vtkPCAStatistics Class Reference

#include <vtkPCAStatistics.h>

Inheritance diagram for vtkPCAStatistics:

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Collaboration diagram for vtkPCAStatistics:

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List of all members.

Detailed Description

A class for principal component analysis.

This class derives from the multi-correlative statistics algorithm and uses the covariance matrix and Cholesky decomposition computed by it. However, when it finalizes the statistics in Learn mode, the PCA class computes the SVD of the covariance matrix in order to obtain its eigenvectors.

In the assess mode, the input data are

projected into the basis defined by the eigenvectors,
the energy associated with each datum is computed,
or some combination thereof. Additionally, the user may specify some threshold energy or eigenvector entry below which the basis is truncated. This allows projection into a lower-dimensional state while minimizing (in a least squares sense) the projection error.

Thanks:: Thanks to David Thompson, Philippe Pebay and Jackson Mayo from Sandia National Laboratories for implementing this class.

Examples:: vtkPCAStatistics (Examples)

Tests:: vtkPCAStatistics (Tests)

Definition at line 57 of file vtkPCAStatistics.h.


Public Types
typedef vtkMultiCorrelativeStatistics	Superclass

enum	NormalizationType { NONE, TRIANGLE_SPECIFIED, DIAGONAL_SPECIFIED, DIAGONAL_VARIANCE, NUM_NORMALIZATION_SCHEMES }

enum	ProjectionType { FULL_BASIS, FIXED_BASIS_SIZE, FIXED_BASIS_ENERGY, NUM_BASIS_SCHEMES }
Public Member Functions
virtual const char *	GetClassName ()
virtual int	IsA (const char *type)
virtual void	PrintSelf (ostream &os, vtkIndent indent)

virtual void	SetNormalizationScheme (int)
virtual int	GetNormalizationScheme ()
virtual void	SetNormalizationSchemeByName (const char *sname)
virtual const char *	GetNormalizationSchemeName (int scheme)

virtual vtkTable *	GetSpecifiedNormalization ()
virtual void	SetSpecifiedNormalization (vtkTable *)

void	GetEigenvalues (int request, vtkDoubleArray *)
void	GetEigenvalues (vtkDoubleArray *)
double	GetEigenvalue (int request, int i)
double	GetEigenvalue (int i)

void	GetEigenvectors (int request, vtkDoubleArray *eigenvectors)
void	GetEigenvectors (vtkDoubleArray *eigenvectors)
void	GetEigenvector (int i, vtkDoubleArray *eigenvector)
void	GetEigenvector (int request, int i, vtkDoubleArray *eigenvector)

virtual void	SetBasisScheme (int)
virtual int	GetBasisScheme ()
virtual const char *	GetBasisSchemeName (int schemeIndex)
virtual void	SetBasisSchemeByName (const char *schemeName)

virtual void	SetFixedBasisSize (int)
virtual int	GetFixedBasisSize ()

virtual void	SetFixedBasisEnergy (double)
virtual double	GetFixedBasisEnergy ()

virtual bool	SetParameter (const char *parameter, int index, vtkVariant value)
Static Public Member Functions
static int	IsTypeOf (const char *type)
static vtkPCAStatistics *	SafeDownCast (vtkObject *o)
static vtkPCAStatistics *	New ()
Protected Member Functions
	vtkPCAStatistics ()
	~vtkPCAStatistics ()
virtual int	FillInputPortInformation (int port, vtkInformation *info)
virtual void	Derive (vtkMultiBlockDataSet *inMeta)

virtual void	Test (vtkTable , vtkMultiBlockDataSet , vtkTable *)

virtual void	Assess (vtkTable , vtkMultiBlockDataSet , vtkTable *)

virtual void	SelectAssessFunctor (vtkTable inData, vtkDataObject inMeta, vtkStringArray rowNames, AssessFunctor &dfunc)
Protected Attributes
int	NormalizationScheme
int	BasisScheme
int	FixedBasisSize
double	FixedBasisEnergy
Static Protected Attributes
static const char *	BasisSchemeEnumNames [NUM_BASIS_SCHEMES+1]
static const char *	NormalizationSchemeEnumNames [NUM_NORMALIZATION_SCHEMES+1]

Member Typedef Documentation

typedef vtkMultiCorrelativeStatistics vtkPCAStatistics::Superclass

Reimplemented from vtkMultiCorrelativeStatistics.

