# 4.3. 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.

## 4.3.1. 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
>>> import numpy as np
>>> X = np.array([[ 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
`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
`sklearn.pipeline.Pipeline`:

```
>>> scaler = preprocessing.StandardScaler().fit(X)
>>> scaler
StandardScaler(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 `StandardScaler`.

### 4.3.1.1. Scaling features to a range¶

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 `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_
array([ 0.5 , 0.5 , 0.33...])
>>> min_max_scaler.min_
array([ 0. , 0.5 , 0.33...])
```

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

Sparse input

`scale` and `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

`scale` and `StandardScaler` work out-of-the-box with 1d arrays.
This is very useful for scaling the target / response variables used
for regression.

### 4.3.1.2. Centering kernel matrices¶

If you have a kernel matrix of a kernel that computes a dot product
in a feature space defined by function ,
a `KernelCenterer` can transform the kernel matrix
so that it contains inner products in the feature space
defined by followed by removal of the mean in that space.

## 4.3.2. 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.

## 4.3.3. Binarization¶

### 4.3.3.1. Feature binarization¶

**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 `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 `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 `StandardScaler` 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.

## 4.3.4. Encoding categorical features¶

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 `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]])
OneHotEncoder(categorical_features='all', dtype=<... 'float'>,
handle_unknown='error', 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 *Loading features from dicts* for categorical features that are represented
as a dict, not as integers.

## 4.3.5. Imputation of missing values¶

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 `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))
[[ 4. 2. ]
[ 6. 3.666...]
[ 7. 6. ]]
```

The `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))
[[ 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.

`Imputer` can be used in a Pipeline as a way to build a composite
estimator that supports imputation. See *Imputing missing values before building an estimator*