7. Preprocessing data

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.

7.1. Standardization or Mean Removal and Variance Scaling

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 scale provides a quick and easy way to perform this operation on a single array-like dataset:

>>> from sklearn import preprocessing
>>> X = [[ 1., -1.,  2.],
...      [ 2.,  0.,  0.],
...      [ 0.,  1., -1.]]
>>> X_scaled = preprocessing.scale(X)

>>> 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.])

The preprocessing module further provides a utility class Scaler 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 sklearn.pipeline.Pipeline:

>>> scaler = preprocessing.Scaler().fit(X)
>>> scaler
Scaler(copy=True, with_mean=True, with_std=True)

>>> scaler.mean_                                      
array([ 1. ...,  0. ...,  0.33...])

>>> scaler.std_                                       
array([ 0.81...,  0.81...,  1.24...])

>>> scaler.transform(X)                               
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.]])                
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 Scaler.

References:

Further discussion on the importance of centering and scaling data is available on this FAQ: Should I normalize/standardize/rescale the data?

Notes

It is sometimes not enough to center and scale the features independently since downstream model can further make assumption on the linear independence of the features.

To address this issue you can use sklearn.decomposition.PCA or sklearn.decomposition.RandomizedPCA with whiten=True to further remove the linear correlation across features.

Also note that the current implementation of scale and Scaler do not yet work with scipy.sparse matrices.

7.2. Normalization

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 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                                      
array([[ 0.40..., -0.40...,  0.81...],
       [ 1.  ...,  0.  ...,  0.  ...],
       [ 0.  ...,  0.70..., -0.70...]])

The 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 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)                            
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.  ...]])

Notes

normalize and 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.

7.3. Binarization

7.3.1. Feature binarization

Feature binarization is the process of thresholding numerical features to get boolean values. This can be useful for downsteam 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 most common class of (Restricted) Boltzmann Machines (not yet implemented in the scikit).

It is also commmon 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 Normalizer, the utility class Binarizer is meant to be used in the early stages of 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 Scaler and Normalizer classes, the preprocessing module provides a companion function binarize to be used when the transformer API is not necessary.

Notes

binarize and 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.