Support Vector Machines (Support Vector Machines (SVM)) More...

#include "generic.h"
#include "svmdataset.h"

Data Structures
struct	VlSvmStatistics
	SVM statistics This structure contains statistics characterising the state of the SVM solver, such as the current value of the objective function. More...

Typedefs
typedef OPAQUE	VlSvm
	SVM solver. This object implements VLFeat SVM solvers (see svm.h).

Enumerations
enum	VlSvmSolverType { VlSvmSolverNone = 0, VlSvmSolverSgd = 1, VlSvmSolverSdca }
	Type of SVM solver. More...
enum	VlSvmLossType { VlSvmLossHinge = 0, VlSvmLossHinge2 = 1, VlSvmLossL1, VlSvmLossL2, VlSvmLossLogistic }
	Type of SVM loss. More...
enum	VlSvmSolverStatus { VlSvmStatusTraining = 1, VlSvmStatusConverged, VlSvmStatusMaxNumIterationsReached }
	Solver status. More...

Functions
Create and destroy
VlSvm *	vl_svm_new (VlSvmSolverType type, double const data, vl_size dimension, vl_size numData, double const labels, double lambda)
	Create a new object with plain data.
VlSvm *	vl_svm_new_with_dataset (VlSvmSolverType type, VlSvmDataset dataset, double const labels, double lambda)
	Create a new object with a dataset.
VlSvm *	vl_svm_new_with_abstract_data (VlSvmSolverType type, void data, vl_size dimension, vl_size numData, double const labels, double lambda)
	Create a new object with abstract data.
void	vl_svm_delete (VlSvm *self)
	Delete object.
Retrieve parameters and data
VlSvmStatistics const *	vl_svm_get_statistics (VlSvm const *self)
	Get the solver statistics.
double const *	vl_svm_get_model (VlSvm const *self)
	Get the SVM model.
double	vl_svm_get_bias (VlSvm const *self)
	Get the value of the bias.
vl_size	vl_svm_get_dimension (VlSvm *self)
	Get the model dimenison.
vl_size	vl_svm_get_num_data (VlSvm *self)
	Get the number of data samples.
double	vl_svm_get_epsilon (VlSvm const *self)
	Get the convergence threshold.
double	vl_svm_get_bias_learning_rate (VlSvm const *self)
	Get the bias leraning rate.
vl_size	vl_svm_get_max_num_iterations (VlSvm const *self)
	Get the maximum number of iterations.
vl_size	vl_svm_get_diagnostic_frequency (VlSvm const *self)
	Get the diagnostic frequency.
VlSvmSolverType	vl_svm_get_solver (VlSvm const *self)
	Get the SVM solver type.
double	vl_svm_get_bias_multiplier (VlSvm const *self)
	Get the bias multiplier.
double	vl_svm_get_lambda (VlSvm const *self)
	Get the regularizer parameter lambda.
vl_size	vl_svm_get_iteration_number (VlSvm const *self)
	Get the current iteration number.
double const *	vl_svm_get_scores (VlSvm const *self)
	Get the scores of the data points.
double const *	vl_svm_get_weights (VlSvm const *self)
	Get the data weights.
Set parameters
void	vl_svm_set_epsilon (VlSvm *self, double epsilon)
	Set the convergence threshold.
void	vl_svm_set_bias_learning_rate (VlSvm *self, double rate)
	Set the bias learning rate.
void	vl_svm_set_max_num_iterations (VlSvm *self, vl_size maxNumIterations)
	Set the maximum number of iterations.
void	vl_svm_set_diagnostic_frequency (VlSvm *self, vl_size f)
	Set the diagnostic frequency.
void	vl_svm_set_bias_multiplier (VlSvm *self, double b)
	Set the bias multiplier.
void	vl_svm_set_model (VlSvm self, double const model)
	Set the SVM model.
void	vl_svm_set_bias (VlSvm *self, double b)
	Set the SVM bias.
void	vl_svm_set_iteration_number (VlSvm *self, vl_uindex n)
	Set the current iteratio number.
void	vl_svm_set_weights (VlSvm self, double const weights)
	Set the data weights.
void	vl_svm_set_diagnostic_function (VlSvm self, VlSvmDiagnosticFunction f, void data)
	Set the diagnostic function callback.
void	vl_svm_set_loss_function (VlSvm *self, VlSvmLossFunction f)
	Set the loss function callback.
void	vl_svm_set_loss_derivative_function (VlSvm *self, VlSvmLossFunction f)
	Set the loss derivative function callback.
void	vl_svm_set_conjugate_loss_function (VlSvm *self, VlSvmLossFunction f)
	Set the conjugate loss function callback.
void	vl_svm_set_dca_update_function (VlSvm *self, VlSvmDcaUpdateFunction f)
	Set the DCA update function callback.
void	vl_svm_set_data_functions (VlSvm *self, VlSvmInnerProductFunction inner, VlSvmAccumulateFunction acc)
	Set the data functions.
void	vl_svm_set_loss (VlSvm *self, VlSvmLossType loss)
	Set the loss function to one of the default types.
Process data
void	vl_svm_train (VlSvm *self)
	Run the SVM solver.
Loss functions
See also: Advanced SVM topics
double	vl_svm_hinge_loss (double label, double inner)
	SVM hinge loss.
double	vl_svm_hinge_loss_derivative (double label, double inner)
	SVM hinge loss derivative.
double	vl_svm_hinge_conjugate_loss (double label, double u)
	SVM hinge loss conjugate.
double	vl_svm_hinge_dca_update (double alpha, double inner, double norm2, double label)
	SVM hinge loss DCA update.
double	vl_svm_hinge2_loss (double label, double inner)
	SVM square hinge loss.
double	vl_svm_hinge2_loss_derivative (double label, double inner)
	SVM square hinge loss derivative.
double	vl_svm_hinge2_conjugate_loss (double label, double u)
	SVM square hinge loss conjugate.
double	vl_svm_hinge2_dca_update (double alpha, double inner, double norm2, double label)
	SVM square hinge loss DCA update.
double	vl_svm_l1_loss (double label, double inner)
	SVM l1 loss.
double	vl_svm_l1_loss_derivative (double label, double inner)
	SVM l1 loss derivative.
double	vl_svm_l1_conjugate_loss (double label, double u)
	SVM l1 loss conjugate.
double	vl_svm_l1_dca_update (double alpha, double inner, double norm2, double label)
	SVM l1 loss DCA update.
double	vl_svm_l2_loss (double label, double inner)
	SVM l2 loss.
double	vl_svm_l2_loss_derivative (double label, double inner)
	SVM l2 loss derivative.
double	vl_svm_l2_conjugate_loss (double label, double u)
	SVM l2 loss conjugate.
double	vl_svm_l2_dca_update (double alpha, double inner, double norm2, double label)
	SVM l2 loss DCA update.
double	vl_svm_logistic_loss (double label, double inner)
	SVM l2 loss.
double	vl_svm_logistic_loss_derivative (double label, double inner)
	SVM l2 loss derivative.
double	vl_svm_logistic_conjugate_loss (double label, double u)
	SVM l2 loss conjugate.
double	vl_svm_logistic_dca_update (double alpha, double inner, double norm2, double label)
	SVM l2 loss DCA update.

