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.
In general, learning algorithms benefit from standardization of the data set. If some outliers are present in the set, robust scalers or transformers are more appropriate. The behaviors of the different scalers, transformers, and normalizers on a dataset containing marginal outliers is highlighted in Compare the effect of different scalers on data with outliers.
Standardization of datasets is a common requirement for many machine learning estimators implemented in scikit-learn; they might behave badly if the individual features 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 than others, it might dominate the objective function and make the estimator unable to learn from other features correctly as expected.
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_train = np.array([[ 1., -1., 2.], ... [ 2., 0., 0.], ... [ 0., 1., -1.]]) >>> X_scaled = preprocessing.scale(X_train) >>> X_scaled 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.])
preprocessing module further provides a utility 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
>>> scaler = preprocessing.StandardScaler().fit(X_train) >>> scaler StandardScaler(copy=True, with_mean=True, with_std=True) >>> scaler.mean_ array([1. ..., 0. ..., 0.33...]) >>> scaler.scale_ array([0.81..., 0.81..., 1.24...]) >>> scaler.transform(X_train) 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:
>>> X_test = [[-1., 1., 0.]] >>> scaler.transform(X_test) array([[-2.44..., 1.22..., -0.26...]])
It is possible to disable either centering or scaling by either passing
with_std=False to the constructor of
An alternative standardization is scaling features to lie between a given minimum and maximum value, often between zero and one, or so that the maximum absolute value of each feature is scaled to unit size. This can be achieved using
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_ array([0.5 , 0.5 , 0.33...]) >>> min_max_scaler.min_ array([0. , 0.5 , 0.33...])
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
MaxAbsScaler works in a very similar fashion, but scales in a way that the training data lies within the range
[-1, 1] by dividing through the largest maximum value in each feature. It is meant for data that is already centered at zero or sparse data.
Here is how to use the toy data from the previous example with this scaler:
>>> X_train = np.array([[ 1., -1., 2.], ... [ 2., 0., 0.], ... [ 0., 1., -1.]]) ... >>> max_abs_scaler = preprocessing.MaxAbsScaler() >>> X_train_maxabs = max_abs_scaler.fit_transform(X_train) >>> X_train_maxabs # doctest +NORMALIZE_WHITESPACE^ array([[ 0.5, -1. , 1. ], [ 1. , 0. , 0. ], [ 0. , 1. , -0.5]]) >>> X_test = np.array([[ -3., -1., 4.]]) >>> X_test_maxabs = max_abs_scaler.transform(X_test) >>> X_test_maxabs array([[-1.5, -1. , 2. ]]) >>> max_abs_scaler.scale_ array([2., 1., 2.])
Centering sparse data would destroy the sparseness structure in the data, and thus rarely is a sensible thing to do. However, it can make sense to scale sparse inputs, especially if features are on different scales.
maxabs_scale were specifically designed for scaling sparse data, and are the recommended way to go about this. However,
StandardScaler can accept
scipy.sparse matrices as input, as long as
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.
RobustScaler cannot be fitted to sparse inputs, but you can use the
transform method on sparse inputs.
Note that the scalers accept both Compressed Sparse Rows and Compressed Sparse Columns format (see
scipy.sparse.csc_matrix). Any other sparse input will be converted to the Compressed Sparse Rows representation. To avoid unnecessary memory copies, it is recommended to choose the CSR or CSC representation upstream.
Finally, if the centered data is expected to be small enough, explicitly converting the input to an array using the
toarray method of sparse matrices is another option.
If your data contains many outliers, scaling using the mean and variance of the data is likely to not work very well. In these cases, you can use
RobustScaler as drop-in replacements instead. They use more robust estimates for the center and range of your data.
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
whiten=True to further remove the linear correlation across features.
Scaling a 1D array
If you have a kernel matrix of a kernel \(K\) that computes a dot product in a feature space defined by function \(phi\), a
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.
QuantileTransformer puts all features into the same, known range or distribution. However, by performing a rank transformation, it smooths out unusual distributions and is less influenced by outliers than scaling methods. It does, however, distort correlations and distances within and across features.
