com.imsl.stat
Class ClusterKMeans

java.lang.Object
  com.imsl.stat.ClusterKMeans

All Implemented Interfaces:

Cloneable, Serializable

public class ClusterKMeans

extends Object

implements Serializable, Cloneable

Perform a K-means (centroid) cluster analysis.

ClusterKMeans is an implementation of Algorithm AS 136 by Hartigan and Wong (1979). It computes K-means (centroid) Euclidean metric clusters for an input matrix starting with initial estimates of the K cluster means. It allows for missing values (coded as NaN, not a number) and for weights and frequencies.

Let p denote the number of variables to be used in computing the Euclidean distance between observations. The idea in K-means cluster analysis is to find a clustering (or grouping) of the observations so as to minimize the total within-cluster sums of squares. In this case, the total sums of squares within each cluster is computed as the sum of the centered sum of squares over all nonmissing values of each variable. That is,

where denotes the row index of the m-th observation in the i-th cluster in the matrix X; is the number of rows of X assigned to group i; f denotes the frequency of the observation; w denotes its weight; d is zero if the j-th variable on observation is missing, otherwise is one; and is the average of the nonmissing observations for variable j in group i. This method sequentially processes each observation and reassigns it to another cluster if doing so results in a decrease in the total within-cluster sums of squares. See Hartigan and Wong (1979) or Hartigan (1975) for details.

See Also:

ClusterKMeans Example, Serialized Form

Nested Class Summary

static class	ClusterKMeans.ClusterNoPointsException There is a cluster with no points
static class	ClusterKMeans.NoConvergenceException Convergence did not occur within the maximum number of iterations.
static class	ClusterKMeans.NonnegativeFreqException Frequencies must be nonnegative.
static class	ClusterKMeans.NonnegativeWeightException Weights must be nonnegative.

Constructor Summary

ClusterKMeans(double[][] x, double[][] cs)
Constructor for ClusterKMeans.

Method Summary

double[][]	compute() Computes the cluster means.
int[]	getClusterCounts() Returns the number of observations in each cluster.
int[]	getClusterMembership() Returns the cluster membership for each observation.
double[]	getClusterSSQ() Returns the within sum of squares for each cluster.
void	setFrequencies(double[] frequencies) Sets the frequency for each observation.
void	setMaxIterations(int iterations) Sets the maximum number of iterations.
void	setWeights(double[] weights) Sets the weight for each observation.

Methods inherited from class java.lang.Object

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

Constructor Detail

ClusterKMeans

public ClusterKMeans(double[][] x,
                     double[][] cs)

Constructor for ClusterKMeans.

Parameters:

x - A double matrix containing the observations to be clustered.

cs - A double matrix containing the cluster seeds, i.e. estimates for the cluster centers.

Throws:

IllegalArgumentException - is thrown if x.length, x[0].length are equal 0, or cs.length is less than 1.

Method Detail

compute

public final double[][] compute()
                         throws ClusterKMeans.NoConvergenceException,
                                ClusterKMeans.ClusterNoPointsException

Computes the cluster means.

Returns:

A double matrix containing computed result.

Throws:

ClusterKMeans.NonnegativeFreqException - is thrown if a frequency is negative.

ClusterKMeans.NonnegativeWeightException - is thrown if a weight is negative.

ClusterKMeans.NoConvergenceException - is thrown if convergence did not occur within the maximum number of iterations.

ClusterKMeans.ClusterNoPointsException - is thrown if the cluster seed yields a cluster with no points.

getClusterCounts

public int[] getClusterCounts()

Returns the number of observations in each cluster.

Returns:

An int array containing the number of observations in each cluster.

getClusterMembership

public int[] getClusterMembership()

Returns the cluster membership for each observation.

Returns:

An int array containing the cluster membership for each observation. Cluster membership 1 indicates the observation belongs to cluster 1, cluster membership 2 indicates the observation belongs to cluster 2, etc.

getClusterSSQ

public double[] getClusterSSQ()

Returns the within sum of squares for each cluster.

Returns:

A double array containing the within sum of squares for each cluster.

setFrequencies

public void setFrequencies(double[] frequencies)
                    throws ClusterKMeans.NonnegativeFreqException

Sets the frequency for each observation.

Parameters:

frequencies - A double array of size x.length containing the frequency for each observation. Default: frequencies[] = 1.

Throws:

ClusterKMeans.NonnegativeFreqException

setMaxIterations

public void setMaxIterations(int iterations)

Sets the maximum number of iterations.

Parameters:

iterations - An int scalar specifying the maximum number of iterations. Default: interations = 30.

setWeights

public void setWeights(double[] weights)
                throws ClusterKMeans.NonnegativeWeightException

Sets the weight for each observation.

Parameters:

weights - A double array of size x.length containing the weight for each observation. Default: weights[] = 1.

Throws:

ClusterKMeans.NonnegativeWeightException