smile.validation

Class AdjustedMutualInformation

java.lang.Object

smile.validation.AdjustedMutualInformation

All Implemented Interfaces:

ClusterMeasure

public class AdjustedMutualInformation
extends java.lang.Object
implements ClusterMeasure

Adjusted Mutual Information (AMI) for comparing clustering. Like the Rand index, the baseline value of mutual information between two random clusterings does not take on a constant value, and tends to be larger when the two partitions have a larger number of clusters (with a fixed number of observations). AMI adopts a hypergeometric model of randomness to adjust for chance. The AMI takes a value of 1 when the two partitions are identical and 0 when the MI between two partitions equals the value expected due to chance alone. WARNING: The computation of adjustment is is really really slow.

References

1. X. Vinh, J. Epps, J. Bailey. Information Theoretic Measures for Clusterings Comparison: Variants, Properties, Normalization and Correction for Chance. JMLR, 2010.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	AdjustedMutualInformation.Method The normalization method.

Constructor Summary

Constructors

Constructor and Description
AdjustedMutualInformation(AdjustedMutualInformation.Method method) Constructor.

Method Summary

Modifier and Type	Method and Description
static double	max(int[] y1, int[] y2) Calculates the adjusted mutual information of (I(y1, y2) - E(MI)) / (max(H(y1), H(y2)) - E(MI)).
double	measure(int[] y1, int[] y2) Returns an index to measure the quality of clustering.
static double	min(int[] y1, int[] y2) Calculates the adjusted mutual information of (I(y1, y2) - E(MI)) / (min(H(y1), H(y2)) - E(MI)).
static double	sqrt(int[] y1, int[] y2) Calculates the adjusted mutual information of (I(y1, y2) - E(MI)) / (sqrt(H(y1) * H(y2)) - E(MI)).
static double	sum(int[] y1, int[] y2) Calculates the adjusted mutual information of (I(y1, y2) - E(MI)) / (0.5 * (H(y1) + H(y2)) - E(MI)).
java.lang.String	toString()

Methods inherited from class java.lang.Object

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

Constructor Detail

AdjustedMutualInformation

public AdjustedMutualInformation(AdjustedMutualInformation.Method method)

Constructor.

Parameters:

method - the normalization method.

Method Detail

measure

public double measure(int[] y1,
                      int[] y2)

Description copied from interface: ClusterMeasure

Returns an index to measure the quality of clustering.

Specified by:

measure in interface ClusterMeasure

Parameters:

y1 - the cluster labels.

y2 - the alternative cluster labels.

max

public static double max(int[] y1,
                         int[] y2)

Calculates the adjusted mutual information of (I(y1, y2) - E(MI)) / (max(H(y1), H(y2)) - E(MI)).

sum

public static double sum(int[] y1,
                         int[] y2)

Calculates the adjusted mutual information of (I(y1, y2) - E(MI)) / (0.5 * (H(y1) + H(y2)) - E(MI)).

sqrt

public static double sqrt(int[] y1,
                          int[] y2)

Calculates the adjusted mutual information of (I(y1, y2) - E(MI)) / (sqrt(H(y1) * H(y2)) - E(MI)).

min

public static double min(int[] y1,
                         int[] y2)

Calculates the adjusted mutual information of (I(y1, y2) - E(MI)) / (min(H(y1), H(y2)) - E(MI)).

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object