Reimplemented in vtkPPCAStatistics.

Definition at line 60 of file vtkPCAStatistics.h.

Member Enumeration Documentation

enum vtkPCAStatistics::NormalizationType

Methods by which the covariance matrix may be normalized.

Enumerator:

NONE	The covariance matrix should be used as computed.
TRIANGLE_SPECIFIED	Normalize cov(i,j) by V(i,j) where V is supplied by the user.
DIAGONAL_SPECIFIED	Normalize cov(i,j) by sqrt(V(i)*V(j)) where V is supplied by the user.
DIAGONAL_VARIANCE	Normalize cov(i,j) by sqrt(cov(i,i)*cov(j,j)).
NUM_NORMALIZATION_SCHEMES	The number of normalization schemes.

Definition at line 67 of file vtkPCAStatistics.h.

enum vtkPCAStatistics::ProjectionType

These are the enumeration values that SetBasisScheme() accepts and GetBasisScheme returns.

Enumerator:

FULL_BASIS	Use all entries in the basis matrix.
FIXED_BASIS_SIZE	Use the first N entries in the basis matrix.
FIXED_BASIS_ENERGY	Use consecutive basis matrix entries whose energies sum to at least T.
NUM_BASIS_SCHEMES	The number of schemes (not a valid scheme).

Definition at line 80 of file vtkPCAStatistics.h.

Constructor & Destructor Documentation

vtkPCAStatistics::vtkPCAStatistics ( ) [protected]

vtkPCAStatistics::~vtkPCAStatistics ( ) [protected]

Member Function Documentation

virtual const char* vtkPCAStatistics::GetClassName ( ) [virtual]

Reimplemented from vtkMultiCorrelativeStatistics.

Reimplemented in vtkPPCAStatistics.

static int vtkPCAStatistics::IsTypeOf ( const char * name ) [static]

Return 1 if this class type is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeMacro found in vtkSetGet.h.

Reimplemented from vtkMultiCorrelativeStatistics.

Reimplemented in vtkPPCAStatistics.

virtual int vtkPCAStatistics::IsA ( const char * name ) [virtual]

Return 1 if this class is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeMacro found in vtkSetGet.h.

Reimplemented from vtkMultiCorrelativeStatistics.

Reimplemented in vtkPPCAStatistics.

static vtkPCAStatistics* vtkPCAStatistics::SafeDownCast ( vtkObject * o ) [static]

Reimplemented from vtkMultiCorrelativeStatistics.

Reimplemented in vtkPPCAStatistics.

virtual void vtkPCAStatistics::PrintSelf	(	ostream &	os,
		vtkIndent	indent
	)			`[virtual]`

Methods invoked by print to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from vtkMultiCorrelativeStatistics.

Reimplemented in vtkPPCAStatistics.

static vtkPCAStatistics* vtkPCAStatistics::New ( ) [static]

Create an object with Debug turned off, modified time initialized to zero, and reference counting on.

Reimplemented from vtkMultiCorrelativeStatistics.

Reimplemented in vtkPPCAStatistics.

virtual void vtkPCAStatistics::SetNormalizationScheme ( int ) [virtual]

This determines how (or if) the covariance matrix cov is normalized before PCA. When set to NONE, no normalization is performed. This is the default. When set to TRIANGLE_SPECIFIED, each entry cov(i,j) is divided by V(i,j). The list V of normalization factors must be set using the SetNormalization method before the filter is executed. When set to DIAGONAL_SPECIFIED, each entry cov(i,j) is divided by sqrt(V(i)*V(j)). The list V of normalization factors must be set using the SetNormalization method before the filter is executed. When set to DIAGONAL_VARIANCE, each entry cov(i,j) is divided by sqrt(cov(i,i)*cov(j,j)). Warning: Although this is accepted practice in some fields, some people think you should not turn this option on unless there is a good physically-based reason for doing so. Much better instead to determine how component magnitudes should be compared using physical reasoning and use DIAGONAL_SPECIFIED, TRIANGLE_SPECIFIED, or perform some pre-processing to shift and scale input data columns appropriately than to expect magical results from a shady normalization hack.

