smile.clustering

Class PartitionClustering

java.lang.Object

smile.clustering.PartitionClustering

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

CentroidClustering, DBSCAN, DENCLUE, MEC, SpectralClustering

public abstract class PartitionClustering
extends java.lang.Object
implements java.io.Serializable

Partition clustering. Partition methods classify the observations into distinct non-overlapping groups.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
int	k The number of clusters.
static int	OUTLIER Cluster label for outliers or noises.
int[]	size The number of observations in each cluster.
int[]	y The cluster labels of data.

Constructor Summary

Constructors

Constructor and Description
PartitionClustering(int k, int[] y) Constructor.

Method Summary

Modifier and Type	Method and Description
static <T extends PartitionClustering & java.lang.Comparable<? super T>> T	run(int runs, java.util.function.Supplier<T> clustering) Runs a clustering algorithm multiple times and return the best one (e.g.
static <T> double[]	seed(T[] data, T[] medoids, int[] y, java.util.function.ToDoubleBiFunction<T,T> distance) Initialize cluster membership of input objects with K-Means++ algorithm.
java.lang.String	toString()

Methods inherited from class java.lang.Object

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

Field Detail

OUTLIER

public static final int OUTLIER

Cluster label for outliers or noises.

See Also:

Constant Field Values

k

public final int k

The number of clusters.

y

public final int[] y

The cluster labels of data.

size

public final int[] size

The number of observations in each cluster.

Constructor Detail

PartitionClustering

public PartitionClustering(int k,
                           int[] y)

Constructor.

Parameters:

k - the number of clusters.

y - the cluster labels.

Method Detail

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

seed

public static <T> double[] seed(T[] data,
                                T[] medoids,
                                int[] y,
                                java.util.function.ToDoubleBiFunction<T,T> distance)

Initialize cluster membership of input objects with K-Means++ algorithm. Many clustering methods, e.g. k-means, need a initial clustering configuration as a seed.

K-Means++ is based on the intuition of spreading the k initial cluster centers away from each other. The first cluster center is chosen uniformly at random from the data points that are being clustered, after which each subsequent cluster center is chosen from the remaining data points with probability proportional to its distance squared to the point's closest cluster center.

The exact algorithm is as follows:

1. Choose one center uniformly at random from among the data points.
2. For each data point x, compute D(x), the distance between x and the nearest center that has already been chosen.
3. Choose one new data point at random as a new center, using a weighted probability distribution where a point x is chosen with probability proportional to D²(x).
4. Repeat Steps 2 and 3 until k centers have been chosen.
5. Now that the initial centers have been chosen, proceed using standard k-means clustering.

This seeding method gives out considerable improvements in the final error of k-means. Although the initial selection in the algorithm takes extra time, the k-means part itself converges very fast after this seeding and thus the algorithm actually lowers the computation time too.

References

1. D. Arthur and S. Vassilvitskii. "K-means++: the advantages of careful seeding". ACM-SIAM symposium on Discrete algorithms, 1027-1035, 2007.
2. Anna D. Peterson, Arka P. Ghosh and Ranjan Maitra. A systematic evaluation of different methods for initializing the K-means clustering algorithm. 2010.

Type Parameters:

T - the type of input object.

Parameters:

data - data objects array of size n.

medoids - an array of size k to store cluster medoids on output.

y - an array of size n to store cluster labels on output.

Returns:

an array of size n to store the distance of each observation to nearest medoid.

run

public static <T extends PartitionClustering & java.lang.Comparable<? super T>> T run(int runs,
                                                                                      java.util.function.Supplier<T> clustering)

Runs a clustering algorithm multiple times and return the best one (e.g. smallest distortion).

Parameters:

runs - the number of runs.