The Bimax Bicluster algorithm

Description

Performs Bimax Biclustering based on the framework by Prelic et. al.(2006). It searches for submatrices of ones in a logical matrix. Uses the original C code of the authors.

Usage

## S4 method for signature 'matrix,BCBimax'
biclust(x, method=BCBimax(), minr=2, minc=2, number=100)
## S4 method for signature 'matrix,BCrepBimax'
biclust(x, method=BCrepBimax(), minr=2, minc=2, number=100, maxc=12)

Arguments

Value

Returns an object of class Biclust.

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

References

Prelic, A.; Bleuler, S.; Zimmermann, P.; Wil, A.; Buhlmann, P.; Gruissem, W.; Hennig, L.; Thiele, L. & Zitzler, E. A Systematic Comparison and Evaluation of Biclustering Methods for Gene Expression Data Bioinformatics, Oxford Univ Press, 2006, 22, 1122-1129

See Also

biclust, Biclust

Examples

 test <- matrix(rnorm(5000), 100, 50)
 test[11:20,11:20] <- rnorm(100, 3, 0.1)
 loma <- binarize(test,2)
 res <- biclust(x=loma, method=BCBimax(), minr=4, minc=4, number=10)
 res

The CC Bicluster algorithm

Description

Performs CC Biclustering based on the framework by Cheng and Church (2000). Searches for submatrices with a score lower than a specific treshold in a standardized data matrix.

Usage

## S4 method for signature 'matrix,BCCC'
biclust(x, method=BCCC(), delta = 1.0, alpha=1.5, number=100)

Arguments

Value

Returns an object of class Biclust.

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

References

Cheng, Y. & Church, G.M. Biclustering of Expression Data Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology, 2000, 1, 93-103

See Also

biclust, Biclust

Examples

test <- matrix(rbinom(400, 50, 0.4), 20, 20)
res <- biclust(test, method=BCCC(), delta=1.5,  alpha=1, number=10)
res

The Plaid Model Bicluster algorithm

Description

Performs Plaid Model Biclustering as described in Turner et al., 2003. This is an improvement of original 'Plaid Models for Gene Expression Data' (Lazzeroni and Owen, 2002). This algorithm models data matrices to a sum of layers, the model is fitted to data through minimization of error.

Usage

## S4 method for signature 'matrix,BCPlaid'
biclust(x, method=BCPlaid(), cluster="b", fit.model = y ~ m + a + b,
  background = TRUE, background.layer = NA, background.df = 1, row.release = 0.7, 
  col.release = 0.7, shuffle = 3, back.fit = 0, max.layers = 20, iter.startup = 5,
  iter.layer = 10, verbose = TRUE)

Arguments

Value

Returns an Biclust object.

Author(s)

Adaptation of original code from Heather Turner from Rodrigo Santamaria rodri@usal.es. rodri@usal.es

References

Heather Turner et al, "Improved biclustering of microarray data demonstrated through systematic performance tests",Computational Statistics and Data Analysis, 2003, vol. 48, pages 235-254.

Lazzeroni and Owen, "Plaid Models for Gene Expression Data", Standford University, 2002.

Examples

  #Random matrix with embedded bicluster
  test <- matrix(rnorm(5000),100,50)
  test[11:20,11:20] <- rnorm(100,3,0.3)
  res<-biclust(test, method=BCPlaid())
  res

  #microarray matrix
  data(BicatYeast)
  res<-biclust(BicatYeast, method=BCPlaid(), verbose=FALSE)
  res
  

The Questmotif Bicluster algorithm

Description

Performs Questmotif Biclustering a Bicluster algorithm for questionairs based on the framework by Murali and Kasif (2003). Searches subgroups of questionairs with same or similar answer to some questions.

Usage

## S4 method for signature 'matrix,BCQuest'
biclust(x, method=BCQuest(), ns=10, nd=10, sd=5, alpha=0.05, number=100)
## S4 method for signature 'matrix,BCQuestord'
biclust(x, method=BCQuestord(), d=1, ns=10, nd=10, sd=5, alpha=0.05, number=100)
## S4 method for signature 'matrix,BCQuestmet'
biclust(x, method=BCQuestmet(), quant=0.25, vari=1, ns=10, nd=10, sd=5, 
  alpha=0.05, number=100)

Arguments

Value

Returns an object of class Biclust.