Detailed Description

See also:: Support Vector Machines (SVM).

Author:: Milan Sulc; Daniele Perrone; Andrea Vedaldi

Enumeration Type Documentation

enum VlSvmLossType

Default SVM loss types. The loss can be set by using vl_svm_set_loss. Note that custom losses can be used too by using vl_svm_set_loss_function, vl_svm_set_loss_derivative_function, etc.

See also:: svm-loss-functions

Enumerator:

VlSvmLossHinge	Standard hinge loss.
VlSvmLossHinge2	Hinge loss squared.
VlSvmLossL1	L1 loss.
VlSvmLossL2	L2 loss.
VlSvmLossLogistic	Logistic loss.

enum VlSvmSolverStatus

Enumerator:

VlSvmStatusTraining	Optimization in progress.
VlSvmStatusConverged	Optimization finished because the convergence criterion was met.
VlSvmStatusMaxNumIterationsReached	Optimization finished without convergence.

enum VlSvmSolverType

Enumerator:

VlSvmSolverNone	No solver (used to evaluate an SVM).
VlSvmSolverSgd	SGD algorithm (Stochastic Gradient Descent).
VlSvmSolverSdca	SDCA algorithm (Stochastic Dual Coordinate Ascent).

Function Documentation

void vl_svm_delete ( VlSvm * self )

Parameters:

self object.

See also:: vl_svm_new

double vl_svm_get_bias ( VlSvm const * self )

Parameters:

self object.

Returns:: bias \(b\).

The value of the bias returned already include the effect of bias mutliplier.

double vl_svm_get_bias_learning_rate ( VlSvm const * self )

Parameters:

self object

Returns:: bias learning rate.

double vl_svm_get_bias_multiplier ( VlSvm const * self )

Parameters:

self object.

Returns:: bias multiplier.

vl_size vl_svm_get_diagnostic_frequency ( VlSvm const * self )

Parameters:

self object.

