Package elki.clustering.correlation

Class ORCLUS

java.lang.Object

elki.clustering.AbstractProjectedClustering<Clustering<Model>>

elki.clustering.correlation.ORCLUS

All Implemented Interfaces:

elki.Algorithm, ClusteringAlgorithm<Clustering<Model>>

@Title("ORCLUS: Arbitrarily ORiented projected CLUSter generation")
@Description("Algorithm to find correlation clusters in high dimensional spaces.")
@Reference(authors="C. C. Aggarwal, P. S. Yu",
           title="Finding Generalized Projected Clusters in High Dimensional Spaces",
           booktitle="Proc. ACM SIGMOD Int. Conf. on Management of Data (SIGMOD \'00)",
           url="https://doi.org/10.1145/342009.335383",
           bibkey="DBLP:conf/sigmod/AggarwalY00")
public class ORCLUS
extends AbstractProjectedClustering<Clustering<Model>>

ORCLUS: Arbitrarily ORiented projected CLUSter generation.

Reference:

C. C. Aggarwal, P. S. Yu
Finding Generalized Projected Clusters in High Dimensional Spaces
Proc. ACM SIGMOD Int. Conf. on Management of Data (SIGMOD '00).

Since:

0.1

Author:

Elke Achtert

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
private static class	ORCLUS.ORCLUSCluster	Encapsulates the attributes of a cluster.
static class	ORCLUS.Par	Parameterization class.
private static class	ORCLUS.ProjectedEnergy	Encapsulates the projected energy for a cluster.

Nested classes/interfaces inherited from interface elki.Algorithm

elki.Algorithm.Utils

Field Summary

Fields

Modifier and Type	Field	Description
private double	alpha	Holds the value of ORCLUS.Par.ALPHA_ID.
private static elki.logging.Logging	LOG	The logger for this class.
private elki.math.linearalgebra.pca.PCARunner	pca	The PCA utility object.
private elki.utilities.random.RandomFactory	rnd	Random generator

Fields inherited from class elki.clustering.AbstractProjectedClustering

k, k_i, l

Constructor Summary

Constructors

Constructor	Description
ORCLUS(int k, int k_i, int l, double alpha, elki.utilities.random.RandomFactory rnd, elki.math.linearalgebra.pca.PCARunner pca)	Java constructor.

Method Summary

Modifier and Type	Method	Description
private void	assign(elki.database.relation.Relation<? extends elki.data.NumberVector> database, java.util.List<ORCLUS.ORCLUSCluster> clusters)	Creates a partitioning of the database by assigning each object to its closest seed.
private double[][]	findBasis(elki.database.relation.Relation<? extends elki.data.NumberVector> database, ORCLUS.ORCLUSCluster cluster, int dim)	Finds the basis of the subspace of dimensionality dim for the specified cluster.
elki.data.type.TypeInformation[]	getInputTypeRestriction()
private java.util.List<ORCLUS.ORCLUSCluster>	initialSeeds(elki.database.relation.Relation<? extends elki.data.NumberVector> database, int k)	Initializes the list of seeds wit a random sample of size k.
private void	merge(elki.database.relation.Relation<? extends elki.data.NumberVector> relation, java.util.List<ORCLUS.ORCLUSCluster> clusters, int k_new, int d_new, elki.logging.progress.IndefiniteProgress cprogress)	Reduces the number of seeds to k_new
private ORCLUS.ProjectedEnergy	projectedEnergy(elki.database.relation.Relation<? extends elki.data.NumberVector> relation, ORCLUS.ORCLUSCluster c_i, ORCLUS.ORCLUSCluster c_j, int i, int j, int dim)	Computes the projected energy of the specified clusters.
Clustering<Model>	run(elki.database.relation.Relation<? extends elki.data.NumberVector> relation)	Performs the ORCLUS algorithm on the given database.
private ORCLUS.ORCLUSCluster	union(elki.database.relation.Relation<? extends elki.data.NumberVector> relation, ORCLUS.ORCLUSCluster c1, ORCLUS.ORCLUSCluster c2, int dim)	Returns the union of the two specified clusters.

