# PolynomialExtender¶

Polynomial feature extender.

Generate features consisting of all polynomial combinations of the features with degree less than or equal to the specified degree.

Be aware that the number of outputted features scales polynomially in the number of input features and exponentially in the degree. High degrees can cause overfitting.

## Parameters¶

• degree – defaults to 2

The maximum degree of the polynomial features.

• interaction_only – defaults to False

If True then only combinations that include an element at most once will be computed.

• include_bias – defaults to False

Whether or not to include a dummy feature which is always equal to 1.

• bias_name – defaults to bias

Name to give to the bias feature.

## Examples¶

>>> from river import feature_extraction as fx

>>> X = [
...     {'x': 0, 'y': 1},
...     {'x': 2, 'y': 3},
...     {'x': 4, 'y': 5}
... ]

>>> poly = fx.PolynomialExtender(degree=2, include_bias=True)
>>> for x in X:
...     print(poly.transform_one(x))
{'x': 0, 'y': 1, 'x*x': 0, 'x*y': 0, 'y*y': 1, 'bias': 1}
{'x': 2, 'y': 3, 'x*x': 4, 'x*y': 6, 'y*y': 9, 'bias': 1}
{'x': 4, 'y': 5, 'x*x': 16, 'x*y': 20, 'y*y': 25, 'bias': 1}

>>> X = [
...     {'x': 0, 'y': 1, 'z': 2},
...     {'x': 2, 'y': 3, 'z': 2},
...     {'x': 4, 'y': 5, 'z': 2}
... ]

>>> poly = fx.PolynomialExtender(degree=3, interaction_only=True)
>>> for x in X:
...     print(poly.transform_one(x))
{'x': 0, 'y': 1, 'z': 2, 'x*y': 0, 'x*z': 0, 'y*z': 2, 'x*y*z': 0}
{'x': 2, 'y': 3, 'z': 2, 'x*y': 6, 'x*z': 4, 'y*z': 6, 'x*y*z': 12}
{'x': 4, 'y': 5, 'z': 2, 'x*y': 20, 'x*z': 8, 'y*z': 10, 'x*y*z': 40}


Polynomial features are typically used for a linear model to capture interactions between features. This may done by setting up a pipeline, as so:

>>> from river import datasets
>>> from river import evaluate
>>> from river import linear_model as lm
>>> from river import metrics
>>> from river import preprocessing as pp

>>> dataset = datasets.Phishing()

>>> model = (
...     fx.PolynomialExtender() |
...     pp.StandardScaler() |
...     lm.LogisticRegression()
... )

>>> metric = metrics.Accuracy()

>>> evaluate.progressive_val_score(dataset, model, metric)
Accuracy: 88.88%


## Methods¶

learn_one

Update with a set of features x.

A lot of transformers don't actually have to do anything during the learn_one step because they are stateless. For this reason the default behavior of this function is to do nothing. Transformers that however do something during the learn_one can override this method.

Parameters

• x (dict)

Returns

Transformer: self

transform_one

Transform a set of features x.

Parameters

• x (dict)

Returns

dict: The transformed values.