., 1., 0.]]) # doctest: +ELLIPSIS
array([[-0.70..., 0.70..., 0. ...]])
Sparse input
:func:`normalize` and :class:`Normalizer` accept both dense array-like and sparse matrices from scipy.sparse as input.
For sparse input the data is converted to the Compressed Sparse Rows
representation (see scipy.sparse.csr_matrix) before being fed to
efficient Cython routines. To avoid unnecessary memory copies, it is
recommended to choose the CSR representation upstream.
Feature binarization is the process of thresholding numerical features to get boolean values. This can be useful for downstream probabilistic estimators that make assumption that the input data is distributed according to a multi-variate Bernoulli distribution. For instance, this is the case for the :class:`sklearn.neural_network.BernoulliRBM`.
It is also common among the text processing community to use binary feature values (probably to simplify the probabilistic reasoning) even if normalized counts (a.k.a. term frequencies) or TF-IDF valued features often perform slightly better in practice.
As for the :class:`Normalizer`, the utility class
:class:`Binarizer` is meant to be used in the early stages of
:class:`sklearn.pipeline.Pipeline`. The fit method does nothing
as each sample is treated independently of others:
>>> X = [[ 1., -1., 2.],
... [ 2., 0., 0.],
... [ 0., 1., -1.]]
>>> binarizer = preprocessing.Binarizer().fit(X) # fit does nothing
>>> binarizer
Binarizer(copy=True, threshold=0.0)
>>> binarizer.transform(X)
array([[ 1., 0., 1.],
[ 1., 0., 0.],
[ 0., 1., 0.]])
It is possible to adjust the threshold of the binarizer:
>>> binarizer = preprocessing.Binarizer(threshold=1.1)
>>> binarizer.transform(X)
array([[ 0., 0., 1.],
[ 1., 0., 0.],
[ 0., 0., 0.]])
As for the :class:`StandardScaler` and :class:`Normalizer` classes, the preprocessing module provides a companion function :func:`binarize` to be used when the transformer API is not necessary.
Sparse input
:func:`binarize` and :class:`Binarizer` accept both dense array-like and sparse matrices from scipy.sparse as input.
For sparse input the data is converted to the Compressed Sparse Rows
representation (see scipy.sparse.csr_matrix).
To avoid unnecessary memory copies, it is recommended to choose the CSR
representation upstream.
Often features are not given as continuous values but categorical.
For example a person could have features ["male", "female"],
["from Europe", "from US", "from Asia"],
["uses Firefox", "uses Chrome", "uses Safari", "uses Internet Explorer"].
Such features can be efficiently coded as integers, for instance
["male", "from US", "uses Internet Explorer"] could be expressed as
[0, 1, 3] while ["female", "from Asia", "uses Chrome"] would be
[1, 2, 1].
Such integer representation can not be used directly with scikit-learn estimators, as these expect continuous input, and would interpret the categories as being ordered, which is often not desired (i.e. the set of browsers was ordered arbitrarily).
One possibility to convert categorical features to features that can be used
with scikit-learn estimators is to use a one-of-K or one-hot encoding, which is
implemented in :class:`OneHotEncoder`. This estimator transforms each
categorical feature with m possible values into m binary features, with
only one active.
Continuing the example above:
>>> enc = preprocessing.OneHotEncoder()
>>> enc.fit([[0, 0, 3], [1, 1, 0], [0, 2, 1], [1, 0, 2]]) # doctest: +ELLIPSIS
OneHotEncoder(categorical_features='all', dtype=<... 'float'>,
n_values='auto', sparse=True)
>>> enc.transform([[0, 1, 3]]).toarray()
array([[ 1., 0., 0., 1., 0., 0., 0., 0., 1.]])
By default, how many values each feature can take is inferred automatically from the dataset.
It is possible to specify this explicitly using the parameter n_values.
There are two genders, three possible continents and four web browsers in our
dataset.
Then we fit the estimator, and transform a data point.
In the result, the first two numbers encode the gender, the next set of three
numbers the continent and the last four the web browser.
See :ref:`dict_feature_extraction` for categorical features that are represented as a dict, not as integers.
