Package elki.datasource.filter.normalization.columnwise

Class AttributeWiseVarianceNormalization<V extends NumberVector>

java.lang.Object

elki.datasource.filter.AbstractConversionFilter<I,O>

elki.datasource.filter.AbstractVectorConversionFilter<V,V>

elki.datasource.filter.normalization.columnwise.AttributeWiseVarianceNormalization<V>

Type Parameters:

V - vector type

All Implemented Interfaces:

Normalization<V>, ObjectFilter

@Alias({"z","standard","standardize","standardization"})
@Priority(200)
public class AttributeWiseVarianceNormalization<V extends NumberVector>
extends AbstractVectorConversionFilter<V,V>
implements Normalization<V>

Class to perform and undo a normalization on real vectors with respect to given mean and standard deviation in each dimension.

We use the biased variance (MeanVariance.getPopulationStddev()), because this produces that with exactly standard deviation 1. While often the unbiased estimate (MeanVariance.getSampleStddev()) is more appropriate, it will not ensure this interesting property. For large data, the difference will be small anyway.

Since:

0.4.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	AttributeWiseVarianceNormalization.Par<V extends NumberVector>	Parameterization class.

Field Summary

Fields

Modifier and Type	Field	Description
private static Logging	LOG	Class logger.
private double[]	mean	Stores the mean in each dimension.
(package private) MeanVariance[]	mvs	Temporary storage used during initialization.
private double[]	stddev	Stores the standard deviation in each dimension.

Fields inherited from class elki.datasource.filter.AbstractVectorConversionFilter

factory

Constructor Summary

Constructors

Constructor	Description
AttributeWiseVarianceNormalization()	Constructor.
AttributeWiseVarianceNormalization(double[] mean, double[] stddev)	Constructor.

Method Summary

Modifier and Type	Method	Description
protected SimpleTypeInformation<? super V>	convertedType(SimpleTypeInformation<V> in)	Get the output type from the input type after conversion.
protected V	filterSingleObject(V featureVector)	Normalize a single instance.
protected SimpleTypeInformation<? super V>	getInputTypeRestriction()	Get the input type restriction used for negotiating the data query.
protected Logging	getLogger()	Class logger.
private double	normalize(int d, double val)	Normalize a single dimension.
protected void	prepareComplete()	Complete the initialization phase.
protected void	prepareProcessInstance(V featureVector)	Process a single object during initialization.
protected boolean	prepareStart(SimpleTypeInformation<V> in)	Return "true" when the normalization needs initialization (two-pass filtering!).
private double	restore(int d, double val)	Restore a single dimension.
V	restore(V featureVector)	Transforms a feature vector to the original attribute ranges.
java.lang.String	toString()
LinearEquationSystem	transform(LinearEquationSystem linearEquationSystem)	Transforms a linear equation system describing linear dependencies derived on the normalized space into a linear equation system describing linear dependencies quantitatively adapted to the original space.

Methods inherited from class elki.datasource.filter.AbstractVectorConversionFilter

initializeOutputType

Methods inherited from class elki.datasource.filter.AbstractConversionFilter

filter

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface elki.datasource.filter.ObjectFilter

filter

Field Detail

LOG

private static final Logging LOG

Class logger.

mean

private double[] mean

Stores the mean in each dimension.

stddev

private double[] stddev

Stores the standard deviation in each dimension.

mvs

MeanVariance[] mvs

Temporary storage used during initialization.

Constructor Detail

AttributeWiseVarianceNormalization

public AttributeWiseVarianceNormalization()

Constructor.

AttributeWiseVarianceNormalization

public AttributeWiseVarianceNormalization(double[] mean,
                                          double[] stddev)

Constructor.

Parameters:

mean - Mean value

stddev - Standard deviation

Method Detail

prepareStart

protected boolean prepareStart(SimpleTypeInformation<V> in)

Description copied from class: AbstractConversionFilter

Return "true" when the normalization needs initialization (two-pass filtering!).

Overrides:

prepareStart in class AbstractConversionFilter<V extends NumberVector,V extends NumberVector>

Parameters:

in - Input type information

Returns:

true or false

prepareProcessInstance

protected void prepareProcessInstance(V featureVector)

Description copied from class: AbstractConversionFilter

Process a single object during initialization.

Overrides:

prepareProcessInstance in class AbstractConversionFilter<V extends NumberVector,V extends NumberVector>

Parameters:

featureVector - Object to process

prepareComplete

protected void prepareComplete()

Description copied from class: AbstractConversionFilter

Complete the initialization phase.

Overrides:

prepareComplete in class AbstractConversionFilter<V extends NumberVector,V extends NumberVector>

filterSingleObject

protected V filterSingleObject(V featureVector)

Description copied from class: AbstractConversionFilter

Normalize a single instance. You can implement this as UnsupportedOperationException if you override both public "normalize" functions!

Specified by:

filterSingleObject in class AbstractConversionFilter<V extends NumberVector,V extends NumberVector>

Parameters:

featureVector - Database object to normalize

Returns:

Normalized database object

restore

public V restore(V featureVector)
          throws NonNumericFeaturesException

Description copied from interface: Normalization

Transforms a feature vector to the original attribute ranges.

Specified by:

restore in interface Normalization<V extends NumberVector>

Parameters:

featureVector - a feature vector to be transformed into original space

Returns:

a feature vector transformed into original space corresponding to the given feature vector

Throws:

NonNumericFeaturesException - feature vector is not compatible with values initialized during normalization

normalize

private double normalize(int d,
                         double val)

Normalize a single dimension.

Parameters:

d - Dimension

val - Value

Returns:

Normalized value

restore

private double restore(int d,
                       double val)

Restore a single dimension.

Parameters:

d - Dimension

val - Value

Returns:

Normalized value

transform

public LinearEquationSystem transform(LinearEquationSystem linearEquationSystem)

Description copied from interface: Normalization

Transforms a linear equation system describing linear dependencies derived on the normalized space into a linear equation system describing linear dependencies quantitatively adapted to the original space.

Specified by:

transform in interface Normalization<V extends NumberVector>

Parameters:

linearEquationSystem - the linear equation system to be transformed

Returns:

a linear equation system describing linear dependencies derived on the normalized space transformed into a linear equation system describing linear dependencies quantitatively adapted to the original space

toString

public java.lang.String toString()

Overrides:

toString in class AbstractConversionFilter<V extends NumberVector,V extends NumberVector>

convertedType

protected SimpleTypeInformation<? super V> convertedType(SimpleTypeInformation<V> in)

Description copied from class: AbstractConversionFilter

Get the output type from the input type after conversion.

Specified by:

convertedType in class AbstractConversionFilter<V extends NumberVector,V extends NumberVector>

Parameters:

in - input type restriction

Returns:

output type restriction

getLogger

protected Logging getLogger()

Description copied from class: AbstractConversionFilter

Class logger.

Specified by:

getLogger in class AbstractConversionFilter<V extends NumberVector,V extends NumberVector>

Returns:

Logger

getInputTypeRestriction

protected SimpleTypeInformation<? super V> getInputTypeRestriction()

Description copied from class: AbstractConversionFilter

Get the input type restriction used for negotiating the data query.

Specified by:

getInputTypeRestriction in class AbstractConversionFilter<V extends NumberVector,V extends NumberVector>

Returns:

Type restriction