$$ \newcommand{\R}{\mathbb{R}} \newcommand{\E}{\mathbb{E}} \newcommand{\x}{\mathbf{x}} \newcommand{\y}{\mathbf{y}} \newcommand{\wv}{\mathbf{w}} \newcommand{\av}{\mathbf{\alpha}} \newcommand{\bv}{\mathbf{b}} \newcommand{\N}{\mathbb{N}} \newcommand{\id}{\mathbf{I}} \newcommand{\ind}{\mathbf{1}} \newcommand{\0}{\mathbf{0}} \newcommand{\unit}{\mathbf{e}} \newcommand{\one}{\mathbf{1}} \newcommand{\zero}{\mathbf{0}} \newcommand\rfrac[2]{^{#1}\!/_{#2}} \newcommand{\norm}[1]{\left\lVert#1\right\rVert} $$

Standard Scaler

Description
Operations
- Fit
- Transform
Parameters
Examples

Description

The standard scaler scales the given data set, so that all features will have a user specified mean and variance. In case the user does not provide a specific mean and standard deviation, the standard scaler transforms the features of the input data set to have mean equal to 0 and standard deviation equal to 1. Given a set of input data $x_1, x_2,… x_n$, with mean:

$\bar{x} = \frac{1}{n}\sum_{i=1}^{n}x_{i}$

and standard deviation:

$\sigma_{x}=\sqrt{ \frac{1}{n} \sum_{i=1}^{n}(x_{i}-\bar{x})^{2}}$

The scaled data set $z_1, z_2,…,z_n$ will be:

$z_{i}= std \left (\frac{x_{i} - \bar{x} }{\sigma_{x}}\right ) + mean$

where $\textit{std}$ and $\textit{mean}$ are the user specified values for the standard deviation and mean.

Operations

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

Fit

StandardScaler is trained on all subtypes of Vector or LabeledVector:

fit[T <: Vector]: DataSet[T] => Unit
fit: DataSet[LabeledVector] => Unit

Transform

StandardScaler transforms all subtypes of Vector or LabeledVector into the respective type:

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

Parameters

The standard scaler implementation can be controlled by the following two parameters:

Parameters	Description
Mean	The mean of the scaled data set. (Default value: 0.0)
Std	The standard deviation of the scaled data set. (Default value: 1.0)

Examples

// Create standard scaler transformer
val scaler = StandardScaler()
.setMean(10.0)
.setStd(2.0)

// Obtain data set to be scaled
val dataSet: DataSet[Vector] = ...

// Learn the mean and standard deviation of the training data
scaler.fit(dataSet)

// Scale the provided data set to have mean=10.0 and std=2.0
val scaledDS = scaler.transform(dataSet)