Returns:: diagnostic frequency.

vl_size vl_svm_get_dimension ( VlSvm * self )

Parameters:

self object.

Returns:: model dimension.

This is the dimensionality of the weight vector \(\bw\).

double vl_svm_get_epsilon ( VlSvm const * self )

Parameters:

self object

Returns:: epsilon threshold.

vl_size vl_svm_get_iteration_number ( VlSvm const * self )

Parameters:

self object.

Returns:: current iteration number.

double vl_svm_get_lambda ( VlSvm const * self )

Parameters:

self object.

Returns:: diagnostic frequency.

vl_size vl_svm_get_max_num_iterations ( VlSvm const * self )

Parameters:

self object.

Returns:: maximum number of iterations.

double const* vl_svm_get_model ( VlSvm const * self )

Parameters:

self object.

Returns:: model.

This is the weight vector \(\bw\).

vl_size vl_svm_get_num_data ( VlSvm * self )

Parameters:

self object.

Returns:: model number of data samples

This is the dimensionality of the weight vector \(\bw\).

double const* vl_svm_get_scores ( VlSvm const * self )

Parameters:

self object.

Returns:: vector of scores.

After training or during the diagnostic callback, this function can be used to retrieve the scores of the points, i.e. \(\langle \bx_i, \bw \rangle + b\).

VlSvmSolverType vl_svm_get_solver ( VlSvm const * self )

Parameters:

self object.

Returns:: SVM solver type.

VlSvmStatistics const* vl_svm_get_statistics ( VlSvm const * self )

Parameters:

self object.

Returns:: statistics.

double const* vl_svm_get_weights ( VlSvm const * self )

Parameters:

self object.

Returns:: data weights.

double vl_svm_hinge2_conjugate_loss	(	double	u,
		double	label
	)

Parameters:

u	dual variable.
label	label value.

Returns:: conjugate loss.

double vl_svm_hinge2_dca_update	(	double	alpha,
		double	inner,
		double	norm2,
		double	label
	)

Parameters:

alpha	current value of the dual variable.
inner	inner product \(\bw^\top \bx\) of the sample with the SVM model.
norm2	normalization factor \(\\|\bx\\|^2/\lambda n\).
label	label \(y\) of the sample.

Returns:: incremental update \(\Delta\alpha\) of the dual variable.

See also:: Stochastic Dual Coordinate Ascent

double vl_svm_hinge2_loss	(	double	inner,
		double	label
	)

Parameters:

inner	inner product between sample and model \(\bw^\top \bx\).
label	sample label \(y\).

Returns:: value of the loss.

The interface is the same for a loss function, its derivative, or the conjugate loss.

See also:: SVM fundamentals

double vl_svm_hinge2_loss_derivative	(	double	inner,
		double	label
	)

Parameters:

inner	inner product between sample and model \(\bw^\top \bx\).
label	sample label \(y\).

Returns:: value of the loss.

The interface is the same for a loss function, its derivative, or the conjugate loss.

See also:: SVM fundamentals

double vl_svm_hinge_conjugate_loss	(	double	u,
		double	label
	)

Parameters:

u	dual variable.
label	label value.

Returns:: conjugate loss.

double vl_svm_hinge_dca_update	(	double	alpha,
		double	inner,
		double	norm2,
		double	label
	)

Parameters:

alpha	current value of the dual variable.
inner	inner product \(\bw^\top \bx\) of the sample with the SVM model.
norm2	normalization factor \(\\|\bx\\|^2/\lambda n\).
label	label \(y\) of the sample.

Returns:: incremental update \(\Delta\alpha\) of the dual variable.

See also:: Stochastic Dual Coordinate Ascent

double vl_svm_hinge_loss	(	double	inner,
		double	label
	)

Parameters:

inner	inner product between sample and model \(\bw^\top \bx\).
label	sample label \(y\).

Returns:: value of the loss.

The interface is the same for a loss function, its derivative, or the conjugate loss.

See also:: SVM fundamentals

double vl_svm_hinge_loss_derivative	(	double	inner,
		double	label
	)

Parameters:

inner	inner product between sample and model \(\bw^\top \bx\).
label	sample label \(y\).

Returns:: value of the loss.

The interface is the same for a loss function, its derivative, or the conjugate loss.

See also:: SVM fundamentals

double vl_svm_l1_conjugate_loss	(	double	u,
		double	label
	)

Parameters:

u	dual variable.
label	label value.

