de.lmu.ifi.dbs.elki.algorithm.clustering.subspace
Class PROCLUS<V extends NumberVector<V,?>>

java.lang.Object
  de.lmu.ifi.dbs.elki.logging.AbstractLoggable
      de.lmu.ifi.dbs.elki.algorithm.AbstractAlgorithm<V,Clustering<Model>>
          de.lmu.ifi.dbs.elki.algorithm.clustering.subspace.ProjectedClustering<V>
              de.lmu.ifi.dbs.elki.algorithm.clustering.subspace.PROCLUS<V>

Type Parameters:

V - the type of NumberVector handled by this Algorithm

All Implemented Interfaces:

Algorithm<V,Clustering<Model>>, ClusteringAlgorithm<Clustering<Model>,V>, Parameterizable

@Title(value="PROCLUS: PROjected CLUStering")
@Description(value="Algorithm to find subspace clusters in high dimensional spaces.")
@Reference(authors="C. C. Aggrawal, C. Procopiuc, J. L. Wolf, P. S. Yu, J. S. Park",
           title="Fast Algorithms for Projected Clustering",
           booktitle="Proc. ACM SIGMOD Int. Conf. on Management of Data (SIGMOD \'99)",
           url="http://dx.doi.org/10.1145/304181.304188")
public class PROCLUS<V extends NumberVector<V,?>>
extends ProjectedClustering<V>

Provides the PROCLUS algorithm, an algorithm to find subspace clusters in high dimensional spaces.

Reference:
C. C. Aggrawal, C. Procopiuc, J. L. Wolf, P. S. Yu, J. S. Park: Fast Algorithms for Projected Clustering.
In: Proc. ACM SIGMOD Int. Conf. on Management of Data (SIGMOD '99).

Author:

Elke Achtert

Nested Class Summary

private class

PROCLUS.PROCLUSCluster Encapsulates the attributes of a cluster.

Field Summary

private int	m_i Holds the value of M_I_PARAM.
static OptionID	M_I_ID OptionID for M_I_PARAM
private IntParameter	M_I_PARAM Parameter to specify the multiplier for the initial number of medoids, must be an integer greater than 0.

Fields inherited from class de.lmu.ifi.dbs.elki.algorithm.clustering.subspace.ProjectedClustering

K_I_ID, K_ID, L_ID

Fields inherited from class de.lmu.ifi.dbs.elki.logging.AbstractLoggable

debug, logger

Constructor Summary

PROCLUS(Parameterization config)
Constructor, adhering to Parameterizable

Method Summary

private Map<Integer,PROCLUS.PROCLUSCluster>	assignPoints(Map<Integer,Set<Integer>> dimensions, Database<V> database) Assigns the objects to the clusters.
private double	avgDistance(V centroid, Set<Integer> objectIDs, Database<V> database, int dimension) Computes the average distance of the objects to the centroid along the specified dimension.
private Set<Integer>	computeBadMedoids(Map<Integer,PROCLUS.PROCLUSCluster> clusters, int threshold) Computes the bad medoids, where the medoid of a cluster with less than the specified threshold of objects is bad.
private Set<Integer>	computeM_current(Set<Integer> m, Set<Integer> m_best, Set<Integer> m_bad) Computes the set of medoids in current iteration.
private double	evaluateClusters(Map<Integer,PROCLUS.PROCLUSCluster> clusters, Map<Integer,Set<Integer>> dimensions, Database<V> database) Evaluates the quality of the clusters.
private Map<Integer,Set<Integer>>	findDimensions(Set<Integer> medoids, Database<V> database, Map<Integer,List<DistanceResultPair<DoubleDistance>>> localities) Determines the set of correlated dimensions for each medoid in the specified medoid set.
private Map<Integer,List<DistanceResultPair<DoubleDistance>>>	getLocalities(Set<Integer> m_c, Database<V> database) Computes the localities of the specified medoids.
private Set<Integer>	greedy(Set<Integer> sampleSet, int m) Returns a piercing set of k medoids from the specified sample set.
private Set<Integer>	initialSet(Set<Integer> sampleSet, int k) Returns a set of k elements from the specified sample set.
private DoubleDistance	manhattanSegmentalDistance(V o1, V o2, Set<Integer> dimensions) Returns the Manhattan segmental distance between o1 and o2 relative to the specified dimensions.
protected Clustering<Model>	runInTime(Database<V> database) Performs the PROCLUS algorithm on the given database.

