java.lang.Object
- elki.clustering.subspace.P3C

All Implemented Interfaces:

elki.Algorithm, ClusteringAlgorithm<Clustering<SubspaceModel>>, SubspaceClusteringAlgorithm<SubspaceModel>
```
@Title("P3C: A Robust Projected Clustering Algorithm.")
@Reference(authors="Gabriela Moise, J\u00f6rg Sander, Martin Ester",
           title="P3C: A Robust Projected Clustering Algorithm",
           booktitle="Proc. Sixth International Conference on Data Mining (ICDM \'06)",
           url="https://doi.org/10.1109/ICDM.2006.123",
           bibkey="DBLP:conf/icdm/MoiseSE06")
@Priority(190)
public class P3C
extends java.lang.Object
implements SubspaceClusteringAlgorithm<SubspaceModel>
```
P3C: A Robust Projected Clustering Algorithm.
Reference:
Gabriela Moise, Jörg Sander, Martin Ester
P3C: A Robust Projected Clustering Algorithm
In: Proc. Sixth International Conference on Data Mining (ICDM '06)
This is not a complete implementation of P3C, but good enough for most users. Improvements are welcome. The most obviously missing step is section 3.5 of P3C, where the cluster subspaces are refined.

Since:

0.6.0

Author:

Florian Nuecke, Erich Schubert

Nested Class Summary

Nested Classes
Modifier and Type	Class	Description
`private static class`	`P3C.ClusterCandidate`	This class is used to represent potential clusters.
`static class`	`P3C.Par`	Parameterization class.
`private static class`	`P3C.Signature`	P3C Cluster signature.

Nested classes/interfaces inherited from interface elki.Algorithm
elki.Algorithm.Utils

Field Summary

Fields
Modifier and Type	Field	Description
`protected double`	`alpha`	Alpha threshold for testing.
`protected double`	`emDelta`	Threshold when to stop EM iterations.
`private static elki.logging.Logging`	`LOG`	The logger for this class.
`protected int`	`maxEmIterations`	Maximum number of iterations for the EM step.
`protected int`	`minClusterSize`	Minimum cluster size for noise flagging.
`protected double`	`poissonThreshold`	Parameter for the Poisson test threshold.

Constructor Summary

Constructors
Constructor Description

P3C(double alpha, double poissonThreshold, int maxEmIterations, double emDelta, int minClusterSize)
Constructor.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`private void`	`assignUnassigned(elki.database.relation.Relation<? extends elki.data.NumberVector> relation, elki.database.datastore.WritableDataStore<double[]> probClusterIGivenX, java.util.List<MultivariateGaussianModel> models, elki.database.ids.ModifiableDBIDs unassigned)`	Assign unassigned objects to best candidate based on shortest Mahalanobis distance.
`private int`	`chiSquaredUniformTest(elki.database.ids.SetDBIDs[] parts, long[] marked, int card)`	Performs a ChiSquared test to determine whether an attribute has a uniform distribution.
`private void`	`computeFuzzyMembership(elki.database.relation.Relation<? extends elki.data.NumberVector> relation, java.util.ArrayList<P3C.Signature> clusterCores, elki.database.ids.ModifiableDBIDs unassigned, elki.database.datastore.WritableDataStore<double[]> probClusterIGivenX, java.util.List<MultivariateGaussianModel> models, int dim)`	Computes a fuzzy membership with the weights based on which cluster cores each data point is part of.
`private java.util.ArrayList<P3C.Signature>`	`constructOneSignatures(elki.database.ids.SetDBIDs[][] partitions, long[][] markers)`	Construct the 1-signatures by merging adjacent dense bins.
`private void`	`findOutliers(elki.database.relation.Relation<? extends elki.data.NumberVector> relation, java.util.List<MultivariateGaussianModel> models, java.util.ArrayList<P3C.ClusterCandidate> clusterCandidates, elki.database.ids.ModifiableDBIDs noise)`	Performs outlier detection by testing the Mahalanobis distance of each point in a cluster against the critical value of the ChiSquared distribution with as many degrees of freedom as the cluster has relevant attributes.
`elki.data.type.TypeInformation[]`	`getInputTypeRestriction()`
`private java.util.ArrayList<P3C.ClusterCandidate>`	`hardClustering(elki.database.datastore.WritableDataStore<double[]> probClusterIGivenX, java.util.List<P3C.Signature> clusterCores, elki.database.ids.DBIDs dbids)`	Creates a hard clustering from the specified soft membership matrix.
`private java.util.ArrayList<P3C.Signature>`	`mergeClusterCores(int binCount, java.util.ArrayList<P3C.Signature> signatures)`	Merge 1-signatures into p-signatures.
`protected P3C.Signature`	`mergeSignatures(P3C.Signature first, P3C.Signature second, int numBins)`	Generates a merged signature of this and another one, where the other signature must be a 1-signature.
`private elki.database.ids.SetDBIDs[][]`	`partitionData(elki.database.relation.Relation<? extends elki.data.NumberVector> relation, int bins)`	Partition the data set into `bins` bins in each dimension independently.
`private java.util.ArrayList<P3C.Signature>`	`pruneRedundantClusterCores(java.util.ArrayList<P3C.Signature> clusterCores)`	Prune redundant cluster cores
`Clustering<SubspaceModel>`	`run(elki.database.relation.Relation<? extends elki.data.NumberVector> relation)`	Performs the P3C algorithm on the given Database.
`protected elki.database.ids.HashSetModifiableDBIDs`	`unionDBIDs(elki.database.ids.DBIDs[] parts, int start, int end)`	Compute the union of multiple DBID sets.

