Local Linear Map implementation (LLM) More...

#include <LLM.h>

Inheritance diagram for icl::math::LLM:

Classes
struct	Kernel
	Internally used Kernel structure. More...

Public Member Functions
	LLM (unsigned int inputDim, unsigned int outputDim)
	Creates a new llm with given input and output dimensions. More...

	LLM (unsigned int inputDim, unsigned int outputDim, unsigned int numCenters, const std::vector< utils::Range< icl32f > > &ranges, const std::vector< float > &var=std::vector< float >(1, 1))

void	init (unsigned int numCenters, const std::vector< utils::Range< icl32f > > &ranges, const std::vector< float > &var=std::vector< float >(1, 1))
	initializes the LLM prototypes with given kernel count More...

void	init (const std::vector< float * > &centers, const std::vector< float > &var=std::vector< float >(1, 1))
	initializes the LLM prototypes with given set of kernels More...

const float *	apply (const float *x)
	applies the LLM and returns current NET output vector More...

void	train (const float x, const float y, int trainflags=TRAIN_ALL)
	applies an update step to the net with given net input x and destination output y More...

void	trainCenters (const float *x)
	trains the input weights w_in More...

void	trainSigmas (const float *x)
	trains the input variances sigma More...

void	trainOutputs (const float x, const float y)
	trains the output weights w_out More...

void	trainMatrices (const float x, const float y)
	trains the output slope matrices A More...

const float *	getErrorVec (const float x, const float y)
	returns the current error vector with respect to a given destination value y More...

void	setEpsilonIn (float val)
	sets up learning rate for input weights to a new value (about 0..1) More...

void	setEpsilonOut (float val)
	sets up learning rate for output weights to a new value (about 0..1) More...

void	setEpsilonA (float val)
	sets up learning rate for slope matrices to a new value (about 0..1) More...

void	setEpsilonSigma (float val)
	sets up learning rate for sigmas to a new value (about 0..1) More...

void	showKernels () const
	Shows all current kernels to std::out. More...

unsigned int	numKernels () const
	returns the current internal kernel count More...

const Kernel &	operator[] (unsigned int i) const
	returns a specifice kernel at given index (const) More...

Kernel &	operator[] (unsigned int i)
	returns a specifice kernel (unconst version) More...

bool	isSoftMaxUsed () const
	returns whether the softmax function for calculation for g_i[x] is used More...

void	setSoftMaxEnabled (bool enabled)
	sets whether the softmax function for calculation for g_i[x] is used More...

Public Member Functions inherited from icl::utils::Configurable
virtual	~Configurable ()
	virtual destructor More...

	Configurable (const Configurable &other)
	Copy constructor. More...

Configurable &	operator= (const Configurable &other)
	Assignment operator. More...

void	setConfigurableID (const std::string &ID)
	sets the ID of this configurable More...

const std::string &	getConfigurableID () const
	returns the configurables static ID More...

bool	isOrderedFlagSet () const
	returns whether the ordered flag is set More...

void	deactivateProperty (const std::string &pattern)
	adds an additional deativation pattern More...

void	deleteDeactivationPattern (const std::string &pattern)
	removed a formerly added deactivation pattern More...

std::vector< std::string >	getPropertyListWithoutDeactivated () const
	this returns a filtered list of properties (using all filters added by deactivateProperty) More...

virtual void	adaptProperty (const std::string &name, const std::string &newType, const std::string &newInfo, const std::string &newToolTip)
	this function can be used to adapt a specific property afterwards More...

void	registerCallback (const Callback &cb)
	add a callback for changed properties More...

void	removedCallback (const Callback &cb)
	removes a callback that was registered before More...

void	syncChangesTo (Configurable *others, int num=1)
	this can be used to let this instance also apply property changes to others More...

virtual void	setPropertyValue (const std::string &propertyName, const Any &value)
	sets a property value More...

virtual std::vector< std::string >	getPropertyList () const
	returns a list of All properties, that can be set using setProperty More...

virtual bool	supportsProperty (const std::string &propertyName) const
	base implementation for property check (seaches in the property list) More...

virtual void	saveProperties (const std::string &filename, const std::vector< std::string > &propertiesToSkip=EMPTY_VEC) const
	writes all available properties into a file More...