>>> from sklearn.datasets import load_iris >>> from sklearn.model_selection import train_test_split >>> iris = load_iris() >>> X, y = iris.data, iris.target >>> X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0) >>> quantile_transformer = preprocessing.QuantileTransformer(random_state=0) >>> X_train_trans = quantile_transformer.fit_transform(X_train) >>> X_test_trans = quantile_transformer.transform(X_test) >>> np.percentile(X_train[:, 0], [0, 25, 50, 75, 100]) array([ 4.3, 5.1, 5.8, 6.5, 7.9])
This feature corresponds to the sepal length in cm. Once the quantile transformation applied, those landmarks approach closely the percentiles previously defined:
>>> np.percentile(X_train_trans[:, 0], [0, 25, 50, 75, 100]) ... array([ 0.00... , 0.24..., 0.49..., 0.73..., 0.99... ])
This can be confirmed on a independent testing set with similar remarks:
>>> np.percentile(X_test[:, 0], [0, 25, 50, 75, 100]) ... array([ 4.4 , 5.125, 5.75 , 6.175, 7.3 ]) >>> np.percentile(X_test_trans[:, 0], [0, 25, 50, 75, 100]) ... array([ 0.01..., 0.25..., 0.46..., 0.60... , 0.94...])
In many modeling scenarios, normality of the features in a dataset is desirable. Power transforms are a family of parametric, monotonic transformations that aim to map data from any distribution to as close to a Gaussian distribution as possible in order to stabilize variance and minimize skewness.
PowerTransformer currently provides two such power transformations, the Yeo-Johnson transform and the Box-Cox transform.
The Yeo-Johnson transform is given by:
while the Box-Cox transform is given by:
Box-Cox can only be applied to strictly positive data. In both methods, the transformation is parameterized by \(\lambda\), which is determined through maximum likelihood estimation. Here is an example of using Box-Cox to map samples drawn from a lognormal distribution to a normal distribution:
>>> pt = preprocessing.PowerTransformer(method='box-cox', standardize=False) >>> X_lognormal = np.random.RandomState(616).lognormal(size=(3, 3)) >>> X_lognormal array([[1.28..., 1.18..., 0.84...], [0.94..., 1.60..., 0.38...], [1.35..., 0.21..., 1.09...]]) >>> pt.fit_transform(X_lognormal) array([[ 0.49..., 0.17..., -0.15...], [-0.05..., 0.58..., -0.57...], [ 0.69..., -0.84..., 0.10...]])
While the above example sets the
standardize option to
PowerTransformer will apply zero-mean, unit-variance normalization to the transformed output by default.
Below are examples of Box-Cox and Yeo-Johnson applied to various probability distributions. Note that when applied to certain distributions, the power transforms achieve very Gaussian-like results, but with others, they are ineffective. This highlights the importance of visualizing the data before and after transformation.
It is also possible to map data to a normal distribution using
QuantileTransformer by setting
output_distribution='normal'. Using the earlier example with the iris dataset:
>>> quantile_transformer = preprocessing.QuantileTransformer( ... output_distribution='normal', random_state=0) >>> X_trans = quantile_transformer.fit_transform(X) >>> quantile_transformer.quantiles_ array([[4.3..., 2..., 1..., 0.1...], [4.31..., 2.02..., 1.01..., 0.1...], [4.32..., 2.05..., 1.02..., 0.1...], ..., [7.84..., 4.34..., 6.84..., 2.5...], [7.87..., 4.37..., 6.87..., 2.5...], [7.9..., 4.4..., 6.9..., 2.5...]])
Thus the median of the input becomes the mean of the output, centered at 0. The normal output is clipped so that the input’s minimum and maximum — corresponding to the 1e-7 and 1 - 1e-7 quantiles respectively — do not become infinite under the transformation.