virtual int vtkPCAStatistics::GetNormalizationScheme ( ) [virtual]

This determines how (or if) the covariance matrix cov is normalized before PCA. When set to NONE, no normalization is performed. This is the default. When set to TRIANGLE_SPECIFIED, each entry cov(i,j) is divided by V(i,j). The list V of normalization factors must be set using the SetNormalization method before the filter is executed. When set to DIAGONAL_SPECIFIED, each entry cov(i,j) is divided by sqrt(V(i)*V(j)). The list V of normalization factors must be set using the SetNormalization method before the filter is executed. When set to DIAGONAL_VARIANCE, each entry cov(i,j) is divided by sqrt(cov(i,i)*cov(j,j)). Warning: Although this is accepted practice in some fields, some people think you should not turn this option on unless there is a good physically-based reason for doing so. Much better instead to determine how component magnitudes should be compared using physical reasoning and use DIAGONAL_SPECIFIED, TRIANGLE_SPECIFIED, or perform some pre-processing to shift and scale input data columns appropriately than to expect magical results from a shady normalization hack.

virtual void vtkPCAStatistics::SetNormalizationSchemeByName ( const char * sname ) [virtual]

This determines how (or if) the covariance matrix cov is normalized before PCA. When set to NONE, no normalization is performed. This is the default. When set to TRIANGLE_SPECIFIED, each entry cov(i,j) is divided by V(i,j). The list V of normalization factors must be set using the SetNormalization method before the filter is executed. When set to DIAGONAL_SPECIFIED, each entry cov(i,j) is divided by sqrt(V(i)*V(j)). The list V of normalization factors must be set using the SetNormalization method before the filter is executed. When set to DIAGONAL_VARIANCE, each entry cov(i,j) is divided by sqrt(cov(i,i)*cov(j,j)). Warning: Although this is accepted practice in some fields, some people think you should not turn this option on unless there is a good physically-based reason for doing so. Much better instead to determine how component magnitudes should be compared using physical reasoning and use DIAGONAL_SPECIFIED, TRIANGLE_SPECIFIED, or perform some pre-processing to shift and scale input data columns appropriately than to expect magical results from a shady normalization hack.

virtual const char* vtkPCAStatistics::GetNormalizationSchemeName ( int scheme ) [virtual]

This determines how (or if) the covariance matrix cov is normalized before PCA. When set to NONE, no normalization is performed. This is the default. When set to TRIANGLE_SPECIFIED, each entry cov(i,j) is divided by V(i,j). The list V of normalization factors must be set using the SetNormalization method before the filter is executed. When set to DIAGONAL_SPECIFIED, each entry cov(i,j) is divided by sqrt(V(i)*V(j)). The list V of normalization factors must be set using the SetNormalization method before the filter is executed. When set to DIAGONAL_VARIANCE, each entry cov(i,j) is divided by sqrt(cov(i,i)*cov(j,j)). Warning: Although this is accepted practice in some fields, some people think you should not turn this option on unless there is a good physically-based reason for doing so. Much better instead to determine how component magnitudes should be compared using physical reasoning and use DIAGONAL_SPECIFIED, TRIANGLE_SPECIFIED, or perform some pre-processing to shift and scale input data columns appropriately than to expect magical results from a shady normalization hack.

virtual vtkTable* vtkPCAStatistics::GetSpecifiedNormalization ( ) [virtual]

These methods allow you to set/get values used to normalize the covariance matrix before PCA. The normalization values apply to all requests, so you do not specify a single vector but a 3-column table. The first two columns contain the names of columns from input 0 and the third column contains the value to normalize the corresponding entry in the covariance matrix. The table must always have 3 columns even when the NormalizationScheme is DIAGONAL_SPECIFIED. When only diagonal entries are to be used, only table rows where the first two columns are identical to one another will be employed. If there are multiple rows specifying different values for the same pair of columns, the entry nearest the bottom of the table takes precedence. These functions are actually convenience methods that set/get the third input of the filter. Because the table is the third input, you may use other filters to produce a table of normalizations and have the pipeline take care of updates. Any missing entries will be set to 1.0 and a warning issued. An error will occur if the third input to the filter is not set and the NormalizationScheme is DIAGONAL_SPECIFIED or TRIANGLE_SPECIFIED.

