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CLDA Class Reference

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:
Inheritance graph
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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_tget_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 CLabelsapply ()
virtual CLabelsapply (CFeatures *data)
virtual float64_t apply (int32_t vec_idx)
 get output for example "vec_idx"
virtual CDotFeaturesget_features ()
- Public Member Functions inherited from CMachine
 CMachine ()
virtual ~CMachine ()
virtual bool train (CFeatures *data=NULL)
virtual void set_labels (CLabels *lab)
virtual CLabelsget_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)
SGIOget_global_io ()
void set_global_parallel (Parallel *parallel)
Parallelget_global_parallel ()
void set_global_version (Version *version)
Versionget_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_tw
float64_t bias
CDotFeaturesfeatures
- Protected Attributes inherited from CMachine
float64_t max_train_time
CLabelslabels
ESolverType solver_type
bool m_store_model_features

Additional Inherited Members

- Public Attributes inherited from CSGObject
SGIOio
Parallelparallel
Versionversion
Parameterm_parameters
Parameterm_model_selection_parameters

Constructor & Destructor Documentation

CLDA ( float64_t  gamma = 0)

constructor

Parameters
gammagamma

Definition at line 23 of file LDA.cpp.

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

constructor

Parameters
gammagamma
traindattraining features
trainlablabels 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
featfeatures to set

Reimplemented from CLinearMachine.

Definition at line 101 of file LDA.h.

void set_gamma ( float64_t  gamma)

set gamme

Parameters
gammathe new gamma

Definition at line 74 of file LDA.h.

bool train_machine ( CFeatures data = NULL)
protectedvirtual

train LDA classifier

Parameters
datatraining 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:

SHOGUN Machine Learning Toolbox - Documentation