virtual void	loadProperties (const std::string &filename, const std::vector< std::string > &propertiesToSkip=EMPTY_VEC)
	reads a camera config file from disc More...

virtual std::string	getPropertyType (const std::string &propertyName) const
	get type of property More...

virtual std::string	getPropertyInfo (const std::string &propertyName) const
	get information of a properties valid values More...

virtual Any	getPropertyValue (const std::string &propertyName) const
	returns the current value of a property or a parameter More...

virtual std::string	getPropertyToolTip (const std::string &propertyName) const
	returns the tooltip description for a given property More...

virtual int	getPropertyVolatileness (const std::string &propertyName) const
	Returns whether this property may be changed internally. More...

Static Public Attributes
static const int	TRAIN_CENTERS = 1

static const int	TRAIN_SIGMAS = 2

static const int	TRAIN_OUTPUTS = 4

static const int	TRAIN_MATRICES = 8

static const int	TRAIN_ALL = TRAIN_CENTERS \| TRAIN_SIGMAS \| TRAIN_OUTPUTS \| TRAIN_MATRICES

Static Public Attributes inherited from icl::utils::Configurable
static const std::vector< std::string >	EMPTY_VEC
	used as shortcut – just an empty vector of std::strings More...

Private Member Functions
void	init_private (unsigned int inputDim, unsigned int outputDim)

const float *	updateGs (const float *x)
	possible usefull utility function (internally used) More...

void	trainCentersIntern (const float x, const float g)
	internal training function for the input weights/prototypes More...

void	trainSigmasIntern (const float x, const float g)
	interal training function for the sigmas More...

void	trainOutputsIntern (const float x, const float y, const float g, const float dy, bool useDeltaWin)
	internal training function for the output weights More...

void	trainMatricesIntern (const float x, const float y, const float g, const float dy)
	internal training function for the slope matrices A More...

const float *	applyIntern (const float x, const float g)
	internal apply function More...

const float *	getErrorVecIntern (const float y, const float ynet)
	internal function to return the current error vector More...

Private Attributes
unsigned int	m_inputDim
	input dimension More...

unsigned int	m_outputDim
	output dimension More...

std::vector< Kernel >	m_kernels
	internal storage for the kernels More...

std::vector< float >	m_outBuf
	internal output value buffer More...

std::vector< float >	m_gBuf
	internal buffer for the g_i[x] More...

std::vector< float >	m_errorBuf
	internal buffer for the current error vector More...

Additional Inherited Members
Public Types inherited from icl::utils::Configurable
typedef Function< void, const Property & >	Callback
	Function type for changed properties. More...

Static Public Member Functions inherited from icl::utils::Configurable
static std::string	create_default_ID (const std::string &prefix)
	this function can be used in subclasses to create a default ID More...

static Configurable *	get (const std::string &id)
	returns configurable by given ID More...

static void	register_configurable_type (const std::string &classname, Function< Configurable * > creator)
	registers a configurable type More...

static std::vector< std::string >	get_registered_configurables ()
	returns a list of all registered configurable classnames More...

static Configurable *	create_configurable (const std::string &classname)
	creates a configurable by given name More...

Protected Member Functions inherited from icl::utils::Configurable
void	addProperty (const std::string &name, const std::string &type, const std::string &info, const Any &value=Any(), const int volatileness=0, const std::string &tooltip=std::string())
	This can be used by derived classes to store supported properties in the internal list. More...

void	addChildConfigurable (Configurable *configurable, const std::string &childPrefix="")
	This adds another configurable as child. More...

void	removeChildConfigurable (Configurable *configurable)
	removes the given child configurable More...

Property &	prop (const std::string &propertyName)
	this CAN be used e.g. to store a property value in internal property-list More...

const Property &	prop (const std::string &propertyName) const
	this CAN be used e.g. to store a property value in internal property-list More...

	Configurable (const std::string &ID="", bool ordered=true)
	create this configurable with given ID More...

void	call_callbacks (const std::string &propertyName, const Configurable *caller) const
	calls all registered callbacks More...

Protected Attributes inherited from icl::utils::Configurable
std::vector< Callback >	callbacks
	internally managed list of callbacks More...