Returns:: conjugate loss.

double vl_svm_l1_dca_update	(	double	alpha,
		double	inner,
		double	norm2,
		double	label
	)

Parameters:

alpha	current value of the dual variable.
inner	inner product \(\bw^\top \bx\) of the sample with the SVM model.
norm2	normalization factor \(\\|\bx\\|^2/\lambda n\).
label	label \(y\) of the sample.

Returns:: incremental update \(\Delta\alpha\) of the dual variable.

See also:: Stochastic Dual Coordinate Ascent

double vl_svm_l1_loss	(	double	inner,
		double	label
	)

Parameters:

inner	inner product between sample and model \(\bw^\top \bx\).
label	sample label \(y\).

Returns:: value of the loss.

The interface is the same for a loss function, its derivative, or the conjugate loss.

See also:: SVM fundamentals

double vl_svm_l1_loss_derivative	(	double	inner,
		double	label
	)

Parameters:

inner	inner product between sample and model \(\bw^\top \bx\).
label	sample label \(y\).

Returns:: value of the loss.

The interface is the same for a loss function, its derivative, or the conjugate loss.

See also:: SVM fundamentals

double vl_svm_l2_conjugate_loss	(	double	u,
		double	label
	)

Parameters:

u	dual variable.
label	label value.

Returns:: conjugate loss.

double vl_svm_l2_dca_update	(	double	alpha,
		double	inner,
		double	norm2,
		double	label
	)

Parameters:

alpha	current value of the dual variable.
inner	inner product \(\bw^\top \bx\) of the sample with the SVM model.
norm2	normalization factor \(\\|\bx\\|^2/\lambda n\).
label	label \(y\) of the sample.

Returns:: incremental update \(\Delta\alpha\) of the dual variable.

See also:: Stochastic Dual Coordinate Ascent

double vl_svm_l2_loss	(	double	inner,
		double	label
	)

Parameters:

inner	inner product between sample and model \(\bw^\top \bx\).
label	sample label \(y\).

Returns:: value of the loss.

The interface is the same for a loss function, its derivative, or the conjugate loss.

See also:: SVM fundamentals

double vl_svm_l2_loss_derivative	(	double	inner,
		double	label
	)

Parameters:

inner	inner product between sample and model \(\bw^\top \bx\).
label	sample label \(y\).

Returns:: value of the loss.

The interface is the same for a loss function, its derivative, or the conjugate loss.

See also:: SVM fundamentals

double vl_svm_logistic_conjugate_loss	(	double	u,
		double	label
	)

Parameters:

u	dual variable.
label	label value.

Returns:: conjugate loss.

double vl_svm_logistic_dca_update	(	double	alpha,
		double	inner,
		double	norm2,
		double	label
	)

Parameters:

alpha	current value of the dual variable.
inner	inner product \(\bw^\top \bx\) of the sample with the SVM model.
norm2	normalization factor \(\\|\bx\\|^2/\lambda n\).
label	label \(y\) of the sample.

Returns:: incremental update \(\Delta\alpha\) of the dual variable.

See also:: Stochastic Dual Coordinate Ascent

double vl_svm_logistic_loss	(	double	inner,
		double	label
	)

Parameters:

inner	inner product between sample and model \(\bw^\top \bx\).
label	sample label \(y\).

Returns:: value of the loss.

The interface is the same for a loss function, its derivative, or the conjugate loss.

See also:: SVM fundamentals

double vl_svm_logistic_loss_derivative	(	double	inner,
		double	label
	)

Parameters:

inner	inner product between sample and model \(\bw^\top \bx\).
label	sample label \(y\).

Returns:: value of the loss.

The interface is the same for a loss function, its derivative, or the conjugate loss.

See also:: SVM fundamentals

VlSvm* vl_svm_new	(	VlSvmSolverType	type,
		double const *	data,
		vl_size	dimension,
		vl_size	numData,
		double const *	labels,
		double	lambda
	)

Parameters:

type	type of SMV solver.
data	a pointer to a matrix of data.
dimension	dimension of the SVM model.
numData	number of training samples.
labels	training labels.
lambda	regularizer parameter.

Returns:: the new object.

data has one column per sample, in double format. More advanced inputs can be used with vl_svm_new_with_dataset and vl_svm_new_with_abstract_data.

See also:: vl_svm_delete

VlSvm* vl_svm_new_with_abstract_data	(	VlSvmSolverType	solver,
		void *	data,
		vl_size	dimension,
		vl_size	numData,
		double const *	labels,
		double	lambda
	)

Parameters:

solver	type of SMV solver.
data	pointer to the data.
dimension	dimension of the SVM model.
numData	num training samples.
labels	training samples labels.
lambda	regularizer parameter.

Returns:: the new object.

After calling this function, vl_svm_set_data_functions must be used to setup suitable callbacks for the inner product and accumulation operations (

See also:: svm-data-abstraction).; vl_svm_delete

VlSvm* vl_svm_new_with_dataset	(	VlSvmSolverType	solver,
		VlSvmDataset *	dataset,
		double const *	labels,
		double	lambda
	)

Parameters:

solver	type of SMV solver.
dataset	SVM dataset object
labels	training samples labels.
lambda	regularizer parameter.

Returns:: the new object.

See also:: vl_svm_delete

void vl_svm_set_bias	(	VlSvm *	self,
		double	b
	)

Parameters:

self	object.
b	bias.

The function set the internal representation of the SVM bias to be equal to b (the bias multiplier is applied). The same remark that applies to vl_svm_set_model applies here too.

void vl_svm_set_bias_learning_rate	(	VlSvm *	self,
		double	rate
	)

Parameters:

self	object
rate	bias learning rate (positive).

This parameter applies only to the SGD solver.

void vl_svm_set_bias_multiplier	(	VlSvm *	self,
		double	b
	)

Parameters:

self	object
b	bias multiplier.

The bias multiplier is the value of the constant feature appended to the data vectors to implement the bias (Adding a bias).

void vl_svm_set_conjugate_loss_function	(	VlSvm *	self,
		VlSvmLossFunction	f
	)

Parameters:

self	object.
f	loss function callback.

Note that setting up a loss requires specifying more than just one callback. See Loss functions for details. .

void vl_svm_set_data_functions	(	VlSvm *	self,
		VlSvmInnerProductFunction	inner,
		VlSvmAccumulateFunction	acc
	)

Parameters:

self	object.
inner	inner product function.
acc	accumulate function.

See Data abstraction: working with compressed data.

void vl_svm_set_dca_update_function	(	VlSvm *	self,
		VlSvmDcaUpdateFunction	f
	)

Parameters:

self	object.
f	loss function callback.

Note that setting up a loss requires specifying more than just one callback. See Loss functions for details. .

void vl_svm_set_diagnostic_frequency	(	VlSvm *	self,
		vl_size	f
	)

Parameters:

self	object.
f	diagnostic frequency (`>=` 1).

A diagnostic round (to test for convergence and to printout information) is performed every f iterations.

void vl_svm_set_diagnostic_function	(	VlSvm *	self,
		VlSvmDiagnosticFunction	f,
		void *	data
	)

Parameters:

self	object.
f	diagnostic function pointer.
data	pointer to data used by the diagnostic function.

void vl_svm_set_epsilon	(	VlSvm *	self,
		double	epsilon
	)

Parameters:

self	object
epsilon	threshold (non-negative).

void vl_svm_set_iteration_number	(	VlSvm *	self,
		vl_uindex	n
	)

Parameters:

self	object.
n	iteration number.

If called before training, this can be used with SGD for a warm start, as the net effect is to slow down the learning rate.

void vl_svm_set_loss	(	VlSvm *	self,
		VlSvmLossType	loss
	)

Parameters:

self	object.
loss	type of loss function.

See also:: Loss functions.

void vl_svm_set_loss_derivative_function	(	VlSvm *	self,
		VlSvmLossFunction	f
	)

Parameters:

self	object.
f	loss function callback.

Note that setting up a loss requires specifying more than just one callback. See Loss functions for details. .

void vl_svm_set_loss_function	(	VlSvm *	self,
		VlSvmLossFunction	f
	)

Parameters:

self	object.
f	loss function callback.

Note that setting up a loss requires specifying more than just one callback. See Loss functions for details.

void vl_svm_set_max_num_iterations	(	VlSvm *	self,
		vl_size	n
	)

Parameters:

self	object.
n	maximum number of iterations.

void vl_svm_set_model	(	VlSvm *	self,
		double const *	model
	)

Parameters:

self	object.
model	model.

The function copies the content of the vector model to the internal model buffer. This operation can be used for warm start with the SGD algorithm, but has undefined effect with the SDCA algorithm.

void vl_svm_set_weights	(	VlSvm *	self,
		double const *	weights
	)

Parameters:

self	object.
weights	data weights.

weights must be an array of non-negative weights. The loss of each data point is multiplied by the corresponding weight.

Set weights to NULL to weight the data uniformly by 1 (default).

Note that the weights array is not copied and must be valid througout the object lifetime (unless it is replaced).

void vl_svm_train ( VlSvm * self )

Parameters:

self object.

The data on which the SVM operates is passed upon the cration of the VlSvm object. This function runs a solver to learn a corresponding model. See Getting started.

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Data Structures

Typedefs

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

Function Documentation