smile.clustering

Class MEC<T>

java.lang.Object

smile.clustering.PartitionClustering

smile.clustering.MEC<T>

All Implemented Interfaces:

java.io.Serializable, java.lang.Comparable<MEC<T>>

public class MEC<T>
extends PartitionClustering
implements java.lang.Comparable<MEC<T>>

Non-parametric Minimum Conditional Entropy Clustering. This method performs very well especially when the exact number of clusters is unknown. The method can also correctly reveal the structure of data and effectively identify outliers simultaneously.

The clustering criterion is based on the conditional entropy H(C | x), where C is the cluster label and x is an observation. According to Fano's inequality, we can estimate C with a low probability of error only if the conditional entropy H(C | X) is small. MEC also generalizes the criterion by replacing Shannon's entropy with Havrda-Charvat's structural α-entropy. Interestingly, the minimum entropy criterion based on structural α-entropy is equal to the probability error of the nearest neighbor method when α= 2. To estimate p(C | x), MEC employs Parzen density estimation, a nonparametric approach.

MEC is an iterative algorithm starting with an initial partition given by any other clustering methods, e.g. k-means, CLARNAS, hierarchical clustering, etc. Note that a random initialization is NOT appropriate.

References

1. Haifeng Li, Keshu Zhang, and Tao Jiang. Minimum Entropy Clustering and Applications to Gene Expression Analysis. CSB, 2004.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
double	entropy The conditional entropy as the objective function.
double	radius The range of neighborhood.

Fields inherited from class smile.clustering.PartitionClustering

k, OUTLIER, size, y

Constructor Summary

Constructors

Constructor and Description
MEC(double entropy, double radius, RNNSearch<T,T> nns, int k, int[] y) Constructor.

Method Summary

Modifier and Type	Method and Description
int	compareTo(MEC<T> o)
static <T> MEC<T>	fit(T[] data, smile.math.distance.Distance<T> distance, int k, double radius) Clustering the data.
static <T> MEC<T>	fit(T[] data, RNNSearch<T,T> nns, int k, double radius, int[] y, double tol) Clustering the data.
int	predict(T x) Cluster a new instance.
java.lang.String	toString()

Methods inherited from class smile.clustering.PartitionClustering

run, seed

Methods inherited from class java.lang.Object

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

Field Detail

entropy

public final double entropy

The conditional entropy as the objective function.

radius

public final double radius

The range of neighborhood.

Constructor Detail

MEC

public MEC(double entropy,
           double radius,
           RNNSearch<T,T> nns,
           int k,
           int[] y)

Constructor.

Parameters:

entropy - the conditional entropy of clusters.

radius - the neighborhood radius.

nns - the data structure for neighborhood search.

k - the number of clusters.

y - the cluster labels.

Method Detail

compareTo

public int compareTo(MEC<T> o)

Specified by:

compareTo in interface java.lang.Comparable<MEC<T>>

fit

public static <T> MEC<T> fit(T[] data,
                             smile.math.distance.Distance<T> distance,
                             int k,
                             double radius)

Clustering the data.

Parameters:

data - the observations.

distance - the distance measure for neighborhood search.

k - the number of clusters. Note that this is just a hint. The final number of clusters may be less.

radius - the neighborhood radius.

fit

public static <T> MEC<T> fit(T[] data,
                             RNNSearch<T,T> nns,
                             int k,
                             double radius,
                             int[] y,
                             double tol)

Clustering the data.

Parameters:

data - the observations.

nns - the neighborhood search data structure.

k - the number of clusters. Note that this is just a hint. The final number of clusters may be less.

radius - the neighborhood radius.

y - the initial clustering labels, which could be produced by any other clustering methods.

tol - the tolerance of convergence test.

predict

public int predict(T x)

Cluster a new instance.

Parameters:

x - a new instance.

Returns:

the cluster label. Note that it may be PartitionClustering.OUTLIER.

toString

public java.lang.String toString()

Overrides:

toString in class PartitionClustering