Detailed Description

Local Linear Map implementation (LLM)

The LLM-network (Local Linear Maps) is a very powerful regression network that uses a superposition of linearily weighted gaussians as regression model:

Net Function y=f(x)

$\vec{y}^{net}(x) = \sum\limits_{i=1}^N ( \vec{w}_i^{out}+A_i ( \vec{x}-\vec{w}_i^{in} ) ) \cdot g_i(\vec{x})$

where each kernel i is defined by a kernel function $g_i(\vec{x})$ that is weighted linearily using $( \vec{w}_i^{out}+A_i ( \vec{x}-\vec{w}_i^{in} ) )$ . $\vec{w}_i^{in}$ is the location in the input space, where kernel i is centered, and $\vec{w}_i^{out}$ resp. $A_i$ are parameters of a linear weighting function.

Kernel functions

Here, normalized Gaussians are always used a kernel functions:

$g_i(\vec{x}) = \frac{\exp(-\frac{\|\vec{x}-\vec{w}_i^{in}\|^2}{2\sigma_i^2})} {\sum\limits_{j=1}^N \exp(-\frac{\|\vec{x}-\vec{w}_j^{in}\|^2}{2\sigma_j^2})}$

Training of input weights and variances(unsuperwised)

The kernel centers (also refered as data prototypes) $\vec{w}_i^{in}$ can be initialized randomly e.g. using a uniform distribution in input data space or by a set of given prototypes. The prototypes can be adapted while the network training process using means of vector quantisation (e.g. KMeans) externally or by using the following internally implemented update rule:

$\Delta \vec{w}_i^{in} = \epsilon_{in} \cdot ( \vec{x} - \vec{w}_i^{in} ) \cdot g_i(\vec{x})$

and

$\Delta \sigma^2 = \epsilon_{\sigma} \cdot ( \vec{x} - \vec{w}_i^{in} )^2 - \sigma^2 \cdot g_i(\vec{x})$

Note: For some initial tries, it turned out, that updating the kernel radii is rather unstable.

Training of output weights and matrices (superwised)

Training rules for output weights $\vec{w}_i^{out}$ and matrices $A_i$ are obtained by simple gradient descent approach (given input tuple $(\vec{x}^{\alpha},\vec{y}^{\alpha})$ ):

$\Delta \vec{w}_i^{out} = \epsilon_{out} \cdot g_i(\vec{x}^{\alpha}) \cdot (\vec{y}^{\alpha} - \vec{y}^{net}(\vec{x}^{\alpha}) ) + A_i \Delta \vec{w}_i^{in}$

and

$\Delta A_i = \epsilon_A \cdot g_i(\vec{x}^{\alpha}) \cdot (\vec{y}^{\alpha} - \vec{y}^{net}(\vec{x}^{\alpha}) ) \cdot \frac{(\vec{x}^{\alpha} - \vec{w}_i^{in} )^{\tau}}{\|\vec{x}^{\alpha} - \vec{w}_i^{in}\|^2}$

Hacks

Delta A_i use sqrt of demonimator (???)

TODO

check for initialized first or initialized later again
check if initialized at all (in train...)
enable soft-max on/off
provide an interface for Batch based VQ using (EM-Algorithm or something like that)
$f_X(x_1, \dots, x_N) = \frac {1} {(2\pi)^{N/2}|\Sigma|^{1/2}} \exp \left( -\frac{1}{2} ( x - \mu)^\top \Sigma^{-1} (x - \mu) \right)$

Constructor & Destructor Documentation

◆ LLM() [1/2]

icl::math::LLM::LLM	(	unsigned int	inputDim,
		unsigned int	outputDim
	)

Creates a new llm with given input and output dimensions.