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.
normalize provides a quick and easy way to perform this operation on a single array-like dataset, either using the
>>> X = [[ 1., -1., 2.], ... [ 2., 0., 0.], ... [ 0., 1., -1.]] >>> X_normalized = preprocessing.normalize(X, norm='l2') >>> X_normalized array([[ 0.40..., -0.40..., 0.81...], [ 1. ..., 0. ..., 0. ...], [ 0. ..., 0.70..., -0.70...]])
preprocessing module further provides a utility 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
>>> 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) array([[ 0.40..., -0.40..., 0.81...], [ 1. ..., 0. ..., 0. ...], [ 0. ..., 0.70..., -0.70...]]) >>> normalizer.transform([[-1., 1., 0.]]) array([[-0.70..., 0.70..., 0. ...]])
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.
Often features are not given as continuous values but categorical. For example a person could have features
["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].
To convert categorical features to such integer codes, we can use the
OrdinalEncoder. This estimator transforms each categorical feature to one new feature of integers (0 to n_categories - 1):
>>> enc = preprocessing.OrdinalEncoder() >>> X = [['male', 'from US', 'uses Safari'], ['female', 'from Europe', 'uses Firefox']] >>> enc.fit(X) OrdinalEncoder(categories='auto', dtype=<... 'numpy.float64'>) >>> enc.transform([['female', 'from US', 'uses Safari']]) array([[0., 1., 1.]])
Such integer representation can, however, not be used directly with all 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).
Another possibility to convert categorical features to features that can be used with scikit-learn estimators is to use a one-of-K, also known as one-hot or dummy encoding. This type of encoding can be obtained with the
OneHotEncoder, which transforms each categorical feature with
n_categories possible values into
n_categories binary features, with one of them 1, and all others 0.
Continuing the example above:
>>> enc = preprocessing.OneHotEncoder() >>> X = [['male', 'from US', 'uses Safari'], ['female', 'from Europe', 'uses Firefox']] >>> enc.fit(X) OneHotEncoder(categorical_features=None, categories=None, dtype=<... 'numpy.float64'>, handle_unknown='error', n_values=None, sparse=True) >>> enc.transform([['female', 'from US', 'uses Safari'], ... ['male', 'from Europe', 'uses Safari']]).toarray() array([[1., 0., 0., 1., 0., 1.], [0., 1., 1., 0., 0., 1.]])
By default, the values each feature can take is inferred automatically from the dataset and can be found in the
>>> enc.categories_ [array(['female', 'male'], dtype=object), array(['from Europe', 'from US'], dtype=object), array(['uses Firefox', 'uses Safari'], dtype=object)]
It is possible to specify this explicitly using the parameter
categories. There are two genders, four possible continents and four web browsers in our dataset:
>>> genders = ['female', 'male'] >>> locations = ['from Africa', 'from Asia', 'from Europe', 'from US'] >>> browsers = ['uses Chrome', 'uses Firefox', 'uses IE', 'uses Safari'] >>> enc = preprocessing.OneHotEncoder(categories=[genders, locations, browsers]) >>> # Note that for there are missing categorical values for the 2nd and 3rd >>> # feature >>> X = [['male', 'from US', 'uses Safari'], ['female', 'from Europe', 'uses Firefox']] >>> enc.fit(X) OneHotEncoder(categorical_features=None, categories=[...], dtype=<... 'numpy.float64'>, handle_unknown='error', n_values=None, sparse=True) >>> enc.transform([['female', 'from Asia', 'uses Chrome']]).toarray() array([[1., 0., 0., 1., 0., 0., 1., 0., 0., 0.]])
If there is a possibility that the training data might have missing categorical features, it can often be better to specify
handle_unknown='ignore' instead of setting the
categories manually as above. When
handle_unknown='ignore' is specified and unknown categories are encountered during transform, no error will be raised but the resulting one-hot encoded columns for this feature will be all zeros (
handle_unknown='ignore' is only supported for one-hot encoding):
>>> enc = preprocessing.OneHotEncoder(handle_unknown='ignore') >>> X = [['male', 'from US', 'uses Safari'], ['female', 'from Europe', 'uses Firefox']] >>> enc.fit(X) OneHotEncoder(categorical_features=None, categories=None, dtype=<... 'numpy.float64'>, handle_unknown='ignore', n_values=None, sparse=True) >>> enc.transform([['female', 'from Asia', 'uses Chrome']]).toarray() array([[1., 0., 0., 0., 0., 0.]])