Extends

Class "BiclustMethod", directly.

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

References

Murali, T. & Kasif, S. Extracting Conserved Gene Expression Motifs from Gene Expression Data Pacific Symposium on Biocomputing, sullivan.bu.edu, 2003, 8, 77-88

See Also

biclust, Biclust

The Spectral Bicluster algorithm

Description

Performs Spectral Biclustering as described in Kluger et al., 2003. Spectral biclustering supposes that normalized microarray data matrices have a checkerboard structure that can be discovered by the use of svd decomposition in eigenvectors, applied to genes (rows) and conditions (columns).

Usage

## S4 method for signature 'matrix,BCSpectral'
biclust(x, method=BCSpectral(), normalization="log", numberOfEigenvalues=6, 
minr=2, minc=2, withinVar=1, n_clusters = NULL, n_best = 3)

Arguments

Value

Returns an object of class Biclust.

Author(s)

Sami Leon Sami_Leon@URMC.Rochester.edu

Rodrigo Santamaria rodri@usal.es

References

Kluger et al., "Spectral Biclustering of Microarray Data: Coclustering Genes and Conditions", Genome Research, 2003, vol. 13, pages 703-716

Examples

# Random matrix with embedded bicluster  
test <- matrix(rnorm(5000),100,50)
test[11:20,11:20] <- rnorm(100,10,0.1)
image(test)

shuffled_test <- test[sample(nrow(test)), sample(ncol(test))]
image(shuffled_test)

# Without specifying the  number of row and column clusters
res1 <- spectral(shuffled_test,normalization="log", numberOfEigenvalues=6, 
                 minr=2, minc=2, withinVar=1, n_clusters = NULL, n_best = 3)
res1
image(shuffled_test[order(res1@info$row_labels), order(res1@info$column_labels)])


# Specifying the  number of row and column clusters
res2 <- spectral(shuffled_test,normalization="log", numberOfEigenvalues=6, 
                 minr=2, minc=2, withinVar=1, n_clusters = 2, n_best = 3)
res2
image(shuffled_test[order(res2@info$row_labels), order(res2@info$column_labels)])
  

The Xmotifs Bicluster algorithm

Description

Performs XMotifs Biclustering based on the framework by Murali and Kasif (2003). Searches for a submatrix where each row as a similar motif through all columns. The Algorihm needs a discret matrix to perform.

Usage

## S4 method for signature 'matrix,BCXmotifs'
biclust(x, method=BCXmotifs(), ns=10, nd=10, sd=5, alpha=0.05, number=100)

Arguments

Value

Returns an object of class Biclust.

Extends

Class "BiclustMethod", directly.

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

References

Murali, T. & Kasif, S. Extracting Conserved Gene Expression Motifs from Gene Expression Data Pacific Symposium on Biocomputing, sullivan.bu.edu, 2003, 8, 77-88

See Also

biclust, Biclust

Examples

data(BicatYeast)
x<-discretize(BicatYeast)
res <- biclust(x, method=BCXmotifs(), ns=20, nd=20, sd=5, alpha=0.01, number=10)
res

BicAT Yeast

Description

Microarray data matrix for 80 experiments with Saccharomyces Cerevisiae organism extracted from BicAT example data set.

Usage

  data(BicatYeast)
  

Format

Data structure with information about the expression levels of 419 probesets over 70 conditions Row names follow Affymetrix probeset notation

Source

BicAT datasets at http://www.tik.ee.ethz.ch/sop/bicat/

The Biclust Class

Description

Biclust is the class structure for results of a bicluster algorithm. It contains all information needed for further processing. The show Method gives the Name of the Algorithm used and the first Bicluster found. The summary Method gives sizes of all bicluster found.

Objects from the Class

Objects can be created by performing a bicluster algorithm via the biclust() function.

Slots

Objects of class Biclust have the following slots:

Parameters:

Saves input Parameters in a list

RowxNumber:

Logical Matrix which contains 1 in [i,j] if Row i is in Bicluster j

NumberxCol:

Logical Matrix which contains 1 in [i,j] if Col j is in Bicluster i

Number:

Number of Bicluster

info:

Additional Outputs from the different bicluster algorithms

Details

RowxNumber and NumberxCol are named after the arrangement of the data they contain. The column results are transposed in order to ensure a easy processing.

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

See Also

biclust, BiclustMethod-class

The BiclustMethod Virtual Class

Description

BiclustMethod is the virtual class structure for algorithms provided in the package. In order to use the biclust() function a algorithm has to have a class inherit from here.

Algorithms

Currently 6 classes inherit from BiclustMethod: BCCC, BCXmotifs, BCPlaid, BCSpectral, BCBimax, BCQuest

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

See Also

biclust, Biclust-class, BCCC, BCXmotifs, BCPlaid, BCSpectral, BCBimax, BCQuest, BiclustMethod-class

Chia and Karuturi Function

Description

Function computing scores as described in the paper of Chia and Karuturi (2010)

Usage

ChiaKaruturi(x, bicResult, number)

Arguments

Details

The function computes row (T) and column (B) effects for a chosen bicluster. The scores for columns within bicluster have index 1, the scores for columns outside the bicluster have index 2. Ranking score is SB, stratification score is TS.

Value

Data.Frame with 6 slots: T, B scores for within and outside bicluster, SB and TS scores

Author(s)

Tatsiana KHAMIAKOVA tatsiana.khamiakova@uhasselt.be

References

Chia, B. K. H. and Karuturi, R. K. M. (2010) Differential co-expression framework to quantify goodness of biclusters and compare biclustering algorithms. Algorithms for Molecular Biology, 5, 23.

See Also

diagnosticPlot, computeObservedFstat, diagnoseColRow

Examples

#---simulate dataset with 1 bicluster ---#
xmat<-matrix(rnorm(50*50,0,0.25),50,50) # background noise only 
rowSize <- 20 #number of rows in a bicluster 
colSize <- 10 #number of columns in a bicluster
a1<-rnorm(rowSize,1,0.1) #sample row effect from N(0,0.1) #adding a coherent values bicluster:
b1<-rnorm((colSize),2,0.25)  #sample column effect from N(0,0.05)
mu<-0.01 #constant value signal
 for ( i in 1 : rowSize){
 	for(j in 1: (colSize)){
 		xmat[i,j] <- xmat[i,j] + mu + a1[i] + b1[j] 	
 	}
 }
 #--obtain a bicluster by running an algorithm---# 
plaidmab <- biclust(x=xmat, method=BCPlaid(), cluster="b", fit.model = y ~ m + a+ b,  
background = TRUE, row.release = 0.6, col.release = 0.7, shuffle = 50, back.fit = 5, 
max.layers = 1, iter.startup = 100, iter.layer = 100, verbose = TRUE)

#Get Chia and Karuturi scores:
ChiaKaruturi(x=xmat, bicResult = plaidmab, number = 1)

Eisen Yeast

Description

Microarray data matrix for 80 experiments with Saccharomyces Cerevisiae organism by Eisen Lab.

Usage

  data(EisenYeast)
  

Format

Data frame with information about the expression levels of 6221 genes over 80 conditions. Missing values have been imputed using k-nearest neighbor averaging implemented in impute.knn() from library 'impute' (using default k=10). Gene names follow ORF (Open Reading Format) notation.

Source

Eisen Lab at http://rana.lbl.gov/EisenData.htm

SynTReN E. coli

Description

Synthetic microarray data matrix generated by Syntren for 20 experiments using 200 genes from Transcription Regulatory Network of Shen-Orr et al. (2002).

Usage

  data(SyntrenEcoli)
  

Format

Data structure with information about the expression levels of 200 genes over 20 conditions. Conditions are named as C1... C20

Source

SynTReN software can be downloaded at http://homes.esat.kuleuven.be/~kmarchal/SynTReN/index.html

References

Shen-Orr et al., "Network motifs in the transcriptional regulation network of Escherichia coli", Nature Genetics 2002, volume 31, pages 64-68.

Tim Van den Bulcke et al., "SynTReN: a generator of synthetic gene expression data for design and analysis of structure learning algorithms", BMC Bioinformatics, 2006, volume 7, number 43.

The biclust Method

Description

The function biclust is the main function of the package. It calculates the bicluster in a data matrix using the algorithm specified in the method-argument. Currently the package contains 5 different methods for the use in biclust. For each algorithm see the class help files for further details. For some algorithms preproccessing is necessary, e.g. BCBimax only runs with a logical matrix.