◆ LLM() [2/2]

icl::math::LLM::LLM	(	unsigned int	inputDim,
		unsigned int	outputDim,
		unsigned int	numCenters,
		const std::vector< utils::Range< icl32f > > &	ranges,
		const std::vector< float > &	var = `std::vector< float >(1, 1)`
	)

Member Function Documentation

◆ apply()

const float* icl::math::LLM::apply ( const float * x )

applies the LLM and returns current NET output vector

the ownership of the returnd float * is not passed to the caller. The output remains valid until apply is called with another x-value

◆ applyIntern()

const float* icl::math::LLM::applyIntern	(	const float *	x,
		const float *	g
	)

private

internal apply function

◆ getErrorVec()

const float* icl::math::LLM::getErrorVec	(	const float *	x,
		const float *	y
	)

returns the current error vector with respect to a given destination value y

◆ getErrorVecIntern()

const float* icl::math::LLM::getErrorVecIntern	(	const float *	y,
		const float *	ynet
	)

private

internal function to return the current error vector

◆ init() [1/2]

void icl::math::LLM::init	(	unsigned int	numCenters,
		const std::vector< utils::Range< icl32f > > &	ranges,
		const std::vector< float > &	var = `std::vector< float >(1, 1)`
	)

initializes the LLM prototypes with given kernel count

Internally creates numCenters kernels for this LLM. Each kernel is initialized as follows:

input weight w_in: created with respect to ranges (w_in[i] becomes a value drawn from a uniform distibution of range ranges[i])
output weight w_out: initialized to 0-vector
Slope Matrix A: initialized to 0-matrix
variance sigma: initialized to given variance vector var

(internally this init function calls the other init function)

Parameters

numCenters	new prototype count
ranges	ranges for uniform distributed prototypes (ranges.size must be equal to the input dimension of the LLM)
var	variance for the new created Gaussians (var.size must be equal to the input dimension of the LLM)

◆ init() [2/2]

void icl::math::LLM::init	(	const std::vector< float * > &	centers,
		const std::vector< float > &	var = `std::vector< float >(1, 1)`
	)

initializes the LLM prototypes with given set of kernels

Internall all centers.size() vectors are used to create that many prototypes. The given vectors are deeply copied and not released internally. Initialization is performend as described in the above function.

◆ init_private()

void icl::math::LLM::init_private	(	unsigned int	inputDim,
		unsigned int	outputDim
	)

private

◆ isSoftMaxUsed()

bool icl::math::LLM::isSoftMaxUsed ( ) const

inline

returns whether the softmax function for calculation for g_i[x] is used

◆ numKernels()

unsigned int icl::math::LLM::numKernels ( ) const

inline

returns the current internal kernel count

◆ operator[]() [1/2]

const Kernel& icl::math::LLM::operator[] ( unsigned int i ) const

inline

returns a specifice kernel at given index (const)

◆ operator[]() [2/2]

Kernel& icl::math::LLM::operator[] ( unsigned int i )

inline

returns a specifice kernel (unconst version)

please note: it is not safe to change the obtained Kernel's value by hand unless you really know what you are doing. For setting the kernel weights manually, it is strongly recommended to use the Kernel::set-method, which does only allow to change the weight values

◆ setEpsilonA()

void icl::math::LLM::setEpsilonA ( float val )

inline

sets up learning rate for slope matrices to a new value (about 0..1)

◆ setEpsilonIn()

void icl::math::LLM::setEpsilonIn ( float val )

inline

sets up learning rate for input weights to a new value (about 0..1)

◆ setEpsilonOut()

void icl::math::LLM::setEpsilonOut ( float val )

inline

sets up learning rate for output weights to a new value (about 0..1)

◆ setEpsilonSigma()

void icl::math::LLM::setEpsilonSigma ( float val )

inline

sets up learning rate for sigmas to a new value (about 0..1)

Note Update of the sigmas does not run very good!

◆ setSoftMaxEnabled()

void icl::math::LLM::setSoftMaxEnabled ( bool enabled )

inline

sets whether the softmax function for calculation for g_i[x] is used

◆ showKernels()

void icl::math::LLM::showKernels ( ) const

Shows all current kernels to std::out.

◆ train()

void icl::math::LLM::train	(	const float *	x,
		const float *	y,
		int	trainflags = `TRAIN_ALL`
	)

applies an update step to the net with given net input x and destination output y

The trainingflags parameter can be used to specify special parameter updates, a list of training targets can be creates using bit-or: e.g.: TRAIN_CENTERS|TRAIN_SIGMAS