Methods inherited from class de.lmu.ifi.dbs.elki.algorithm.clustering.subspace.ProjectedClustering

getDistanceFunction, getK_i, getK, getL

Methods inherited from class de.lmu.ifi.dbs.elki.algorithm.AbstractAlgorithm

isTime, isVerbose, run, setTime, setVerbose

Methods inherited from class de.lmu.ifi.dbs.elki.logging.AbstractLoggable

debugFine, debugFiner, debugFinest, exception, progress, verbose, warning

Methods inherited from class java.lang.Object

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

Methods inherited from interface de.lmu.ifi.dbs.elki.algorithm.clustering.ClusteringAlgorithm

run

Methods inherited from interface de.lmu.ifi.dbs.elki.algorithm.Algorithm

setTime, setVerbose

Field Detail

M_I_ID

public static final OptionID M_I_ID

OptionID for M_I_PARAM

M_I_PARAM

private final IntParameter M_I_PARAM

Parameter to specify the multiplier for the initial number of medoids, must be an integer greater than 0.

Default value: 10

Key: -proclus.mi

m_i

private int m_i

Holds the value of M_I_PARAM.

Constructor Detail

PROCLUS

public PROCLUS(Parameterization config)

Constructor, adhering to Parameterizable

Parameters:

config - Parameterization

Method Detail

runInTime

protected Clustering<Model> runInTime(Database<V> database)
                               throws IllegalStateException

Performs the PROCLUS algorithm on the given database.

Specified by:

runInTime in class AbstractAlgorithm<V extends NumberVector<V,?>,Clustering<Model>>

Parameters:

database - the database to run the algorithm on

Returns:

the Result computed by this algorithm

Throws:

IllegalStateException - if the algorithm has not been initialized properly (e.g. the setParameters(String[]) method has been failed to be called).

greedy

private Set<Integer> greedy(Set<Integer> sampleSet,
                            int m)

Returns a piercing set of k medoids from the specified sample set.

Parameters:

sampleSet - the sample set

m - the number of medoids to be returned

Returns:

a piercing set of m medoids from the specified sample set

initialSet

private Set<Integer> initialSet(Set<Integer> sampleSet,
                                int k)

Returns a set of k elements from the specified sample set.

Parameters:

sampleSet - the sample set

k - the number of samples to be returned

Returns:

a set of k elements from the specified sample set

computeM_current

private Set<Integer> computeM_current(Set<Integer> m,
                                      Set<Integer> m_best,
                                      Set<Integer> m_bad)

Computes the set of medoids in current iteration.

Parameters:

m - the medoids

m_best - the best set of medoids found so far

m_bad - the bad medoids

Returns:

m_current, the set of medoids in current iteration

getLocalities

private Map<Integer,List<DistanceResultPair<DoubleDistance>>> getLocalities(Set<Integer> m_c,
                                                                            Database<V> database)

Computes the localities of the specified medoids.

Parameters:

m_c - the ids of the medoids

database - the database holding the objects

Returns:

a mapping of the medoid's id to its locality

findDimensions

private Map<Integer,Set<Integer>> findDimensions(Set<Integer> medoids,
                                                 Database<V> database,
                                                 Map<Integer,List<DistanceResultPair<DoubleDistance>>> localities)

Determines the set of correlated dimensions for each medoid in the specified medoid set.

Parameters:

medoids - the set of medoids

database - the database containing the objects

localities - the localities of the specified medoids

Returns:

the set of correlated dimensions for each medoid in the specified medoid set

assignPoints

private Map<Integer,PROCLUS.PROCLUSCluster> assignPoints(Map<Integer,Set<Integer>> dimensions,
                                                         Database<V> database)

Assigns the objects to the clusters.

Parameters:

dimensions - set of correlated dimensions for each medoid of the cluster

database - the database containing the objects

Returns:

the assignments of the object to the clusters

manhattanSegmentalDistance

private DoubleDistance manhattanSegmentalDistance(V o1,
                                                  V o2,
                                                  Set<Integer> dimensions)

Returns the Manhattan segmental distance between o1 and o2 relative to the specified dimensions.

Parameters:

o1 - the first object

o2 - the second object

dimensions - the dimensions to be considered

Returns:

the Manhattan segmental distance between o1 and o2 relative to the specified dimensions

evaluateClusters

private double evaluateClusters(Map<Integer,PROCLUS.PROCLUSCluster> clusters,
                                Map<Integer,Set<Integer>> dimensions,
                                Database<V> database)

Evaluates the quality of the clusters.

Parameters:

clusters - the clusters to be evaluated

dimensions - the dimensions associated with each cluster

database - the database holding the objects

Returns:

a measure for the cluster quality

avgDistance

private double avgDistance(V centroid,
                           Set<Integer> objectIDs,
                           Database<V> database,
                           int dimension)

Computes the average distance of the objects to the centroid along the specified dimension.

Parameters:

centroid - the centroid

objectIDs - the set of objects ids

database - the database holding the objects

dimension - the dimension for which the average distance is computed

Returns:

the average distance of the objects to the centroid along the specified dimension

computeBadMedoids

private Set<Integer> computeBadMedoids(Map<Integer,PROCLUS.PROCLUSCluster> clusters,
                                       int threshold)

Computes the bad medoids, where the medoid of a cluster with less than the specified threshold of objects is bad.

Parameters:

clusters - the clusters

threshold - the threshold

Returns:

the bad medoids