MinimumVolumeClassifier¶

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class MinimumVolumeClassifier(*args)¶

Classifier define by a minimum volume level set.

Parameters

mixtDistDistribution: A distribution.
alphasequence of float, unique and sorted: Confidence levels

See also

Classifier

Notes

This implements a mixture classifier which is a particular classifier based on a minimum volume confidence domain.

The minimum volume confidence domain $A^*_{\alpha_i}$ is the set of minimum volume and which measure is at least $\alpha_i$ . It is defined by:

$A^*_{\alpha_i} = \argmin_{A \in \Rset^d\, | \, \mu(A) \geq \alpha_i} \lambda(A)$

where $\lambda$ is the Lebesgue measure on $\Rset^d$ . Under some general conditions on $\mu$ (for example, no flat regions), the set $A^*_{\alpha_i}$ is unique and realises the minimum: $\mu(A^*_{\alpha_i}) = \alpha$ . We show that $A^*_{\alpha_i}$ writes:

$A^*_{\alpha_i} = \{ \vect{x} \in \Rset^d \, | \, p(\vect{x}) \geq p_{\alpha_i} \}$

The classifier proposes 2 classes. The rule to assign a point $\vect{x}$ to a class k is defined as follows: $k = \argmin_i \text{with} p(\vect{x}) > p_{\alpha_i}$

The grade of $\vect{x}$ with respect to the class k is $log p(\vect{x})$ if $\vect{x}$ belongs to class k else $- log p(\vect{x})$ .

Examples

>>> import openturns as ot
>>> R2 = ot.CorrelationMatrix(2)
>>> dists = [ot.Normal([-1.0, 2.0], [1.0]*2, R2), ot.Normal([1.0, -2.0], [1.5]*2, R2)]
>>> mixture = ot.Mixture(dists)
>>> sample = mixture.getSample(1000)
>>> distribution = ot.KernelSmoothing().build(sample)
>>> algo = ot.MinimumVolumeClassifier(distribution, [0.8])
>>> algo.classify(distribution.getMean())
0
>>> algo.classify([100.0]*2)
1
>>> sample = distribution.getSample(100)
>>> graph = algo.drawSample(sample, [0, 1])

Methods

`classify`(*args)	Classify points according to the classifier.
`drawContour`(alpha)	Draw distribution contours.
`drawContourAndSample`(alpha, sample, classes)	Draw distribution contour and classified sample.
`drawSample`(sample, classes)	Draw classified sample.
`getClassName`()	Accessor to the object's name.
`getDimension`()	Accessor to the dimension.
`getDistribution`()	Accessor to the distribution.
`getId`()	Accessor to the object's id.
`getLevelSet`([j])	LevelSet accessor.
`getName`()	Accessor to the object's name.
`getNumberOfClasses`()	Accessor to the number of classes.
`getShadowedId`()	Accessor to the object's shadowed id.
`getThreshold`()	Accessor to the threshold.
`getVerbose`()	Accessor to the verbosity.
`getVisibility`()	Accessor to the object's visibility state.
`grade`(inP, outC)	Grade points according to the classifier.
`hasName`()	Test if the object is named.
`hasVisibleName`()	Test if the object has a distinguishable name.
`isParallel`()	Accessor to the parallel flag.
`setName`(name)	Accessor to the object's name.
`setParallel`(flag)	Accessor to the parallel flag.
`setShadowedId`(id)	Accessor to the object's shadowed id.
`setVerbose`(verbose)	Accessor to the verbosity.
`setVisibility`(visible)	Accessor to the object's visibility state.

__init__(*args)¶

classify(*args)¶

Classify points according to the classifier.

Parameters

inputsequence of float or 2-d a sequence of float: A point or set of points to classify.

Returns

clsint or Indices: The class index of the input points, or indices of the classes of each points.

drawContour(alpha)¶

Draw distribution contours.

Parameters

alphasequence of float: Confidence levels

Returns

graphGraph: The value of the density function defining the frontier of the domain.

drawContourAndSample(alpha, sample, classes)¶

Draw distribution contour and classified sample.

Parameters

alphasequence of float: Confidence levels
sampleSample: A sample to classifiy.
classessequence of int: Classes to select

Returns

graphGraph: The value of the density function defining the frontier of the domain.

drawSample(sample, classes)¶

Draw classified sample.

Parameters

sampleSample: A sample to classifiy.
classessequence of int: Classes to select

Returns

graphGraph: The value of the density function defining the frontier of the domain.

getClassName()¶

Accessor to the object’s name.

Returns

class_namestr: The object class name (object.__class__.__name__).

getDimension()¶

Accessor to the dimension.

Returns

dimint: The dimension of the classifier.

getDistribution()¶

Accessor to the distribution.

Returns

distDistribution: The distribution.

getId()¶

Accessor to the object’s id.

Returns

idint: Internal unique identifier.

getLevelSet(j=0)¶

LevelSet accessor.

Parameters

iint: Index

Returns

levelsetLevelSet: The levelset defining the domain.

getName()¶

Accessor to the object’s name.

Returns

namestr: The name of the object.

getNumberOfClasses()¶

Accessor to the number of classes.

Returns

n_classesint: The number of classes

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns

idint: Internal unique identifier.

getThreshold()¶

Accessor to the threshold.

Returns

thresholdPoint: The values $p_{\alpha_i}$ of the density function defining the frontier of the domain.

getVerbose()¶

Accessor to the verbosity.

Returns

verbbool: Logical value telling if the verbose mode has been activated.

getVisibility()¶

Accessor to the object’s visibility state.

Returns

visiblebool: Visibility flag.

grade(inP, outC)¶

Grade points according to the classifier.

Parameters

inputPointsequence of float or 2-d a sequence of float: A point or set of points to grade.
kint or sequence of int: The class index, or class indices.

Returns

gradefloat or Point: Grade or list of grades of each input point with respect to each class index

hasName()¶

Test if the object is named.

Returns

hasNamebool: True if the name is not empty.

hasVisibleName()¶

Test if the object has a distinguishable name.

Returns

hasVisibleNamebool: True if the name is not empty and not the default one.

isParallel()¶

Accessor to the parallel flag.

Returns

flagbool: Logical value telling if the parallel mode has been activated.

setName(name)¶

Accessor to the object’s name.

Parameters

namestr: The name of the object.

setParallel(flag)¶

Accessor to the parallel flag.

Parameters

flagbool: Logical value telling if the classification and grading are done in parallel.

setShadowedId(id)¶

Accessor to the object’s shadowed id.

Parameters

idint: Internal unique identifier.

setVerbose(verbose)¶

Accessor to the verbosity.

Parameters

verbbool: Logical value telling if the verbose mode has been activated.

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters

visiblebool: Visibility flag.

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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