virtual void vtkPCAStatistics::SetSpecifiedNormalization ( vtkTable * ) [virtual]

These methods allow you to set/get values used to normalize the covariance matrix before PCA. The normalization values apply to all requests, so you do not specify a single vector but a 3-column table. The first two columns contain the names of columns from input 0 and the third column contains the value to normalize the corresponding entry in the covariance matrix. The table must always have 3 columns even when the NormalizationScheme is DIAGONAL_SPECIFIED. When only diagonal entries are to be used, only table rows where the first two columns are identical to one another will be employed. If there are multiple rows specifying different values for the same pair of columns, the entry nearest the bottom of the table takes precedence. These functions are actually convenience methods that set/get the third input of the filter. Because the table is the third input, you may use other filters to produce a table of normalizations and have the pipeline take care of updates. Any missing entries will be set to 1.0 and a warning issued. An error will occur if the third input to the filter is not set and the NormalizationScheme is DIAGONAL_SPECIFIED or TRIANGLE_SPECIFIED.

void vtkPCAStatistics::GetEigenvalues	(	int	request,
		vtkDoubleArray *
	)

Get the eigenvalues. This function: void GetEigenvalues(int request, int i, vtkDoubleArray*); does all of the work. The other functions simply call this function with the appropriate parameters. These functions are not valid unless Update() has been called and the Derive option is turned on.

void vtkPCAStatistics::GetEigenvalues ( vtkDoubleArray * )

Get the eigenvalues. This function: void GetEigenvalues(int request, int i, vtkDoubleArray*); does all of the work. The other functions simply call this function with the appropriate parameters. These functions are not valid unless Update() has been called and the Derive option is turned on.

double vtkPCAStatistics::GetEigenvalue	(	int	request,
		int	i
	)

Get the eigenvalues. This function: void GetEigenvalues(int request, int i, vtkDoubleArray*); does all of the work. The other functions simply call this function with the appropriate parameters. These functions are not valid unless Update() has been called and the Derive option is turned on.

double vtkPCAStatistics::GetEigenvalue ( int i )

Get the eigenvalues. This function: void GetEigenvalues(int request, int i, vtkDoubleArray*); does all of the work. The other functions simply call this function with the appropriate parameters. These functions are not valid unless Update() has been called and the Derive option is turned on.

void vtkPCAStatistics::GetEigenvectors	(	int	request,
		vtkDoubleArray *	eigenvectors
	)

Get the eigenvectors. This function: void GetEigenvectors(int request, vtkDoubleArray* eigenvectors) does all of the work. The other functions are convenience functions that call this function with default arguments. These functions are not valid unless Update() has been called and the Derive option is turned on.

void vtkPCAStatistics::GetEigenvectors ( vtkDoubleArray * eigenvectors )

Get the eigenvectors. This function: void GetEigenvectors(int request, vtkDoubleArray* eigenvectors) does all of the work. The other functions are convenience functions that call this function with default arguments. These functions are not valid unless Update() has been called and the Derive option is turned on.

void vtkPCAStatistics::GetEigenvector	(	int	i,
		vtkDoubleArray *	eigenvector
	)

Get the eigenvectors. This function: void GetEigenvectors(int request, vtkDoubleArray* eigenvectors) does all of the work. The other functions are convenience functions that call this function with default arguments. These functions are not valid unless Update() has been called and the Derive option is turned on.

void vtkPCAStatistics::GetEigenvector	(	int	request,
		int	i,
		vtkDoubleArray *	eigenvector
	)

Get the eigenvectors. This function: void GetEigenvectors(int request, vtkDoubleArray* eigenvectors) does all of the work. The other functions are convenience functions that call this function with default arguments. These functions are not valid unless Update() has been called and the Derive option is turned on.

