MutualInformationEquiwidthDependence (ELKI: Environment for DeveLoping KDD-Applications Supported by Index-Structures)

java.lang.Object
- elki.math.statistics.dependence.MutualInformationEquiwidthDependence

All Implemented Interfaces:

Dependence
```
public class MutualInformationEquiwidthDependence
extends java.lang.Object
implements Dependence
```
Mutual Information (MI) dependence measure by dividing each attribute into equal-width bins. MI can be seen as Kullback–Leibler divergence of the joint distribution and the product of the marginal distributions.
For normalization, the resulting values are scaled by mi/log(nbins). This both cancels out the logarithm base, and normalizes for the number of bins (a uniform distribution will yield a MI with itself of 1).
TODO: Offer normalized and non-normalized variants?
For a median-based discretization, see MaximumConditionalEntropy.

Since:

0.7.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes
Modifier and Type Class Description

static class MutualInformationEquiwidthDependence.Par
Parameterization class.
- Nested classes/interfaces inherited from interface elki.math.statistics.dependence.Dependence
  Dependence.Utils

Field Summary

Fields
Modifier and Type Field Description

static MutualInformationEquiwidthDependence STATIC
Static instance.

Constructor Summary

Constructors
Modifier Constructor Description

protected MutualInformationEquiwidthDependence()
Constructor - use STATIC instance.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`<A,B> double`	`dependence(NumberArrayAdapter<?,A> adapter1, A data1, NumberArrayAdapter<?,B> adapter2, B data2)`	Measure the dependence of two variables.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface elki.math.statistics.dependence.Dependence
dependence, dependence, dependence

- Field Detail
  - STATIC
```
public static final MutualInformationEquiwidthDependence STATIC
```
    Static instance.
- Constructor Detail
  - MutualInformationEquiwidthDependence
```
protected MutualInformationEquiwidthDependence()
```
    Constructor - use STATIC instance.
- Method Detail
  - dependence
```
public <A,B> double dependence(NumberArrayAdapter<?,A> adapter1,
                                     A data1,
                                     NumberArrayAdapter<?,B> adapter2,
                                     B data2)
```
    Description copied from interface: Dependence
    
    Measure the dependence of two variables.
    This is the more flexible API, which allows using different internal data representations.
    
    Specified by:
    
    dependence in interface Dependence
    
    Type Parameters:
    
    A - First array type
    
    B - Second array type
    
    Parameters:
    
    adapter1 - First data adapter
    
    data1 - First data set
    
    adapter2 - Second data adapter
    
    data2 - Second data set
    
    Returns:
    
    Dependence measure