Detailed Description

Class LDA implements regularized Linear Discriminant Analysis.

LDA learns a linear classifier and requires examples to be CSimpleFeatures. The learned linear classification rule is optimal under the assumption that both classes a gaussian distributed with equal co-variance. To find a linear separation ${\bf w}$ in training, the in-between class variance is maximized and the within class variance is minimized, i.e.

$J({\bf w})=\frac{{\bf w^T} S_B {\bf w}}{{\bf w^T} S_W {\bf w}}$

is maximized, where

$S_b := ({\bf m_{+1}} - {\bf m_{-1}})({\bf m_{+1}} - {\bf m_{-1}})^T$

is the between class scatter matrix and

$S_w := \sum_{c\in\{-1,+1\}}\sum_{{\bf x}\in X_{c}}({\bf x} - {\bf m_c})({\bf x} - {\bf m_c})^T$

is the within class scatter matrix with mean ${\bf m_c} := \frac{1}{N}\sum_{j=1}^N {\bf x_j^c}$ and $X_c:=\{x_1^c, \dots, x_N^c\}$ the set of examples of class c.

LDA is very fast for low-dimensional samples. The regularization parameter $\gamma$ (especially useful in the low sample case) should be tuned in cross-validation.

See Also: CLinearMachine; http://en.wikipedia.org/wiki/Linear_discriminant_analysis

Definition at line 52 of file LDA.h.

Inheritance diagram for CLDA:

[legend]

Public Member Functions
	CLDA (float64_t gamma=0)
	CLDA (float64_t gamma, CSimpleFeatures< float64_t > traindat, CLabels trainlab)
virtual	~CLDA ()
void	set_gamma (float64_t gamma)
float64_t	get_gamma ()
virtual EClassifierType	get_classifier_type ()
virtual void	set_features (CDotFeatures *feat)
virtual const char *	get_name () const
Public Member Functions inherited from CLinearMachine
	CLinearMachine ()
virtual	~CLinearMachine ()
void	get_w (float64_t *&dst_w, int32_t &dst_dims)
SGVector< float64_t >	get_w ()
void	set_w (SGVector< float64_t > src_w)
void	set_bias (float64_t b)
float64_t	get_bias ()
virtual bool	load (FILE *srcfile)
virtual bool	save (FILE *dstfile)
virtual CLabels *	apply ()
virtual CLabels *	apply (CFeatures *data)
virtual float64_t	apply (int32_t vec_idx)
	get output for example "vec_idx"
virtual CDotFeatures *	get_features ()
Public Member Functions inherited from CMachine
	CMachine ()
virtual	~CMachine ()
virtual bool	train (CFeatures *data=NULL)
virtual void	set_labels (CLabels *lab)
virtual CLabels *	get_labels ()
virtual float64_t	get_label (int32_t i)
void	set_max_train_time (float64_t t)
float64_t	get_max_train_time ()
void	set_solver_type (ESolverType st)
ESolverType	get_solver_type ()
virtual void	set_store_model_features (bool store_model)
Public Member Functions inherited from CSGObject
	CSGObject ()
	CSGObject (const CSGObject &orig)
virtual	~CSGObject ()
virtual bool	is_generic (EPrimitiveType *generic) const
template<class T >
void	set_generic ()
void	unset_generic ()
virtual void	print_serializable (const char *prefix="")
virtual bool	save_serializable (CSerializableFile file, const char prefix="")
virtual bool	load_serializable (CSerializableFile file, const char prefix="")
void	set_global_io (SGIO *io)
SGIO *	get_global_io ()
void	set_global_parallel (Parallel *parallel)
Parallel *	get_global_parallel ()
void	set_global_version (Version *version)
Version *	get_global_version ()
SGVector< char * >	get_modelsel_names ()
char *	get_modsel_param_descr (const char *param_name)
index_t	get_modsel_param_index (const char *param_name)

Protected Member Functions
virtual bool	train_machine (CFeatures *data=NULL)
Protected Member Functions inherited from CLinearMachine
virtual void	store_model_features ()

Protected Attributes
float64_t	m_gamma
Protected Attributes inherited from CLinearMachine
int32_t	w_dim
float64_t *	w
float64_t	bias
CDotFeatures *	features
Protected Attributes inherited from CMachine
float64_t	max_train_time
CLabels *	labels
ESolverType	solver_type
bool	m_store_model_features

Additional Inherited Members
Public Attributes inherited from CSGObject
SGIO *	io
Parallel *	parallel
Version *	version
Parameter *	m_parameters
Parameter *	m_model_selection_parameters

Constructor & Destructor Documentation

CLDA ( float64_t gamma = 0 )

constructor

Parameters

gamma gamma

Definition at line 23 of file LDA.cpp.

CLDA	(	float64_t	gamma,
		CSimpleFeatures< float64_t > *	traindat,
		CLabels *	trainlab
	)

constructor

Parameters

gamma	gamma
traindat	training features
trainlab	labels for training features

Definition at line 28 of file LDA.cpp.

~CLDA ( )

virtual

Definition at line 36 of file LDA.cpp.

Member Function Documentation

virtual EClassifierType get_classifier_type ( )

virtual

get classifier type

Returns: classifier type LDA

Reimplemented from CMachine.

Definition at line 92 of file LDA.h.

float64_t get_gamma ( )

get gamma

Returns: gamma

Definition at line 83 of file LDA.h.

virtual const char* get_name ( ) const

virtual

Returns: object name

Reimplemented from CLinearMachine.

Definition at line 111 of file LDA.h.

virtual void set_features ( CDotFeatures * feat )

virtual

set features

Parameters

feat	features to set

Reimplemented from CLinearMachine.

Definition at line 101 of file LDA.h.

void set_gamma ( float64_t gamma )

set gamme

Parameters

gamma the new gamma

Definition at line 74 of file LDA.h.

bool train_machine ( CFeatures * data = NULL )

protectedvirtual

train LDA classifier

Parameters

data	training data (parameter can be avoided if distance or kernel-based classifiers are used and distance/kernels are initialized with train data)

Returns: whether training was successful

Reimplemented from CMachine.

Definition at line 40 of file LDA.cpp.

Member Data Documentation

float64_t m_gamma

protected

gamma

Definition at line 126 of file LDA.h.

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

Detailed Description

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation