Package edu.cmu.tetrad.search

Class Bpc

java.lang.Object

edu.cmu.tetrad.search.Bpc

public final class Bpc
extends Object

Implements the Build Pure Clusters (BPC) algorithm, which allows one to identify clusters of measured variables in a dataset that are explained by a single latent. The algorithm outputs these clusters, which can then be used for further analysis, such as inferring structure over the latents. For the latter, see for instance the MimBuild algorithm.

The reference for BPC is this:

Silva, R., Scheines, R., Glymour, C., Spirtes, P., & Chickering, D. M. (2006). Learning the Structure of Linear Latent Variable Models. Journal of Machine Learning Research, 7(2).

For a more detailed description of the algorithm, see the paper above. The algorithm is based on the idea of finding cliques in the graph of the covariance matrix. The algorithm is initialized by finding all maximal cliques in the graph of the covariance matrix. Then, the algorithm iterates over the cliques, and for each clique, it tests whether the clique is explained by a single latent. If so, the clique is added to the set of clusters. If not, the clique is partitioned into smaller cliques, and the process is repeated for each of the smaller cliques. The algorithm stops when all cliques have been tested.

Some more References:

Silva, R.; Scheines, R.; Spirtes, P.; Glymour, C. (2003). "Learning measurement models". Technical report CMU-CALD-03-100, Center for Automated Learning and Discovery, Carnegie Mellon University.

Bollen, K. (1990). "Outlier screening and distribution-free test for vanishing tetrads." Sociological Methods and Research 19, 80-92.

Wishart, J. (1928). "Sampling errors in the theory of two factors". British Journal of Psychology 19, 180-187.

Bron, C. and Kerbosch, J. (1973) "Algorithm 457: Finding all cliques of an undirected graph". Communications of ACM 16, 575-577.

This class is not configured to respect knowledge of forbidden and required edges.

Author:

Ricardo Silva

See Also:

• Fofc
• Ftfc

Constructor Summary

Constructors

Constructor	Description
Bpc(DataSet dataSet, double alpha, BpcTestType sigTestType)	Constructor.
Bpc(ICovarianceMatrix covarianceMatrix, double alpha, BpcTestType sigTestType)	Constructor.

Method Summary

Modifier and Type	Method	Description
ICovarianceMatrix	getCovarianceMatrix()	Returns the wrapped covariance matrix.
Graph	search()	Runs the search and returns the graph, or null if there is no model.
void	setCheckType(ClusterSignificance.CheckType checkType)	Sets the cluster significance type.

Methods inherited from class java.lang.Object

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

Constructor Details

Bpc

public Bpc(ICovarianceMatrix covarianceMatrix,
 double alpha,
 BpcTestType sigTestType)

Constructor.

Parameters:

covarianceMatrix - The covariance matrix to analyze.

alpha - The significance cutoff to use.

sigTestType - The type of the significance test to use.

See Also:

• BpcTestType

Bpc

public Bpc(DataSet dataSet,
 double alpha,
 BpcTestType sigTestType)

Constructor.

Parameters:

dataSet - The dataset to analyze.

alpha - The significance cutoff to use.

sigTestType - The type of the significance test to use.

See Also:

• BpcTestType

Method Details

search

public Graph search()

Runs the search and returns the graph, or null if there is no model. This will be a graph with clusters having their latents as parents.

Returns:

This graph.

getCovarianceMatrix

public ICovarianceMatrix getCovarianceMatrix()

Returns the wrapped covariance matrix.

Returns:

This.

setCheckType

public void setCheckType(ClusterSignificance.CheckType checkType)

Sets the cluster significance type.

Parameters:

checkType - This type

See Also:

• ClusterSignificance