lti::sammonsMapping Class Reference

Performs Sammon's Mapping. More...

#include <ltiSammonsMapping.h>

Inheritance diagram for lti::sammonsMapping:

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Collaboration diagram for lti::sammonsMapping:

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List of all members.

Classes
class	parameters
	the parameters for the class sammonsMapping More...
Public Member Functions
	sammonsMapping ()
	sammonsMapping (const sammonsMapping &other)
virtual	~sammonsMapping ()
virtual const char *	getTypeName () const
bool	apply (const dmatrix &src, dmatrix &dest, double &error) const
bool	apply (const dmatrix &src, dmatrix &dest) const
sammonsMapping &	copy (const sammonsMapping &other)
sammonsMapping &	operator= (const sammonsMapping &other)
virtual functor *	clone () const
const parameters &	getParameters () const
void	setProgressObject (const progressInfo &progBox)
void	removeProgressObject ()
bool	validProgressObject () const
progressInfo &	getProgressObject ()
const progressInfo &	getProgressObject () const
Protected Member Functions
void	initRandom (dmatrix &dest) const
void	initPca (const dmatrix &data, dmatrix &dest) const
Protected Attributes
progressInfo *	progressBox

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Detailed Description

Performs Sammon's Mapping.

The data from some high dimensional source space is mapped to a destination space of lower dimensionality. In the process Sammon's Mapping tries to keep distances between samples in the destination space as close to those in the source space. Typical uses are data analysis or visualization of SOFM networks. For details see:

John W. Sammon, Jr. A nonlinear mapping for data structure analysis. IEEE Transactions on Computers, C-18(5):401-409, May 1969.

There are several parameters the algorithm can be tuned with. Initialization is usually performed using principal component analysis. It projects the data from the original space into the destination space using the eigenvectors with largest eingenvalues. The other option --- random initialization --- seems to be useful for demonstration purposes, only.

Three methods are available for minimizing the error or stress of the mapping: gradient descent, gradient descent with momentum and steepest descent. Of these, steepest descent usually requires the smallest number of iterations, but each iteration is more costly. Further, with many planes in the error surface, the computation of the second derivative might not be possible. In case of 0 this value is set to 1.E-4 as a work-around. The gradient descent methods are much more stable. Their convergence, however, is much slower. Using momentum can lead to faster convergence than regular gradient descent but also needs more computation per iteration. According to Sammon, errors should be below 1E-2 to be considered good. Usually, much smaller errors are achieved.

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Constructor & Destructor Documentation

lti::sammonsMapping::sammonsMapping

(

)

default constructor

lti::sammonsMapping::sammonsMapping

(

const sammonsMapping &

other

)

copy constructor

Parameters:

other

the object to be copied

virtual lti::sammonsMapping::~sammonsMapping

(

)

[virtual]

destructor

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Member Function Documentation

bool lti::sammonsMapping::apply	(	const dmatrix &	src,
		dmatrix &	dest
	)			const

operates on a copy of the given parameters.

Parameters:

	src	dmatrix with the source data.
	dest	dmatrix where the result will be left.

Returns:

true if apply successful or false otherwise.

bool lti::sammonsMapping::apply	(	const dmatrix &	src,
		dmatrix &	dest,
		double &	error
	)			const

operates on a copy of the given parameters.

Parameters:

	src	dmatrix with the source data.
	dest	dmatrix where the result will be left.
	error	the error of the mapping

Returns:

true if apply successful or false otherwise.

Referenced by lti::SOFM2DVisualizer::sammonsMapper().

virtual functor* lti::sammonsMapping::clone

(

)

const [virtual]

returns a pointer to a clone of this functor.

Implements lti::functor.

sammonsMapping& lti::sammonsMapping::copy

(

const sammonsMapping &

other

)

copy data of "other" functor.

Parameters:

other

the functor to be copied

Returns:

a reference to this functor object

Reimplemented from lti::functor.

const parameters& lti::sammonsMapping::getParameters

(

)

const

returns used parameters

Reimplemented from lti::functor.

const progressInfo& lti::sammonsMapping::getProgressObject

(

)

const

get progress object

progressInfo& lti::sammonsMapping::getProgressObject

(

)

get progress object

virtual const char* lti::sammonsMapping::getTypeName

(

)

const [virtual]

returns the name of this type ("sammonsMapping")

Reimplemented from lti::functor.

void lti::sammonsMapping::initPca	(	const dmatrix &	data,
		dmatrix &	dest
	)			const [protected]

Initialization using PCA.

void lti::sammonsMapping::initRandom

(

dmatrix &

dest

)

const [protected]

Random initialization.

sammonsMapping& lti::sammonsMapping::operator=

(

const sammonsMapping &

other

)

alias for copy member

Parameters:

other

the functor to be copied

Returns:

a reference to this functor object

Reimplemented from lti::functor.

void lti::sammonsMapping::removeProgressObject

(

)

remove the active progress object

void lti::sammonsMapping::setProgressObject

(

const progressInfo &

progBox

)

set a progress object

A clone of the given object will be generated.

bool lti::sammonsMapping::validProgressObject

(

)

const

return true if a valid progressInfo object has already been setted

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Member Data Documentation

progressInfo* lti::sammonsMapping::progressBox [mutable, protected]

current progress object

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

• ltiSammonsMapping.h