◆ trainCenters()

void icl::math::LLM::trainCenters ( const float * x )

trains the input weights w_in

◆ trainCentersIntern()

void icl::math::LLM::trainCentersIntern	(	const float *	x,
		const float *	g
	)

private

internal training function for the input weights/prototypes

◆ trainMatrices()

void icl::math::LLM::trainMatrices	(	const float *	x,
		const float *	y
	)

trains the output slope matrices A

◆ trainMatricesIntern()

void icl::math::LLM::trainMatricesIntern	(	const float *	x,
		const float *	y,
		const float *	g,
		const float *	dy
	)

private

internal training function for the slope matrices A

◆ trainOutputs()

void icl::math::LLM::trainOutputs	(	const float *	x,
		const float *	y
	)

trains the output weights w_out

◆ trainOutputsIntern()

void icl::math::LLM::trainOutputsIntern	(	const float *	x,
		const float *	y,
		const float *	g,
		const float *	dy,
		bool	useDeltaWin
	)

private

internal training function for the output weights

◆ trainSigmas()

void icl::math::LLM::trainSigmas ( const float * x )

trains the input variances sigma

◆ trainSigmasIntern()

void icl::math::LLM::trainSigmasIntern	(	const float *	x,
		const float *	g
	)

private

interal training function for the sigmas

◆ updateGs()

const float* icl::math::LLM::updateGs ( const float * x )

private

possible usefull utility function (internally used)

updates an internal variable vector containing provisional results for all g_i[x]. This internally speeds up performance (please dont call this function!, propably it can be made private)

Member Data Documentation

◆ m_errorBuf

std::vector<float> icl::math::LLM::m_errorBuf

private

internal buffer for the current error vector

◆ m_gBuf

std::vector<float> icl::math::LLM::m_gBuf

private

internal buffer for the g_i[x]

◆ m_inputDim

unsigned int icl::math::LLM::m_inputDim

private

input dimension

◆ m_kernels

std::vector<Kernel> icl::math::LLM::m_kernels

private

internal storage for the kernels

◆ m_outBuf

std::vector<float> icl::math::LLM::m_outBuf

private

internal output value buffer

◆ m_outputDim

unsigned int icl::math::LLM::m_outputDim

private

output dimension

◆ TRAIN_ALL

const int icl::math::LLM::TRAIN_ALL = TRAIN_CENTERS | TRAIN_SIGMAS | TRAIN_OUTPUTS | TRAIN_MATRICES

static

training flag for updating all

◆ TRAIN_CENTERS

const int icl::math::LLM::TRAIN_CENTERS = 1

static

training flag for updating input weights/prototype vectors

◆ TRAIN_MATRICES

const int icl::math::LLM::TRAIN_MATRICES = 8

static

training flag for updating output matrices

◆ TRAIN_OUTPUTS

const int icl::math::LLM::TRAIN_OUTPUTS = 4

static

training flag for updating output weights

◆ TRAIN_SIGMAS

const int icl::math::LLM::TRAIN_SIGMAS = 2

static

training flag for updating input sigmas

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

/Users/alneuman/vm/icl/ICLMath/src/ICLMath/LLM.h

Classes

Public Member Functions

Static Public Attributes

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Net Function y=f(x)

Kernel functions

Training of input weights and variances(unsuperwised)

Training of output weights and matrices (superwised)

Hacks

TODO

Constructor & Destructor Documentation

◆ LLM() [1/2]

◆ LLM() [2/2]

Member Function Documentation

◆ apply()

◆ applyIntern()

◆ getErrorVec()

◆ getErrorVecIntern()

◆ init() [1/2]

◆ init() [2/2]

◆ init_private()

◆ isSoftMaxUsed()

◆ numKernels()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ setEpsilonA()

◆ setEpsilonIn()

◆ setEpsilonOut()

◆ setEpsilonSigma()

◆ setSoftMaxEnabled()

◆ showKernels()

◆ train()

◆ trainCenters()

◆ trainCentersIntern()

◆ trainMatrices()

◆ trainMatricesIntern()

◆ trainOutputs()

◆ trainOutputsIntern()

◆ trainSigmas()

◆ trainSigmasIntern()

◆ updateGs()

Member Data Documentation

◆ m_errorBuf

◆ m_gBuf

◆ m_inputDim

◆ m_kernels

◆ m_outBuf

◆ m_outputDim

◆ TRAIN_ALL

◆ TRAIN_CENTERS

◆ TRAIN_MATRICES

◆ TRAIN_OUTPUTS

◆ TRAIN_SIGMAS