virtual void vtkPCAStatistics::SetBasisScheme ( int ) [virtual]

This variable controls the dimensionality of output tuples in Assess mode. Consider the case where you have requested a PCA on D columns. When set to vtkPCAStatistics::FULL_BASIS, the entire set of basis vectors is used to derive new coordinates for each tuple being assessed. In this mode, you are guaranteed to have output tuples of the same dimension as the input tuples. (That dimension is D, so there will be D additional columns added to the table for the request.) When set to vtkPCAStatistics::FIXED_BASIS_SIZE, only the first N basis vectors are used to derive new coordinates for each tuple being assessed. In this mode, you are guaranteed to have output tuples of dimension min(N,D). You must set N prior to assessing data using the SetFixedBasisSize() method. When N < D, this turns the PCA into a projection (instead of change of basis). When set to vtkPCAStatistics::FIXED_BASIS_ENERGY, the number of basis vectors used to derive new coordinates for each tuple will be the minimum number of columns N that satisfy

$\frac{\sum_{i=1}^{N} \lambda_i}{\sum_{i=1}^{D} \lambda_i} < T$

You must set T prior to assessing data using the SetFixedBasisEnergy() method. When T < 1, this turns the PCA into a projection (instead of change of basis). By default BasisScheme is set to vtkPCAStatistics::FULL_BASIS.

virtual int vtkPCAStatistics::GetBasisScheme ( ) [virtual]

This variable controls the dimensionality of output tuples in Assess mode. Consider the case where you have requested a PCA on D columns. When set to vtkPCAStatistics::FULL_BASIS, the entire set of basis vectors is used to derive new coordinates for each tuple being assessed. In this mode, you are guaranteed to have output tuples of the same dimension as the input tuples. (That dimension is D, so there will be D additional columns added to the table for the request.) When set to vtkPCAStatistics::FIXED_BASIS_SIZE, only the first N basis vectors are used to derive new coordinates for each tuple being assessed. In this mode, you are guaranteed to have output tuples of dimension min(N,D). You must set N prior to assessing data using the SetFixedBasisSize() method. When N < D, this turns the PCA into a projection (instead of change of basis). When set to vtkPCAStatistics::FIXED_BASIS_ENERGY, the number of basis vectors used to derive new coordinates for each tuple will be the minimum number of columns N that satisfy

$\frac{\sum_{i=1}^{N} \lambda_i}{\sum_{i=1}^{D} \lambda_i} < T$

You must set T prior to assessing data using the SetFixedBasisEnergy() method. When T < 1, this turns the PCA into a projection (instead of change of basis). By default BasisScheme is set to vtkPCAStatistics::FULL_BASIS.

virtual const char* vtkPCAStatistics::GetBasisSchemeName ( int schemeIndex ) [virtual]

This variable controls the dimensionality of output tuples in Assess mode. Consider the case where you have requested a PCA on D columns. When set to vtkPCAStatistics::FULL_BASIS, the entire set of basis vectors is used to derive new coordinates for each tuple being assessed. In this mode, you are guaranteed to have output tuples of the same dimension as the input tuples. (That dimension is D, so there will be D additional columns added to the table for the request.) When set to vtkPCAStatistics::FIXED_BASIS_SIZE, only the first N basis vectors are used to derive new coordinates for each tuple being assessed. In this mode, you are guaranteed to have output tuples of dimension min(N,D). You must set N prior to assessing data using the SetFixedBasisSize() method. When N < D, this turns the PCA into a projection (instead of change of basis). When set to vtkPCAStatistics::FIXED_BASIS_ENERGY, the number of basis vectors used to derive new coordinates for each tuple will be the minimum number of columns N that satisfy

$\frac{\sum_{i=1}^{N} \lambda_i}{\sum_{i=1}^{D} \lambda_i} < T$

You must set T prior to assessing data using the SetFixedBasisEnergy() method. When T < 1, this turns the PCA into a projection (instead of change of basis). By default BasisScheme is set to vtkPCAStatistics::FULL_BASIS.