Usage

## S4 method for signature 'matrix,BiclustMethod'
biclust(x,method,...)
## S4 method for signature 'matrix,character'
biclust(x,method,...)

Arguments

Value

Returns an object of class Biclust.

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

See Also

Biclust-class, BCCC, BCXmotifs, BCPlaid, BCSpectral, BCBimax, BCQuest, BiclustMethod-class

Examples

test <- matrix(rbinom(400, 50, 0.4), 20, 20)
res1 <- biclust(test, method=BCCC(), delta=1.5,  alpha=1, number=10)

Bicluster Barchart

Description

Draws a barchart for a Bicluster result representing the columns

Usage

biclustbarchart(x, Bicres, which=NULL, ...)

Arguments

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

See Also

bubbleplot for simultaneous representation of biclusters, parallelCoordinatesfor single representation of biclusters as lines of gene or condition profiles, drawHeatmapfor Heatmap representation of biclusters and biclustmember for a membership graph.

Examples

  set.seed(1)
  x=matrix(rnorm(900),30,30)
  x[1:5,1:5]=rnorm(25,3,0.3)
  x[11:15,11:15]=rnorm(25,-3,0.3)
  x[21:25,21:25]=rnorm(25,6,0.3)
  colnames(x)<-paste("Var.",1:30)
  bics <- biclust(x,BCPlaid(), back.fit = 2, shuffle = 3, fit.model = ~m
+ a + b, iter.startup = 5, iter.layer = 30,  verbose = TRUE)  
  biclustbarchart(x,bics, col="#A3E0D8")
  ord<-bicorder(bics, cols=TRUE, rev=TRUE)
  biclustbarchart(x,bics,which=ord)
  

Extract Bilcuster

Description

Function to extract the bicluster or the row and column numbers from a given bicluster result

Usage

bicluster(x, BicRes, number= 1:BicRes@Number)
biclusternumber(BicRes, number= 1:BicRes@Number)

Arguments

Value

Returns a list containing all extracted bicluster

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

See Also

writeclust,writeBiclusterResults

Examples

  s2=matrix(rnorm(400),20,20)
  s2[12:16,12:16]=rnorm(25,3,0.3)
  set.seed(1)
  bics <- biclust(s2,BCPlaid(), back.fit = 2, shuffle = 3, fit.model = ~m + a + b,
  iter.startup = 5, iter.layer = 30,  verbose = TRUE)
  bicluster(s2, bics)
  biclusternumber(bics)

Bicluster Membership Graph

Description

Draws a membership graph cluster x columns

Usage

biclustmember(bicResult, x, mid = T, cl_label = "", which=NA, 
  main = "BiCluster Membership Graph", xlab="Cluster", 
  color=diverge_hcl(101, h = c(0, 130)), ...)

clustmember(res, x, mid = T, cl_label = "", which=NA, 
  main = "Cluster Membership Graph", xlab="Cluster", 
  color=diverge_hcl(101, h = c(0, 130)), ...)

bicorder(bicResult, cols=TRUE, rev=FALSE)

Arguments

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

See Also

bubbleplot for simultaneous representation of biclusters, parallelCoordinatesfor single representation of biclusters as lines of gene or condition profiles, drawHeatmapfor Heatmap representation of biclusters and biclustbarchart for a barchart.

Examples

  set.seed(1)
  x=matrix(rnorm(900),30,30)
  x[1:5,1:5]=rnorm(25,3,0.3)
  x[11:15,11:15]=rnorm(25,-3,0.3)
  x[21:25,21:25]=rnorm(25,6,0.3)
  colnames(x)<-paste("Var.",1:30)
  bics <- biclust(x,BCPlaid(), back.fit = 2, shuffle = 3, fit.model = ~m + a + b,
  iter.startup = 5, iter.layer = 30,  verbose = TRUE)
  
  biclustmember(bics,x)
  
  ord<-bicorder(bics, cols=TRUE, rev=TRUE)
  
  biclustmember(bics,x,which=ord)
  

Parameter Grid for BCBimax Biclustering

Description

Generates a list containing parameter settings for the ensemble algorithm.

Usage

bimax.grid(method = "BCBimax", minr = c(10, 11), minc = c(10, 11), number = 10)

Arguments

Value

A list containing parameter settings

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

See Also

ensemble, BCBimax

Examples

bimax.grid()

Binarize

Description

Methods to convert a real matrix to a binary matrix.