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.
- poissonThreshold
```
protected double poissonThreshold
```
  Parameter for the Poisson test threshold.
- maxEmIterations
```
protected int maxEmIterations
```
  Maximum number of iterations for the EM step.
- emDelta
```
protected double emDelta
```
  Threshold when to stop EM iterations.
- minClusterSize
```
protected int minClusterSize
```
  Minimum cluster size for noise flagging. (Not existing in the original publication).
- alpha
```
protected double alpha
```
  Alpha threshold for testing.

Constructor Detail
- P3C
```
public P3C(double alpha,
           double poissonThreshold,
           int maxEmIterations,
           double emDelta,
           int minClusterSize)
```
  Constructor.
  
  Parameters:
  
  alpha - ChiSquared test threshold
  
  poissonThreshold - Poisson test threshold
  
  maxEmIterations - Maximum number of EM iterations
  
  emDelta - EM stopping threshold
  
  minClusterSize - Minimum cluster size

Method Detail

getInputTypeRestriction
```
public elki.data.type.TypeInformation[] getInputTypeRestriction()
```
Specified by:

getInputTypeRestriction in interface elki.Algorithm

run

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

Performs the P3C algorithm on the given Database.

Parameters:: relation - Input data

constructOneSignatures

private java.util.ArrayList<P3C.Signature> constructOneSignatures(elki.database.ids.SetDBIDs[][] partitions,
                                                                  long[][] markers)

Construct the 1-signatures by merging adjacent dense bins.

Parameters:: partitions - Initial partitions.; markers - Markers for dense partitions.
Returns:: 1-signatures

mergeClusterCores

private java.util.ArrayList<P3C.Signature> mergeClusterCores(int binCount,
                                                             java.util.ArrayList<P3C.Signature> signatures)

Merge 1-signatures into p-signatures.

Parameters:: binCount - Number of bins in each dimension.; signatures - 1-signatures
Returns:: p-signatures

pruneRedundantClusterCores

private java.util.ArrayList<P3C.Signature> pruneRedundantClusterCores(java.util.ArrayList<P3C.Signature> clusterCores)

Prune redundant cluster cores

Parameters:: clusterCores - Cluster cores
Returns:: Pruned cluster cores

partitionData
```
private elki.database.ids.SetDBIDs[][] partitionData(elki.database.relation.Relation<? extends elki.data.NumberVector> relation,
                                                     int bins)
```
Partition the data set into bins bins in each dimension independently.
This can be used to construct a grid approximation of the data using O(d n) memory.
When a dimension is found to be constant, it will not be partitioned, but instead the corresponding array will be set to null.

