Linear Discriminant Analysis (LDA) More...

#include <shark/Algorithms/Trainers/LDA.h>

Inheritance diagram for shark::LDA:

Public Member Functions
	LDA (double regularization=0.0)
	constructor More...

std::string	name () const
	From INameable: return the class name. More...

double	regularization () const
	return the regularization constant More...

void	setRegularization (double regularization)
	set the regularization constant. 0 means no regularization. More...

RealVector	parameterVector () const
	inherited from IParameterizable; read the regularization parameter More...

void	setParameterVector (RealVector const &param)
	inherited from IParameterizable; set the regularization parameter More...

size_t	numberOfParameters () const
	inherited from IParameterizable More...

SHARK_EXPORT_SYMBOL void	train (LinearClassifier<> &model, LabeledData< RealVector, unsigned int > const &dataset)
	Compute the LDA solution for a multi-class problem. More...

SHARK_EXPORT_SYMBOL void	train (LinearClassifier<> &model, WeightedLabeledData< RealVector, unsigned int > const &dataset)
	Compute the LDA solution for a weighted multi-class problem. More...

Public Member Functions inherited from shark::AbstractWeightedTrainer< LinearClassifier<>, unsigned int >
virtual void	train (ModelType &model, WeightedDatasetType const &dataset)=0
	Executes the algorithm and trains a model on the given weighted data. More...

virtual void	train (ModelType &model, DatasetType const &dataset)
	Executes the algorithm and trains a model on the given unweighted data. More...

Public Member Functions inherited from shark::INameable
virtual	~INameable ()

Public Member Functions inherited from shark::ISerializable
virtual	~ISerializable ()
	Virtual d'tor. More...

virtual void	read (InArchive &archive)
	Read the component from the supplied archive. More...

virtual void	write (OutArchive &archive) const
	Write the component to the supplied archive. More...

void	load (InArchive &archive, unsigned int version)
	Versioned loading of components, calls read(...). More...

void	save (OutArchive &archive, unsigned int version) const
	Versioned storing of components, calls write(...). More...

	BOOST_SERIALIZATION_SPLIT_MEMBER ()

Public Member Functions inherited from shark::IParameterizable<>
virtual	~IParameterizable ()

Protected Attributes
double	m_regularization

Additional Inherited Members
Public Types inherited from shark::AbstractWeightedTrainer< LinearClassifier<>, unsigned int >
typedef base_type::ModelType	ModelType

typedef base_type::InputType	InputType

typedef base_type::LabelType	LabelType

typedef base_type::DatasetType	DatasetType

typedef WeightedLabeledData< InputType, LabelType >	WeightedDatasetType

Public Types inherited from shark::AbstractTrainer< LinearClassifier<>, unsigned int >
typedef LinearClassifier<>	ModelType

typedef ModelType::InputType	InputType

typedef unsigned int	LabelType

typedef LabeledData< InputType, LabelType >	DatasetType

Public Types inherited from shark::IParameterizable<>
typedef RealVector	ParameterVectorType

Detailed Description

Linear Discriminant Analysis (LDA)

This classes implements the well known linear discriminant analysis. LDA assumes that every point is drawn from a multivariate normal distributions. Every class has its own mean but all classes have the same covariance.

An arbitrary number of classes is supported. The resulting model is of the form

\[ \arg \max_c \log(p(x|c)*P(c)) \]

where \( p(x|c) = \exp(-(x-m_c)^T(C+\alpha I)(x-m_c)) \). \( m_c\) are the means of class c, \( C \) is the covariance matrix formed by all data points. The regularization paramter \( \alpha \) is by default 0. The trainer is implemented such, that it still works when C is singular, in this case the singular directions are ignored.

Definition at line 58 of file LDA.h.