smile.validation.metric

Class AdjustedMutualInformation

java.lang.Object

smile.validation.metric.AdjustedMutualInformation

All Implemented Interfaces:

java.io.Serializable, ClusteringMetric

public class AdjustedMutualInformation
extends java.lang.Object
implements ClusteringMetric

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.

See Also:

Serialized Form

Nested Class Summary

Nested Classes

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

Field Summary

Fields

Modifier and Type	Field and Description
static AdjustedMutualInformation	MAX Default instance with max normalization.
static AdjustedMutualInformation	MIN Default instance with min normalization.
static AdjustedMutualInformation	SQRT Default instance with sqrt normalization.
static AdjustedMutualInformation	SUM Default instance with sum normalization.

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)).
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)).
double	score(int[] y1, int[] y2) Returns a score to measure the quality of clustering.
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

Field Detail

MAX

public static final AdjustedMutualInformation MAX

Default instance with max normalization.

MIN

public static final AdjustedMutualInformation MIN

Default instance with min normalization.

SUM

public static final AdjustedMutualInformation SUM

Default instance with sum normalization.

SQRT

public static final AdjustedMutualInformation SQRT

Default instance with sqrt normalization.

Constructor Detail

AdjustedMutualInformation

public AdjustedMutualInformation(AdjustedMutualInformation.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.

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