Parameters:

relation - Data relation to partition

bins - Number of bins

Returns:

Partitions of each dimension.

unionDBIDs

protected elki.database.ids.HashSetModifiableDBIDs unionDBIDs(elki.database.ids.DBIDs[] parts,
                                                              int start,
                                                              int end)

Compute the union of multiple DBID sets.

Parameters:: parts - Parts array; start - Array start index; end - Array end index (exclusive)
Returns:: Union

chiSquaredUniformTest
```
private int chiSquaredUniformTest(elki.database.ids.SetDBIDs[] parts,
                                  long[] marked,
                                  int card)
```
Performs a ChiSquared test to determine whether an attribute has a uniform distribution.

Parameters:

parts - Data partitions.

marked - the marked bins that should be ignored.

card - Cardinality

Returns:

Position of maximum, or -1 when uniform.

computeFuzzyMembership

private void computeFuzzyMembership(elki.database.relation.Relation<? extends elki.data.NumberVector> relation,
                                    java.util.ArrayList<P3C.Signature> clusterCores,
                                    elki.database.ids.ModifiableDBIDs unassigned,
                                    elki.database.datastore.WritableDataStore<double[]> probClusterIGivenX,
                                    java.util.List<MultivariateGaussianModel> models,
                                    int dim)

Computes a fuzzy membership with the weights based on which cluster cores each data point is part of.

Parameters:: relation - Data relation; clusterCores - the cluster cores.; unassigned - set to which to add unassigned points.; probClusterIGivenX - Membership probabilities.; models - Cluster models.; dim - Dimensionality

assignUnassigned

private void assignUnassigned(elki.database.relation.Relation<? extends elki.data.NumberVector> relation,
                              elki.database.datastore.WritableDataStore<double[]> probClusterIGivenX,
                              java.util.List<MultivariateGaussianModel> models,
                              elki.database.ids.ModifiableDBIDs unassigned)

Assign unassigned objects to best candidate based on shortest Mahalanobis distance.

Parameters:: relation - Data relation; probClusterIGivenX - fuzzy membership matrix.; models - Cluster models.; unassigned - the list of points not yet assigned.

hardClustering

private java.util.ArrayList<P3C.ClusterCandidate> hardClustering(elki.database.datastore.WritableDataStore<double[]> probClusterIGivenX,
                                                                 java.util.List<P3C.Signature> clusterCores,
                                                                 elki.database.ids.DBIDs dbids)

Creates a hard clustering from the specified soft membership matrix.

Parameters:: probClusterIGivenX - the membership matrix.; dbids - mapping matrix row to DBID.
Returns:: a hard clustering based on the matrix.

findOutliers
```
private void findOutliers(elki.database.relation.Relation<? extends elki.data.NumberVector> relation,
                          java.util.List<MultivariateGaussianModel> models,
                          java.util.ArrayList<P3C.ClusterCandidate> clusterCandidates,
                          elki.database.ids.ModifiableDBIDs noise)
```
Performs outlier detection by testing the Mahalanobis distance of each point in a cluster against the critical value of the ChiSquared distribution with as many degrees of freedom as the cluster has relevant attributes.

Parameters:

relation - Data relation

models - Cluster models

clusterCandidates - the list of clusters to check.

noise - the set to which to add points deemed outliers.

mergeSignatures
```
protected P3C.Signature mergeSignatures(P3C.Signature first,
                                        P3C.Signature second,
                                        int numBins)
```
Generates a merged signature of this and another one, where the other signature must be a 1-signature.

Parameters:

first - First signature.

second - Second signature, must be a 1-signature.

numBins - Number of bins per dimension.

Returns:

the merged signature, or null if the merge failed.

Class P3C

Nested Class Summary

Nested classes/interfaces inherited from interface elki.Algorithm

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface elki.clustering.ClusteringAlgorithm

Field Detail

LOG

poissonThreshold

maxEmIterations

emDelta

minClusterSize

alpha

Constructor Detail

P3C

Method Detail

getInputTypeRestriction

run

constructOneSignatures

mergeClusterCores

pruneRedundantClusterCores

partitionData

unionDBIDs

chiSquaredUniformTest

computeFuzzyMembership

assignUnassigned

hardClustering

findOutliers

mergeSignatures