docs/libs/ml/polynomial_features.md

---
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htmlTitle: FlinkML - Polynomial Features
title: <a href="../ml">FlinkML</a> - Polynomial Features
---
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* This will be replaced by the TOC
{:toc}

## Description

The polynomial features transformer maps a vector into the polynomial feature space of degree $d$.
The dimension of the input vector determines the number of polynomial factors whose values are the respective vector entries.
Given a vector $(x, y, z, \ldots)^T$ the resulting feature vector looks like:

$$\left(x, y, z, x^2, xy, y^2, yz, z^2, x^3, x^2y, x^2z, xy^2, xyz, xz^2, y^3, \ldots\right)^T$$

Flink's implementation orders the polynomials in decreasing order of their degree.

Given the vector $\left(3,2\right)^T$, the polynomial features vector of degree 3 would look like
 
 $$\left(3^3, 3^2\cdot2, 3\cdot2^2, 2^3, 3^2, 3\cdot2, 2^2, 3, 2\right)^T$$

This transformer can be prepended to all `Transformer` and `Predictor` implementations which expect an input of type `LabeledVector` or any sub-type of `Vector`.

## Operations

`PolynomialFeatures` is a `Transformer`.
As such, it supports the `fit` and `transform` operation.

### Fit

PolynomialFeatures is not trained on data and, thus, supports all types of input data.

### Transform

PolynomialFeatures transforms all subtypes of `Vector` and `LabeledVector` into their respective types: 

* `transform[T <: Vector]: DataSet[T] => DataSet[T]`
* `transform: DataSet[LabeledVector] => DataSet[LabeledVector]`

## Parameters

The polynomial features transformer can be controlled by the following parameters:

<table class="table table-bordered">
    <thead>
      <tr>
        <th class="text-left" style="width: 20%">Parameters</th>
        <th class="text-center">Description</th>
      </tr>
    </thead>

    <tbody>
      <tr>
        <td><strong>Degree</strong></td>
        <td>
          <p>
            The maximum polynomial degree. 
            (Default value: <strong>10</strong>)
          </p>
        </td>
      </tr>
    </tbody>
  </table>

## Examples

{% highlight scala %}
// Obtain the training data set
val trainingDS: DataSet[LabeledVector] = ...

// Setup polynomial feature transformer of degree 3
val polyFeatures = PolynomialFeatures()
.setDegree(3)

// Setup the multiple linear regression learner
val mlr = MultipleLinearRegression()

// Control the learner via the parameter map
val parameters = ParameterMap()
.add(MultipleLinearRegression.Iterations, 20)
.add(MultipleLinearRegression.Stepsize, 0.5)

// Create pipeline PolynomialFeatures -> MultipleLinearRegression
val pipeline = polyFeatures.chainPredictor(mlr)

// train the model
pipeline.fit(trainingDS)
{% endhighlight %}