See Loading features from dicts for categorical features that are represented as a dict, not as scalars.
Discretization (otherwise known as quantization or binning) provides a way to partition continuous features into discrete values. Certain datasets with continuous features may benefit from discretization, because discretization can transform the dataset of continuous attributes to one with only nominal attributes.
KBinsDiscretizer discretizers features into
k equal width bins:
>>> X = np.array([[ -3., 5., 15 ], ... [ 0., 6., 14 ], ... [ 6., 3., 11 ]]) >>> est = preprocessing.KBinsDiscretizer(n_bins=[3, 2, 2], encode='ordinal').fit(X)
By default the output is one-hot encoded into a sparse matrix (See Encoding categorical features) and this can be configured with the
encode parameter. For each feature, the bin edges are computed during
fit and together with the number of bins, they will define the intervals. Therefore, for the current example, these intervals are defined as:
Based on these bin intervals,
X is transformed as follows:
>>> est.transform(X) array([[ 0., 1., 1.], [ 1., 1., 1.], [ 2., 0., 0.]])
The resulting dataset contains ordinal attributes which can be further used in a
Discretization is similar to constructing histograms for continuous data. However, histograms focus on counting features which fall into particular bins, whereas discretization focuses on assigning feature values to these bins.
KBinsDiscretizer implements different binning strategies, which can be selected with the
strategy parameter. The ‘uniform’ strategy uses constant-width bins. The ‘quantile’ strategy uses the quantiles values to have equally populated bins in each feature. The ‘kmeans’ strategy defines bins based on a k-means clustering procedure performed on each feature independently.
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
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.
>>> 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.]])
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.
Tools for imputing missing values are discussed at Imputation of missing values.
Often it’s useful to add complexity to the model by considering nonlinear features of the input data. A simple and common method to use is polynomial features, which can get features’ high-order and interaction terms. It is implemented in
>>> 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.]])
The features of X have been transformed from \((X_1, X_2)\) to \((1, X_1, X_2, X_1^2, X_1X_2, X_2^2)\).
In some cases, only interaction terms among features are required, and it can be gotten with the setting
>>> X = np.arange(9).reshape(3, 3) >>> X array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> poly = PolynomialFeatures(degree=3, interaction_only=True) >>> poly.fit_transform(X) array([[ 1., 0., 1., 2., 0., 0., 2., 0.], [ 1., 3., 4., 5., 12., 15., 20., 60.], [ 1., 6., 7., 8., 42., 48., 56., 336.]])
The features of X have been transformed from \((X_1, X_2, X_3)\) to \((1, X_1, X_2, X_3, X_1X_2, X_1X_3, X_2X_3, X_1X_2X_3)\).
See Polynomial interpolation for Ridge regression using created polynomial features.
Often, you will want to convert an existing Python function into a transformer to assist in data cleaning or processing. You can implement a transformer from an arbitrary function with
FunctionTransformer. For example, to build a transformer that applies a log transformation in a pipeline, do:
>>> import numpy as np >>> from sklearn.preprocessing import FunctionTransformer >>> transformer = FunctionTransformer(np.log1p, validate=True) >>> X = np.array([[0, 1], [2, 3]]) >>> transformer.transform(X) array([[0. , 0.69314718], [1.09861229, 1.38629436]])
You can ensure that
inverse_func are the inverse of each other by setting
check_inverse=True and calling
transform. Please note that a warning is raised and can be turned into an error with a
>>> import warnings >>> warnings.filterwarnings("error", message=".*check_inverse*.", ... category=UserWarning, append=False)
© 2007–2018 The scikit-learn developers
Licensed under the 3-clause BSD License.