Methods inherited from class java.lang.Object

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

Methods inherited from interface elki.clustering.ClusteringAlgorithm

autorun

Field Detail

LOG

private static final elki.logging.Logging LOG

The logger for this class.

alpha

private double alpha

Holds the value of ORCLUS.Par.ALPHA_ID.

rnd

private elki.utilities.random.RandomFactory rnd

Random generator

pca

private elki.math.linearalgebra.pca.PCARunner pca

The PCA utility object.

Constructor Detail

ORCLUS

public ORCLUS(int k,
              int k_i,
              int l,
              double alpha,
              elki.utilities.random.RandomFactory rnd,
              elki.math.linearalgebra.pca.PCARunner pca)

Java constructor.

Parameters:

k - k Parameter

k_i - k_i Parameter

l - l Parameter

alpha - Alpha Parameter

rnd - Random generator

pca - PCA runner

Method Detail

getInputTypeRestriction

public elki.data.type.TypeInformation[] getInputTypeRestriction()

run

public Clustering<Model> run(elki.database.relation.Relation<? extends elki.data.NumberVector> relation)

Performs the ORCLUS algorithm on the given database.

Parameters:

relation - Relation

initialSeeds

private java.util.List<ORCLUS.ORCLUSCluster> initialSeeds(elki.database.relation.Relation<? extends elki.data.NumberVector> database,
                                                          int k)

Initializes the list of seeds wit a random sample of size k.

Parameters:

database - the database holding the objects

k - the size of the random sample

Returns:

the initial seed list

assign

private void assign(elki.database.relation.Relation<? extends elki.data.NumberVector> database,
                    java.util.List<ORCLUS.ORCLUSCluster> clusters)

Creates a partitioning of the database by assigning each object to its closest seed.

Parameters:

database - the database holding the objects

clusters - the array of clusters to which the objects should be assigned to

findBasis

private double[][] findBasis(elki.database.relation.Relation<? extends elki.data.NumberVector> database,
                             ORCLUS.ORCLUSCluster cluster,
                             int dim)

Finds the basis of the subspace of dimensionality dim for the specified cluster.

Parameters:

database - the database to run the algorithm on

cluster - the cluster

dim - the dimensionality of the subspace

Returns:

matrix defining the basis of the subspace for the specified cluster

merge

private void merge(elki.database.relation.Relation<? extends elki.data.NumberVector> relation,
                   java.util.List<ORCLUS.ORCLUSCluster> clusters,
                   int k_new,
                   int d_new,
                   elki.logging.progress.IndefiniteProgress cprogress)

Reduces the number of seeds to k_new

Parameters:

relation - the database holding the objects

clusters - the set of current seeds

k_new - the new number of seeds

d_new - the new dimensionality of the subspaces for each seed

projectedEnergy

private ORCLUS.ProjectedEnergy projectedEnergy(elki.database.relation.Relation<? extends elki.data.NumberVector> relation,
                                               ORCLUS.ORCLUSCluster c_i,
                                               ORCLUS.ORCLUSCluster c_j,
                                               int i,
                                               int j,
                                               int dim)

Computes the projected energy of the specified clusters. The projected energy is given by the mean square distance of the points to the centroid of the union cluster c, when all points in c are projected to the subspace of c.

Parameters:

relation - the relation holding the objects

c_i - the first cluster

c_j - the second cluster

i - the index of cluster c_i in the cluster list

j - the index of cluster c_j in the cluster list

dim - the dimensionality of the clusters

Returns:

the projected energy of the specified cluster

union

private ORCLUS.ORCLUSCluster union(elki.database.relation.Relation<? extends elki.data.NumberVector> relation,
                                   ORCLUS.ORCLUSCluster c1,
                                   ORCLUS.ORCLUSCluster c2,
                                   int dim)

Returns the union of the two specified clusters.

Parameters:

relation - the database holding the objects

c1 - the first cluster

c2 - the second cluster

dim - the dimensionality of the union cluster

Returns:

the union of the two specified clusters