Fisher's Linear Discriminant Analysis for data compression. More...
#include <shark/Algorithms/Trainers/FisherLDA.h>
Inheritance diagram for shark::FisherLDA:
Public Member Functions | |
| SHARK_EXPORT_SYMBOL | FisherLDA (bool whitening=false, std::size_t subspaceDimension=0) |
| Constructor. More... | |
| std::string | name () const |
| From INameable: return the class name. More... | |
| void | setSubspaceDimensions (std::size_t dimensions) |
| std::size_t | subspaceDimensions () const |
| bool | whitening () const |
| check whether whitening mode is on More... | |
| void | setWhitening (bool newWhitening) |
| if active, the model whitenes the inputs More... | |
| SHARK_EXPORT_SYMBOL void | train (LinearModel<> &model, LabeledData< RealVector, unsigned int > const &dataset) |
| Compute the FisherLDA solution for a multi-class problem. More... | |
| Public Member Functions inherited from shark::AbstractTrainer< LinearModel<>, unsigned int > | |
| virtual void | train (ModelType &model, DatasetType const &dataset)=0 |
| Core of the Trainer interface. 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 () | |
Protected Member Functions | |
| SHARK_EXPORT_SYMBOL void | meanAndScatter (LabeledData< RealVector, unsigned int > const &dataset, RealVector &mean, RealMatrix &scatter) |
Protected Attributes | |
| bool | m_whitening |
| std::size_t | m_subspaceDimensions |
Additional Inherited Members | |
| Public Types inherited from shark::AbstractTrainer< LinearModel<>, unsigned int > | |
| typedef LinearModel<> | ModelType |
| typedef ModelType::InputType | InputType |
| typedef unsigned int | LabelType |
| typedef LabeledData< InputType, LabelType > | DatasetType |
Detailed Description
Fisher's Linear Discriminant Analysis for data compression.
Similar to PCA, Fisher's Linear Discriminant Analysis is a method for reducing the datas dimensionality. In contrast to PCA it also uses class information.
Consider the data's covariance matrix \( S \) and a unit vector \( u \) which defines a one-dimensional subspace of the data. Then, PCA would maximmize the objective \( J(u) = u^T S u \), namely the datas variance in the subspace. Fisher-LDA, however, maximizes
\[ J(u) = ( u^T S_W u )^{-1} ( u^T S_B u ), \]
where \( S_B \) is the covariance matrix of the class-means and \( S_W \) is the average covariance matrix of all classes (in both cases, each class' influence is weighted by it's size). As a result, Fisher-LDA finds a subspace in which the class means are wide-spread while (in average) the variance of each class becomes small. This leads to good lower-dimensional representations of the data in cases where the classes are linearly separable.
If a subspace with more than one dimension is requested, the above step is executed consecutively to find the next optimal subspace-dimension orthogonally to the others.
Note: the max. dimensionality for the subspace is #NumOfClasses-1.
It is possible to choose how many dimnsions are used by setting the appropriate value by calling setSubspaceDImension or in the constructor. Also optionally whitening can be applied. For more detailed information about Fisher-LDA, see Bishop, Pattern Recognition and Machine Learning.
Definition at line 79 of file FisherLDA.h.
Constructor & Destructor Documentation
◆ FisherLDA()
| SHARK_EXPORT_SYMBOL shark::FisherLDA::FisherLDA | ( | bool | whitening = false, |
| std::size_t | subspaceDimension = 0 |
||
| ) |
Constructor.
Member Function Documentation
◆ meanAndScatter()
|
protected |
Referenced by setWhitening().
◆ name()
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inlinevirtual |
From INameable: return the class name.
Reimplemented from shark::INameable.
Definition at line 86 of file FisherLDA.h.
◆ setSubspaceDimensions()
|
inline |
Definition at line 89 of file FisherLDA.h.
References m_subspaceDimensions.
◆ setWhitening()
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inline |
if active, the model whitenes the inputs
Definition at line 103 of file FisherLDA.h.
References m_whitening, shark::mean(), meanAndScatter(), SHARK_EXPORT_SYMBOL, and train().
◆ subspaceDimensions()
|
inline |
Definition at line 93 of file FisherLDA.h.
References m_subspaceDimensions.
◆ train()
| SHARK_EXPORT_SYMBOL void shark::FisherLDA::train | ( | LinearModel<> & | model, |
| LabeledData< RealVector, unsigned int > const & | dataset | ||
| ) |
Compute the FisherLDA solution for a multi-class problem.
Referenced by setWhitening().
◆ whitening()
|
inline |
check whether whitening mode is on
Definition at line 98 of file FisherLDA.h.
References m_whitening.
Member Data Documentation
◆ m_subspaceDimensions
|
protected |
Definition at line 113 of file FisherLDA.h.
Referenced by setSubspaceDimensions(), and subspaceDimensions().
◆ m_whitening
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protected |
Definition at line 112 of file FisherLDA.h.
Referenced by setWhitening(), and whitening().
The documentation for this class was generated from the following file:
- include/shark/Algorithms/Trainers/FisherLDA.h