Package elki.clustering.correlation

Class LMCLUS

java.lang.Object

elki.clustering.correlation.LMCLUS

All Implemented Interfaces:

elki.Algorithm, ClusteringAlgorithm<Clustering<Model>>

@Reference(authors="R. Haralick, R. Harpaz",
           title="Linear manifold clustering in high dimensional spaces by stochastic search",
           booktitle="Pattern Recognition volume 40, Issue 10",
           url="https://doi.org/10.1016/j.patcog.2007.01.020",
           bibkey="DBLP:journals/pr/HaralickH07")
public class LMCLUS
extends java.lang.Object
implements ClusteringAlgorithm<Clustering<Model>>

Linear manifold clustering in high dimensional spaces by stochastic search.

Reference:

R. Haralick, R. Harpaz
Linear manifold clustering in high dimensional spaces by stochastic search
In: Pattern Recognition volume 40, Issue 10

Implementation note: the LMCLUS algorithm seems to lack good stopping criterions. We can't entirely reproduce the good results from the original publication, in particular not on noisy data. But the questionable parts are as in the original publication, associated thesis and published source code. The minimum cluster size however can serve as a hidden stopping criterion.

Since:

0.5.0

Author:

Ernst Waas, Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	LMCLUS.Par	Parameterization class
private static class	LMCLUS.Separation	Class to represent a linear manifold separation

Nested classes/interfaces inherited from interface elki.Algorithm

elki.Algorithm.Utils

Field Summary

Fields

Modifier and Type	Field	Description
private static int	BINS	Histogram resolution
private static elki.logging.Logging	LOG	The logger for this class.
private static double	LOG_NOT_FROM_ONE_CLUSTER_PROBABILITY	Epsilon
private int	maxLMDim	Maximum cluster dimensionality
private int	minsize	Minimum cluster size
private elki.utilities.random.RandomFactory	rnd	Random factory
private int	samplingLevel	Number of sampling rounds to find a good split
private double	sensitivityThreshold	The current threshold value calculated by the findSeperation Method.

Constructor Summary

Constructors

Constructor	Description
LMCLUS(int maxdim, int minsize, int samplingLevel, double sensitivityThreshold, elki.utilities.random.RandomFactory rnd)	Constructor.

Method Summary

Modifier and Type	Method	Description
private double	deviation(double[] delta, double[][] beta)	Deviation from a manifold described by beta.
private double[]	findAndEvaluateThreshold(elki.utilities.datastructures.histogram.DoubleDynamicHistogram histogram)	Evaluate the histogram to find a suitable threshold
private LMCLUS.Separation	findSeparation(elki.database.relation.Relation<? extends elki.data.NumberVector> relation, elki.database.ids.DBIDs currentids, int dimension, java.util.Random r)	This method samples a number of linear manifolds an tries to determine which the one with the best cluster is.
private double[][]	generateOrthonormalBasis(java.util.List<double[]> vectors)	This Method generates an orthonormal basis from a set of Vectors.
elki.data.type.TypeInformation[]	getInputTypeRestriction()
Clustering<Model>	run(elki.database.relation.Relation<? extends elki.data.NumberVector> relation)	The main LMCLUS (Linear manifold clustering algorithm) is processed in this method.

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.

LOG_NOT_FROM_ONE_CLUSTER_PROBABILITY

private static final double LOG_NOT_FROM_ONE_CLUSTER_PROBABILITY

Epsilon

BINS

private static final int BINS

Histogram resolution

See Also:

Constant Field Values

sensitivityThreshold

private final double sensitivityThreshold

The current threshold value calculated by the findSeperation Method.

maxLMDim

private final int maxLMDim

Maximum cluster dimensionality

minsize

private final int minsize

Minimum cluster size

samplingLevel

private final int samplingLevel

Number of sampling rounds to find a good split

rnd

private final elki.utilities.random.RandomFactory rnd

Random factory

Constructor Detail

LMCLUS

public LMCLUS(int maxdim,
              int minsize,
              int samplingLevel,
              double sensitivityThreshold,
              elki.utilities.random.RandomFactory rnd)

Constructor.

Parameters:

maxdim - Maximum dimensionality

minsize - Minimum cluster size

samplingLevel - Sampling level

sensitivityThreshold - Threshold

rnd - Random factory

Method Detail

getInputTypeRestriction

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

Specified by:

getInputTypeRestriction in interface elki.Algorithm

run

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

The main LMCLUS (Linear manifold clustering algorithm) is processed in this method.

The algorithm samples random linear manifolds and tries to find clusters in it. It calculates a distance histogram searches for a threshold and partitions the points in two groups the ones in the cluster and everything else. Then the best fitting linear manifold is searched and registered as a cluster. The process is started over until all points are clustered. The last cluster should contain all the outliers (or the whole data if no clusters have been found.)

Parameters:

relation - Relation

Returns:

Clustering result

deviation

private double deviation(double[] delta,
                         double[][] beta)

Deviation from a manifold described by beta.

Parameters:

delta - Delta from origin vector

beta - Manifold

Returns:

Deviation score

findSeparation

private LMCLUS.Separation findSeparation(elki.database.relation.Relation<? extends elki.data.NumberVector> relation,
                                         elki.database.ids.DBIDs currentids,
                                         int dimension,
                                         java.util.Random r)

This method samples a number of linear manifolds an tries to determine which the one with the best cluster is.

 A number of sample points according to the dimension of the linear manifold are taken.
 The basis (B) and the origin(o) of the manifold are calculated.
 A distance histogram using  the distance function ||x-o|| -||B^t*(x-o)|| is generated.
 The best threshold is searched using the elevate threshold function.
 The overall goodness of the threshold is determined.
 The process is redone until a specific number of samples is taken.
 

Parameters:

relation - The vector relation

currentids - Current DBIDs

dimension - the dimension of the linear manifold to sample.

r - Random generator

Returns:

the overall goodness of the separation. The values origin basis and threshold are returned indirectly over class variables.

generateOrthonormalBasis

private double[][] generateOrthonormalBasis(java.util.List<double[]> vectors)

This Method generates an orthonormal basis from a set of Vectors. It uses the established Gram-Schmidt algorithm for orthonormalisation:

 u_1 = v_1
 u_k = v_k -proj_u1(v_k)...proj_u(k-1)(v_k);

 Where proj_u(v) = <v,u>/<u,u> *u
 

Parameters:

vectors - The set of vectors to generate the orthonormal basis from

Returns:

the orthonormal basis generated by this method.

Throws:

java.lang.RuntimeException - if the given vectors are not linear independent.

findAndEvaluateThreshold

private double[] findAndEvaluateThreshold(elki.utilities.datastructures.histogram.DoubleDynamicHistogram histogram)

Evaluate the histogram to find a suitable threshold

Parameters:

histogram - Histogram to evaluate

Returns:

Position and goodness