Polynominal Expansion
===========

Perform feature expansion in a polynomial space

Input
--------------
It takes in a DataFrame and transforms it to another DataFrame

Output
--------------
The output DataFrame contains a new column of type vector, Expanding your features into a polynomial space, which is formulated by an n-degree combination of original dimensions.

Type
--------- 

ml-transformer

Class
--------- 

fire.nodes.ml.NodePolynominalExpansion

Fields
--------- 

.. list-table::
      :widths: 10 5 10
      :header-rows: 1

      * - Name
        - Title
        - Description
      * - inputCol
        - Input Column
        - The input column name
      * - outputCol
        - Output Column
        - The output column name
      * - degree
        - Degree
        - The polynomial degree to expand, which should be >= 1. A value of 1 means no expansion.


Details
-------
Polynominal Expansion Node Details
+++++++++++++++


The Polynomial expansion Node helps in the process of expanding your features into a polynomial space, which is formulated by an n-degree combination of original dimensions.


For example, if a dataset had one input feature X, then a polynomial feature would be the addition of a new feature (column) where values were calculated by squaring the values in X, e.g. X^2. This process can be repeated for each input variable in the dataset, creating a transformed version of each.



Input Parameters
+++++++++++++++


* OUTPUT STORAGE LEVEL : Keep this as DEFAULT.
* INPUT COLUMN : Select the required vector column from the list of input schema fields.
* OUTPUT COLUMN : Set a name for the output column.
* DEGREE : The polynomial degree to expand, which should be greater than or equal to 1.  A value of 1 means no  expansion. Default : 2.


Examples
-------
Polynominal Expansion Node Example
+++++++++++++++


Consider the below dataset which contains a vector field **features**


::

    |features  |
    |:--------:|
    |[2.0,1.0] |
    |[3.0,-1.0]|


On applying the **Polynominal Expansion Node** to the input  column of **features** with a **degree** of 3, we get the below output dataframe with the output vector column of **polyFeatures**.


::

    |features  |          polyFeatures                    |
    |:--------:|:----------------------------------------:|
    |[2.0,1.0] |[2.0,4.0,8.0,1.0,2.0,4.0,1.0,2.0,1.0]     |
    |[3.0,-1.0]|[3.0,9.0,27.0,-1.0,-3.0,-9.0,1.0,3.0,-1.0]|