Usage

binarize(x, threshold=NA)
binarizeByPercentage(x,percentage, error=0.2, gap=0.1)
densityOnes(x)

Arguments

Details

The binarize function returns a matrix binarized by input threshold, or by the median if no threshold is given.

The binarizeByPercentage function returns a matrix binarize by input percentage, given as desired density of ones against zeros.

The densityOnes function returns the percentage of ones against zeros in a logical matrix

Author(s)

Rodrigo Santamaria rodri@usal.es

Examples

  data(BicatYeast)
  m1=binarize(BicatYeast)
  m2=binarize(BicatYeast, 0.2)
  m3=binarizeByPercentage(BicatYeast, 5)
  densityOnes(m3)
  densityOnes(m2)
  densityOnes(m1)
  drawHeatmap(BicatYeast)
  drawHeatmap(m1)
  drawHeatmap(m2)
  drawHeatmap(m3)

Bubbleplot

Description

Draws a bubble plot where each bicluster is represented as a circle (bubble). Color represents the bicluster set to which bicluster pertains (up to three bicluster sets can be represented simultaneously). Brightness represents the bicluster homogeneity (darker, less homogeneous). Size represents the size of the bicluster, as (number of genes)x(number of conditions). Location is a 2D-projection of gene and condition profiles.

Usage

bubbleplot(x, bicResult1, bicResult2=NULL, bicResult3=NULL, projection="mean", 
  showLabels=FALSE)

Arguments

Details

Position of circles depend on a 2D projection of the multidimensional point formed by rows and columns present in the bicluster. For example, if we have a 3x3 matrix to analyze and we find a bicluster with rows 1 and 3 and columns 2 and 3, the corresponding multidimensional point will be p=(1,0,1,0,1,1). For this example, 'mean' projection will map the bicluster with the point x=(1+3)/2=2 and y=(2+3)/2=2,5. Other projections will take the point p and project it following the corresponding algorithms (see the corresponding help pages for details)

Note

Bubbleplot 2D-projection, as any multidimensional scaling, loses information, trying to take the main relationships and trends of n-dimensional data. Thus, locations and intersections between bubbles-biclusters are only an estimate of its similarity. This visualization should be used just as a help to understand overall behavior of biclustering methods, detect trends and outliers, etc.

Author(s)

Rodrigo Santamaria rodri@usal.es

See Also

drawHeatmap for single representation of biclusters inside data matrix, parallelCoordinates for single representation of biclusters as lines of gene or condition profiles, cmdscale, isomds for multidimensional scaling and plot for other point representations.

Examples

  
  #Simplified yeast microarray data
  ## Not run:  
  data(BicatYeast)
  set.seed(1)
  bics1 <- biclust(BicatYeast,BCPlaid(), back.fit = 2, shuffle = 3, fit.model = ~m + a + b,
  row.release = 0.7, col.release = 0.7,
  verbose = FALSE, max.layers = 10, iter.startup = 5,
  iter.layer = 30)
  bubbleplot(BicatYeast,bics1, showLabels=TRUE)

  loma=binarize(BicatYeast,2)
  bics2=biclust(loma,BCBimax(), minr=4, minc=4, number=10)
  bubbleplot(BicatYeast,bics1,bics2)
  
## End(Not run)
  

Coherence measures

Description

Different preliminary measures of how much constant or (additive, multiplicative, sign) coherent a bicluster is, following Madeira and Oliveira classification of biclusters.

Usage

constantVariance(x, resultSet, number, dimension="both")
additiveVariance(x, resultSet, number, dimension="both")
multiplicativeVariance(x, resultSet, number, dimension="both")
signVariance(x, resultSet, number, dimension="both")

Arguments

Details

Returns the corresponding variance of genes or conditions as the average of the sum of euclidean distances between all rows and/or columns of the bicluster. For additive, multiplicative and sign variance first a transformation of the bicluster is done, so variance is computed on a matrix that reflects difference, rest or change of sign between rows, columns or both.

The lower the value returned, the more constant or coherent the bicluster is. If the value returned is 0, the bicluster is ideally constant or coherent. Usually, a value above 1-1.5 is enough to determine the bicluster is not constant or coherent.

Note

There are preliminary measures for coherence. Since transformations are different, measures are not normalized and comparison between, for example, additive and multiplicative variance is not meaningful. Only comparisons between different measures of the same kind of variance are reliable by now.

