cmp::scaler::StandardScaler Class Reference

Standardizes features by removing the mean and scaling to unit variance using Cholesky decomposition. More...

#include <scaler.h>

Inheritance diagram for cmp::scaler::StandardScaler:

Collaboration diagram for cmp::scaler::StandardScaler:

Public Member Functions
	StandardScaler ()=default
	Default constructor.
	StandardScaler (const Eigen::Ref< const Eigen::VectorXd > &mean, const Eigen::Ref< const Eigen::MatrixXd > &scale)
	Constructs a StandardScaler with a pre-computed mean and covariance scale.
	StandardScaler (const StandardScaler &other)=default
	StandardScaler (StandardScaler &&other)=default
	~StandardScaler ()=default
StandardScaler &	operator= (const StandardScaler &other)=default
StandardScaler &	operator= (StandardScaler &&other)=default
Eigen::VectorXd	transform (const Eigen::Ref< const Eigen::VectorXd > &data) const override
	Transforms the input data from physical space to the scaled latent space.
Eigen::VectorXd	inverseTransform (const Eigen::Ref< const Eigen::VectorXd > &data) const override
	Reconstructs the data from the scaled latent space back to physical space.
Eigen::VectorXd	getIntercept () const override
	Retrieves the intercept vector \( \mu \) used in the transformation.
Eigen::MatrixXd	getScale () const override
	Retrieves the scaling matrix \( S \) used in the transformation.
void	fit (const Eigen::Ref< const Eigen::MatrixXd > &data) override
	Learns the scaling parameters (e.g., mean, variance) from the training data.
Eigen::MatrixXd	fit_transform (const Eigen::Ref< const Eigen::MatrixXd > &data) override
	Fits the scaling parameters to the data and subsequently transforms the data.

Private Attributes
Eigen::VectorXd	mean_
	The empirical mean vector \( \mu \) of the training dataset.
Eigen::LLT< Eigen::MatrixXd >	lltDecomposition_
	The LLT (Cholesky) decomposition of the covariance matrix \( \Sigma \).

Detailed Description

Standardizes features by removing the mean and scaling to unit variance using Cholesky decomposition.

Mathematical Formulation

Given data matrix \( X \in \mathbb{R}^{n \times d} \), let \( \mu \in \mathbb{R}^d \) be the column-wise mean and \( \Sigma \in \mathbb{R}^{d \times d} \) be the covariance matrix. We decompose the covariance matrix via the lower Cholesky factor \( L \) such that:

\[ \Sigma = L L^T \]

The transformation maps:

\[ y = L^{-1}(x - \mu) \]

The inverse transformation maps:

\[ x = L y + \mu \]

• ### Implementation Algorithm

1. Fit: Calculate mean vector \( \mu \) and covariance matrix \( \Sigma \) of \( X \), then perform Cholesky LLT decomposition to obtain \( L \).
2. Transform: Solve the lower triangular system \( L y = x - \mu \) to compute standardized data.
3. Inverse Transform: Compute \( L y + \mu \) via matrix multiplication and vector addition.

Constructor & Destructor Documentation

StandardScaler() [1/4]

cmp::scaler::StandardScaler::StandardScaler ( )

default

Default constructor.

StandardScaler() [2/4]

cmp::scaler::StandardScaler::StandardScaler ( const Eigen::Ref< const Eigen::VectorXd > &  mean, const Eigen::Ref< const Eigen::MatrixXd > &  scale  )

inline

Constructs a StandardScaler with a pre-computed mean and covariance scale.

Parameters

mean	Pre-computed mean vector \( \mu \).
scale	Pre-computed covariance matrix \( \Sigma \) (will be decomposed internally).

StandardScaler() [3/4]

cmp::scaler::StandardScaler::StandardScaler ( const StandardScaler &  other )

default

StandardScaler() [4/4]

cmp::scaler::StandardScaler::StandardScaler ( StandardScaler &&  other )

default

~StandardScaler()

cmp::scaler::StandardScaler::~StandardScaler ( )

default

Member Function Documentation

fit()

void cmp::scaler::StandardScaler::fit ( const Eigen::Ref< const Eigen::MatrixXd > &  data )

overridevirtual

Learns the scaling parameters (e.g., mean, variance) from the training data.

Parameters

data	A matrix \( X \in \mathbb{R}^{n \times d} \) of training samples.

Implements cmp::scaler::Scaler.

fit_transform()

Eigen::MatrixXd cmp::scaler::StandardScaler::fit_transform ( const Eigen::Ref< const Eigen::MatrixXd > &  data )

overridevirtual

Fits the scaling parameters to the data and subsequently transforms the data.

Parameters

data	A matrix \( X \in \mathbb{R}^{n \times d} \) of training samples.

Returns

The transformed dataset matrix \( Y \).

Implements cmp::scaler::Scaler.

getIntercept()

Eigen::VectorXd cmp::scaler::StandardScaler::getIntercept ( ) const

inlineoverridevirtual

Retrieves the intercept vector \( \mu \) used in the transformation.

Returns

The intercept vector.

Implements cmp::scaler::Scaler.

getScale()

Eigen::MatrixXd cmp::scaler::StandardScaler::getScale ( ) const

inlineoverridevirtual

Retrieves the scaling matrix \( S \) used in the transformation.

Returns

The scaling matrix.

Implements cmp::scaler::Scaler.

inverseTransform()

Eigen::VectorXd cmp::scaler::StandardScaler::inverseTransform ( const Eigen::Ref< const Eigen::VectorXd > &  data ) const

overridevirtual

Reconstructs the data from the scaled latent space back to physical space.

Parameters

data	A column vector \( y \) in the scaled space.

Returns

The unscaled physical data vector \( x \).

Implements cmp::scaler::Scaler.

operator=() [1/2]

StandardScaler & cmp::scaler::StandardScaler::operator= ( const StandardScaler &  other )

default

operator=() [2/2]

StandardScaler & cmp::scaler::StandardScaler::operator= ( StandardScaler &&  other )

default

transform()

Eigen::VectorXd cmp::scaler::StandardScaler::transform ( const Eigen::Ref< const Eigen::VectorXd > &  data ) const

overridevirtual

Transforms the input data from physical space to the scaled latent space.

Parameters

data	A column vector \( x \) representing a single data point in physical space.

Returns

The scaled data vector \( y \).

Implements cmp::scaler::Scaler.

Member Data Documentation

lltDecomposition_

Eigen::LLT<Eigen::MatrixXd> cmp::scaler::StandardScaler::lltDecomposition_

private

The LLT (Cholesky) decomposition of the covariance matrix \( \Sigma \).

mean_

Eigen::VectorXd cmp::scaler::StandardScaler::mean_

private

The empirical mean vector \( \mu \) of the training dataset.

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The documentation for this class was generated from the following files:

• include/scaler.h
• src/scaler.cpp