virtual void vtkPCAStatistics::SetBasisSchemeByName ( const char * schemeName ) [virtual]

This variable controls the dimensionality of output tuples in Assess mode. Consider the case where you have requested a PCA on D columns. When set to vtkPCAStatistics::FULL_BASIS, the entire set of basis vectors is used to derive new coordinates for each tuple being assessed. In this mode, you are guaranteed to have output tuples of the same dimension as the input tuples. (That dimension is D, so there will be D additional columns added to the table for the request.) When set to vtkPCAStatistics::FIXED_BASIS_SIZE, only the first N basis vectors are used to derive new coordinates for each tuple being assessed. In this mode, you are guaranteed to have output tuples of dimension min(N,D). You must set N prior to assessing data using the SetFixedBasisSize() method. When N < D, this turns the PCA into a projection (instead of change of basis). When set to vtkPCAStatistics::FIXED_BASIS_ENERGY, the number of basis vectors used to derive new coordinates for each tuple will be the minimum number of columns N that satisfy

$\frac{\sum_{i=1}^{N} \lambda_i}{\sum_{i=1}^{D} \lambda_i} < T$

You must set T prior to assessing data using the SetFixedBasisEnergy() method. When T < 1, this turns the PCA into a projection (instead of change of basis). By default BasisScheme is set to vtkPCAStatistics::FULL_BASIS.

virtual void vtkPCAStatistics::SetFixedBasisSize ( int ) [virtual]

The number of basis vectors to use. See SetBasisScheme() for more information. When FixedBasisSize <= 0 (the default), the fixed basis size scheme is equivalent to the full basis scheme.

virtual int vtkPCAStatistics::GetFixedBasisSize ( ) [virtual]

The number of basis vectors to use. See SetBasisScheme() for more information. When FixedBasisSize <= 0 (the default), the fixed basis size scheme is equivalent to the full basis scheme.

virtual void vtkPCAStatistics::SetFixedBasisEnergy ( double ) [virtual]

The minimum energy the new basis should use, as a fraction. See SetBasisScheme() for more information. When FixedBasisEnergy >= 1 (the default), the fixed basis energy scheme is equivalent to the full basis scheme.

virtual double vtkPCAStatistics::GetFixedBasisEnergy ( ) [virtual]

The minimum energy the new basis should use, as a fraction. See SetBasisScheme() for more information. When FixedBasisEnergy >= 1 (the default), the fixed basis energy scheme is equivalent to the full basis scheme.

virtual bool vtkPCAStatistics::SetParameter	(	const char *	parameter,
		int	index,
		vtkVariant	value
	)			`[virtual]`

A convenience method (in particular for access from other applications) to set parameter values. Return true if setting of requested parameter name was excuted, false otherwise.

Reimplemented from vtkStatisticsAlgorithm.

virtual int vtkPCAStatistics::FillInputPortInformation	(	int	port,
		vtkInformation *	info
	)			`[protected, virtual]`

This algorithm accepts a vtkTable containing normalization values for its fourth input (port 3). We override FillInputPortInformation to indicate this.

Reimplemented from vtkStatisticsAlgorithm.

virtual void vtkPCAStatistics::Derive ( vtkMultiBlockDataSet * inMeta ) [protected, virtual]

Execute the calculations required by the Derive option.

Reimplemented from vtkMultiCorrelativeStatistics.

virtual void vtkPCAStatistics::Test	(	vtkTable *	,
		vtkMultiBlockDataSet *	,
		vtkTable *
	)			`[protected, virtual]`

Execute the calculations required by the Test option.

Reimplemented from vtkMultiCorrelativeStatistics.

virtual void vtkPCAStatistics::Assess	(	vtkTable *	,
		vtkMultiBlockDataSet *	,
		vtkTable *
	)			`[protected, virtual]`

Execute the calculations required by the Assess option.

Reimplemented from vtkMultiCorrelativeStatistics.

virtual void vtkPCAStatistics::SelectAssessFunctor	(	vtkTable *	inData,
		vtkDataObject *	inMeta,
		vtkStringArray *	rowNames,
		AssessFunctor *&	dfunc
	)			`[protected, virtual]`