Author(s)

Rodrigo Santamaria rodri@usal.es

Examples

  #Simplified yeast microarray data
  data(BicatYeast)
  set.seed(1)
  bics1 <- biclust(BicatYeast,BCPlaid(), back.fit = 2, shuffle = 3, fit.model = ~m + a + b,
  row.release = 0.7, col.release = 0.7,
  verbose = FALSE, max.layers = 10, iter.startup = 5,
  iter.layer = 30)
  
  constantVariance(BicatYeast, bics1,1,"row")
  constantVariance(BicatYeast, bics1,1,"col")
  constantVariance(BicatYeast, bics1,1,"both")
  additiveVariance(BicatYeast, bics1,1,"both")
  multiplicativeVariance(BicatYeast, bics1,1,"both")
  signVariance(BicatYeast, bics1,1,"both")
  

Diagnostic F Statistic Calculation

Description

Functions for obtaining F statistics within bicluster and the significance levels. The main effects considered are row, column and interaction effect.

Usage

computeObservedFstat(x, bicResult, number)

Arguments

Details

F-statistics are calculated from the two-way ANOVA mode with row anc column effect. The full model with interaction is unidentifiable, thus, Tukey's test for non-additivity is used to detect an interaction within a bicluster. p-values are obtained from assymptotic F distributions.

Value

Data frame with three rows ("Row Effect", "Column Effect", "Tukey test") and 2 columns for corresponding statistics (Fstat) and their p-values (PValue). 2

Author(s)

Tatsiana KHAMIAKOVA tatsiana.khamiakova@uhasselt.be

See Also

diagnosticTest, diagnosticPlot2, ChiaKaruturi, diagnoseColRow

Examples

#---simulate dataset with 1 bicluster ---#
xmat<-matrix(rnorm(50*50,0,0.25),50,50) # background noise only 
rowSize <- 20 #number of rows in a bicluster 
colSize <- 10 #number of columns in a bicluster
a1<-rnorm(rowSize,1,0.1) #sample row effect from N(0,0.1) #adding a coherent values bicluster:
b1<-rnorm((colSize),2,0.25)  #sample column effect from N(0,0.05)
mu<-0.01 #constant value signal
 for ( i in 1 : rowSize){
 	for(j in 1: (colSize)){
 		xmat[i,j] <- xmat[i,j] + mu + a1[i] + b1[j] 	
 	}
 }
 #--obtain a bicluster by running an algorithm---# 
plaidmab <- biclust(x=xmat, method=BCPlaid(), cluster="b", fit.model = y ~ m + a+ b,  
background = TRUE, row.release = 0.6, col.release = 0.7, shuffle = 50, back.fit = 5, 
max.layers = 1, iter.startup = 100, iter.layer = 100, verbose = TRUE)

#Calculate statistics and their p-values to infer about the structure within bicluster:
Structure <- computeObservedFstat(x=xmat, bicResult = plaidmab, number = 1)

Bootstrap Procedure for Bicluster Diagnostics

Description

Calculate the significance of the discovered patter in the data based on the bootstrapping procedure.

Usage

diagnoseColRow(x, bicResult, number, nResamplings, replace = TRUE)

Arguments

Details

The function computes observed F statistics for row and column effect based on two-way ANOVA model. Bootstrap procedure is used to evaluate the significance of discovered bicluster. Based on nResamplings replicates, the disribution of F statistics for row and column effects are obtained. The p-value is computed as

P(A) = \frac{ \# \left \{ F^{*}(A)_{b} > F(A)^{obs} \right \} } {nResamplings+1}

Low p-values denote non-random selection of columns for a given bicluster. Large p-values show that in other columns for a given set of genes in the bicluster structure is similar. Hence, bicluster columns were just randomly picked by an algorithm for a set of co-regulated genes.

