# 6.1. 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.

## 6.1.1. 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?

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 `sklearn.decomposition.PCA`
or `sklearn.decomposition.RandomizedPCA` with `whiten=True`
to further remove the linear correlation across features.

Sparse input

`scale` and `Scaler` 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.

## 6.1.2. 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. ...]])
```

Sparse input

`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.

## 6.1.3. Binarization¶

### 6.1.3.1. 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.

Sparse input

`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.