NormalizedMutualInformation

java.lang.Object
- smile.validation.metric.NormalizedMutualInformation

All Implemented Interfaces:

java.io.Serializable, ClusteringMetric
```
public class NormalizedMutualInformation
extends java.lang.Object
implements ClusteringMetric
```
Normalized Mutual Information (NMI) for comparing clustering. Normalized mutual information is between 0 (no mutual information) and 1 (perfect correlation). Normalization has been shown to improve the sensitiveness with respect to the difference in cluster distribution in the two clusterings.
References
1. X. Vinh, J. Epps, J. Bailey. Information Theoretic Measures for Clusterings Comparison: Variants, Properties, Normalization and Correction for Chance. JMLR, 2010.
See Also:

Serialized Form

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

static class NormalizedMutualInformation.Method
The normalization method.

Nested Classes
Modifier and Type	Class and Description
`static class`	`NormalizedMutualInformation.Method` The normalization method.

Field Summary

Fields
Modifier and Type	Field and Description
`static NormalizedMutualInformation`	`JOINT` Default instance with max normalization.
`static NormalizedMutualInformation`	`MAX` Default instance with max normalization.
`static NormalizedMutualInformation`	`MIN` Default instance with min normalization.
`static NormalizedMutualInformation`	`SQRT` Default instance with sqrt normalization.
`static NormalizedMutualInformation`	`SUM` Default instance with sum normalization.

Constructor Summary

Constructors
Constructor and Description

NormalizedMutualInformation(NormalizedMutualInformation.Method method)
Constructor.

Constructors
Constructor and Description
`NormalizedMutualInformation(NormalizedMutualInformation.Method method)` Constructor.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`static double`	`joint(int[] y1, int[] y2)` Calculates the normalized mutual information of I(y1, y2) / H(y1, y2).
`static double`	`max(int[] y1, int[] y2)` Calculates the normalized mutual information of I(y1, y2) / max(H(y1), H(y2)).
`static double`	`min(int[] y1, int[] y2)` Calculates the normalized mutual information of I(y1, y2) / min(H(y1), H(y2)).
`double`	`score(int[] y1, int[] y2)` Returns a score to measure the quality of clustering.
`static double`	`sqrt(int[] y1, int[] y2)` Calculates the normalized mutual information of I(y1, y2) / sqrt(H(y1) * H(y2)).
`static double`	`sum(int[] y1, int[] y2)` Calculates the normalized mutual information of 2 * I(y1, y2) / (H(y1) + H(y2)).
`java.lang.String`	`toString()`

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

- Field Detail
  - JOINT
```
public static final NormalizedMutualInformation JOINT
```
    Default instance with max normalization.
  - MAX
```
public static final NormalizedMutualInformation MAX
```
    Default instance with max normalization.
  - MIN
```
public static final NormalizedMutualInformation MIN
```
    Default instance with min normalization.
  - SUM
```
public static final NormalizedMutualInformation SUM
```
    Default instance with sum normalization.
  - SQRT
```
public static final NormalizedMutualInformation SQRT
```
    Default instance with sqrt normalization.
- Constructor Detail
  - NormalizedMutualInformation
```
public NormalizedMutualInformation(NormalizedMutualInformation.Method method)
```
    Constructor.
    
    Parameters:
    
    method - the normalization method.
- Method Detail
  - score
```
public double score(int[] y1,
                    int[] y2)
```
    Description copied from interface: ClusteringMetric
    
    Returns a score to measure the quality of clustering.
    
    Specified by:
    
    score in interface ClusteringMetric
    
    Parameters:
    
    y1 - the cluster labels.
    
    y2 - the alternative cluster labels.
  - joint
```
public static double joint(int[] y1,
                           int[] y2)
```
    Calculates the normalized mutual information of I(y1, y2) / H(y1, y2).
  - max
```
public static double max(int[] y1,
                         int[] y2)
```
    Calculates the normalized mutual information of I(y1, y2) / max(H(y1), H(y2)).
  - sum
```
public static double sum(int[] y1,
                         int[] y2)
```
    Calculates the normalized mutual information of 2 * I(y1, y2) / (H(y1) + H(y2)).
  - sqrt
```
public static double sqrt(int[] y1,
                          int[] y2)
```
    Calculates the normalized mutual information of I(y1, y2) / sqrt(H(y1) * H(y2)).
  - min
```
public static double min(int[] y1,
                         int[] y2)
```
    Calculates the normalized mutual information of I(y1, y2) / min(H(y1), H(y2)).
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class NormalizedMutualInformation

References

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

JOINT

MAX

MIN

SUM

SQRT

Constructor Detail

NormalizedMutualInformation

Method Detail

score

joint

max

sum

sqrt

min

toString