:class:`LabelBinarizer` is a utility class to help create a label indicator matrix from a list of multi-class labels:
>>> lb = preprocessing.LabelBinarizer()
>>> lb.fit([1, 2, 6, 4, 2])
LabelBinarizer(neg_label=0, pos_label=1, sparse_output=False)
>>> lb.classes_
array([1, 2, 4, 6])
>>> lb.transform([1, 6])
array([[1, 0, 0, 0],
[0, 0, 0, 1]])
For multiple labels per instance, use :class:`MultiLabelBinarizer`:
>>> lb = preprocessing.MultiLabelBinarizer()
>>> lb.fit_transform([(1, 2), (3,)])
array([[1, 1, 0],
[0, 0, 1]])
>>> lb.classes_
array([1, 2, 3])
:class:`LabelEncoder` is a utility class to help normalize labels such that they contain only values between 0 and n_classes-1. This is sometimes useful for writing efficient Cython routines. :class:`LabelEncoder` can be used as follows:
>>> from sklearn import preprocessing >>> le = preprocessing.LabelEncoder() >>> le.fit([1, 2, 2, 6]) LabelEncoder() >>> le.classes_ array([1, 2, 6]) >>> le.transform([1, 1, 2, 6]) array([0, 0, 1, 2]) >>> le.inverse_transform([0, 0, 1, 2]) array([1, 1, 2, 6])
It can also be used to transform non-numerical labels (as long as they are hashable and comparable) to numerical labels:
>>> le = preprocessing.LabelEncoder() >>> le.fit(["paris", "paris", "tokyo", "amsterdam"]) LabelEncoder() >>> list(le.classes_) ['amsterdam', 'paris', 'tokyo'] >>> le.transform(["tokyo", "tokyo", "paris"]) array([2, 2, 1]) >>> list(le.inverse_transform([2, 2, 1])) ['tokyo', 'tokyo', 'paris']
For various reasons, many real world datasets contain missing values, often encoded as blanks, NaNs or other placeholders. Such datasets however are incompatible with scikit-learn estimators which assume that all values in an array are numerical, and that all have and hold meaning. A basic strategy to use incomplete datasets is to discard entire rows and/or columns containing missing values. However, this comes at the price of losing data which may be valuable (even though incomplete). A better strategy is to impute the missing values, i.e., to infer them from the known part of the data.
The :class:`Imputer` class provides basic strategies for imputing missing values, either using the mean, the median or the most frequent value of the row or column in which the missing values are located. This class also allows for different missing values encodings.
The following snippet demonstrates how to replace missing values,
encoded as np.nan, using the mean value of the columns (axis 0)
that contain the missing values:
>>> import numpy as np >>> from sklearn.preprocessing import Imputer >>> imp = Imputer(missing_values='NaN', strategy='mean', axis=0) >>> imp.fit([[1, 2], [np.nan, 3], [7, 6]]) Imputer(axis=0, copy=True, missing_values='NaN', strategy='mean', verbose=0) >>> X = [[np.nan, 2], [6, np.nan], [7, 6]] >>> print(imp.transform(X)) # doctest: +ELLIPSIS [[ 4. 2. ] [ 6. 3.666...] [ 7. 6. ]]
The :class:`Imputer` class also supports sparse matrices:
>>> import scipy.sparse as sp >>> X = sp.csc_matrix([[1, 2], [0, 3], [7, 6]]) >>> imp = Imputer(missing_values=0, strategy='mean', axis=0) >>> imp.fit(X) Imputer(axis=0, copy=True, missing_values=0, strategy='mean', verbose=0) >>> X_test = sp.csc_matrix([[0, 2], [6, 0], [7, 6]]) >>> print(imp.transform(X_test)) # doctest: +ELLIPSIS [[ 4. 2. ] [ 6. 3.666...] [ 7. 6. ]]
Note that, here, missing values are encoded by 0 and are thus implicitly stored in the matrix. This format is thus suitable when there are many more missing values than observed values.
:class:`Imputer` can be used in a Pipeline as a way to build a composite estimator that supports imputation. See :ref:`example_imputation.py`
If your number of features is high, it may be useful to reduce it with an
unsupervised step prior to supervised steps. Many of the
:ref:`unsupervised-learning` methods implement a transform method that
can be used to reduce the dimensionality. Below we discuss two specific
example of this pattern that are heavily used.
Pipelining
The unsupervised data reduction and the supervised estimator can be chained in one step. See :ref:`pipeline`.
.. currentmodule:: sklearn
:class:`decomposition.PCA` looks for a combination of features that capture well the variance of the original features.
The module: :mod:`random_projection` provides several tools for data reduction by random projections. See the relevant section of the documentation: :ref:`random_projection`.
:class:`cluster.FeatureAgglomeration` applies :ref:`hierarchical_clustering` to group together features that behave similarly.
Examples
Feature scaling
Note that if features have very different scaling or statistical properties, :class:`cluster.FeatureAgglomeration` maye not be able to capture the links between related features. Using a :class:`preprocessing.StandardScaler` can be useful in these settings.