MultiClassSVM Class Reference

Multi Class Support Vector Machine Model. More...

#include <Svm.h>

Inheritance diagram for MultiClassSVM:

Public Member Functions
	MultiClassSVM (KernelFunction *pKernel, unsigned int numberOfClasses, bool bOrthogonalVectors, bool bNumberOutput=true)
	Constructor.
	MultiClassSVM (KernelFunction *pKernel, Array< double > prototypes, bool bNumberOutput=true)
	Constructor.
	~MultiClassSVM ()
	Destructor.
void	SetTrainingData (const Array< double > &input, bool copy=false)
	Make the training data known to the SVM.
void	model (const Array< double > &input, Array< double > &output)
	compute the SVM prediction on data
unsigned int	model (const Array< double > &input)
	compute the SVM prediction on data
void	Normalize ()
	normalize the class-wise decision functions
KernelFunction *	getKernel ()
	return the kernel function object
const Array< double > &	getPoints ()
	return the training data points
double	getAlpha (unsigned int index, unsigned int c) const
	return the coefficient of a given example and label
double	getOffset (unsigned int c) const
	return the solution offset vector
unsigned int	getClasses () const
	return the number of classes
const ArrayReference< double >	getClassPrototype (unsigned int c) const
	return the class representing prototype vector
unsigned int	VectorToClass (const Array< double > &v)
	convert a label vector into a class index
Protected Member Functions
void	Predict (const Array< double > &input, Array< double > &output)
void	Predict (const Array< double > &input, ArrayReference< double > output)
Protected Attributes
KernelFunction *	kernel
	kernel function
bool	bOwnMemory
	true if x and y are allocated by LoadModel
const Array< double > *	x
	training data points
bool	numberOutput
	true if the SVM outputs the class label only false if the SVM outputs the value of the linear feature space function.
unsigned int	examples
	number of training data points and labels
unsigned int	classes
	number of classes
Array< double >	prototypes
	vectors associated with the classes

Detailed Description

Multi Class Support Vector Machine Model.

Author:: T. Glasmachers

Date:: 2007

The MultiClassSVM class provides a Support Vector: Machine as a parametric Model, that is, it computes a linear expansion of the kernel function with fixed training examples as one component. It can be viewed as a parametrized family of maps from the input space to the output space. In this formulation the output space is some .

In constrast to the binary classification or: regression SVM the MultiClassSVM maps inputs not to the reals but to a vector space. For each class there exists a prototype label vector in this space. The classifier predicts the class label whose prototype vector has the largest inner product to the output vector. That is, the label prototype most similar to the output vector is used for prediction.

Due to the fact that the number of classes is: always finite we use the linear kernel on the outputs without loss of generality. However, there are two concurrent standard initializations of the label prototypes: Either the standard basis of can be used, or the corners of a symmetric simplex in $R^{n-1}$ centered at the origin, which coincides with the labels $\pm 1 \in R$ of the binary case.

The parameters of this machine are organized: into one decision function per class. Therefore there exist as many parameters as there are training examples times classes. For some formulations of multi class SVMs some of these are dummy variables which are always zero. Furthermore, for most training procedures available by now the offset or bias term is set to zero.

Definition at line 374 of file Svm.h.

Constructor & Destructor Documentation

MultiClassSVM::MultiClassSVM	(	KernelFunction *	pKernel,
		unsigned int	numberOfClasses,
		bool	bOrthogonalVectors,
		bool	bNumberOutput = `true`
	)

Constructor.

Parameters:

	pKernel	input space kernel
	numberOfClasses	number of classes with indices starting from 0
	bOrthogonalVectors	true: standard basis prototypes; false: simplex prototypes
	bNumberOutput	true: output class index; false: output vector