Value

Author(s)

Tatsiana KHAMIAKOVA tatsiana.khamiakova@uhasselt.be

See Also

diagnosticTest, diagnosticPlot2, diagnosticPlot, computeObservedFstat, ChiaKaruturi

Examples

#---simulate dataset with 1 bicluster ---#
xmat<-matrix(rnorm(50*50,0,0.25),50,50) # background noise only 
rowSize <- 20 #number of rows in a bicluster 
colSize <- 10 #number of columns in a bicluster
a1<-rnorm(rowSize,1,0.1) #sample row effect from N(0,0.1) #adding a coherent values bicluster:
b1<-rnorm((colSize),2,0.25)  #sample column effect from N(0,0.05)
mu<-0.01 #constant value signal
 for ( i in 1 : rowSize){
 	for(j in 1: (colSize)){
 		xmat[i,j] <- xmat[i,j] + mu + a1[i] + b1[j] 	
 	}
 }
 #--obtain a bicluster by running an algorithm---# 
plaidmab <- biclust(x=xmat, method=BCPlaid(), cluster="b", fit.model = y ~ m + a+ b,  
background = TRUE, row.release = 0.6, col.release = 0.7, shuffle = 50, back.fit = 5, 
max.layers = 1, iter.startup = 100, iter.layer = 100, verbose = TRUE)

#Run boosotrap procedure:
Bootstrap <- diagnoseColRow(x=xmat, bicResult = plaidmab, number = 1, nResamplings = 999,
  replace = TRUE)
diagnosticPlot(bootstrapOutput = Bootstrap) 	# plotting distribution of bootstrap replicates

Diagnostic F Statistics Visualization

Description

Plots distributions of bootstrap replicates of F-statistics for row and column effect and highlights the observed statistics

Usage

diagnosticPlot(bootstrapOutput)

Arguments

Value

No value is returned. The plot is constructed in a current device.

Author(s)

Tatsiana KHAMIAKOVA tatsiana.khamiakova@uhasselt.be

See Also

diagnoseColRow, computeObservedFstat

Examples

#---simulate dataset with 1 bicluster ---#
xmat<-matrix(rnorm(50*50,0,0.25),50,50) # background noise only 
rowSize <- 20 #number of rows in a bicluster 
colSize <- 10 #number of columns in a bicluster
a1<-rnorm(rowSize,1,0.1) #sample row effect from N(0,0.1) #adding a coherent values bicluster:
b1<-rnorm((colSize),2,0.25)  #sample column effect from N(0,0.05)
mu<-0.01 #constant value signal
 for ( i in 1 : rowSize){
 	for(j in 1: (colSize)){
 		xmat[i,j] <- xmat[i,j] + mu + a1[i] + b1[j] 	
 	}
 }
 #--obtain a bicluster by running an algorithm---# 
plaidmab <- biclust(x=xmat, method=BCPlaid(), cluster="b", fit.model = y ~ m + a+ b,  
background = TRUE, row.release = 0.6, col.release = 0.7, shuffle = 50, back.fit = 5, 
max.layers = 1, iter.startup = 100, iter.layer = 100, verbose = TRUE)

#Run bootsrap procedure:
Bootstrap <- diagnoseColRow(x=xmat, bicResult = plaidmab, number = 1, 
  nResamplings = 999, replace = TRUE)

# plotting distribution of bootstrap replicates
diagnosticPlot(bootstrapOutput = Bootstrap) 	

Diagnostics F Statistiics Visualization

Description

Plots distributions of bootstrap replicates of F-statistics for row, column and multiplicative effects obtained from diagnosticTest (when save_F=TRUE). Contains an option to highlight the observed statistics.

Usage

diagnosticPlot2(diagnosticTest, number = 1, StatVal = TRUE,
  binwidth = NULL)

Arguments

Value

Returns a ggplot object.

Author(s)

Ewoud De Troyer

Examples

## Not run: 
#Random matrix with embedded bicluster (with multiplicative effect)
test <- matrix(rnorm(5000),100,50)
roweff <- sample(1:5,10,replace=TRUE)
coleff <- sample(1:5,10,replace=TRUE)
test[11:20,11:20] <- test[11:20,11:20] +
  matrix(coleff,nrow=10,ncol=10,byrow=TRUE) +
  matrix(roweff,nrow=10,ncol=10) +
  roweff %*% t(coleff)


#Apply Plaid Biclustering
res <- biclust(test, method=BCPlaid())

#Apply default diagnosticTest
out <- diagnosticTest(BCresult=res, data=test, save_F=TRUE, number=1,
                      statistics=c("F","Tukey","ModTukey","Tusell","Mandel","LBI","JandG"),
                      samplingtypes=c("Permutation","SemiparPerm","SemiparBoot",
                      "PermutationCor","SamplingCor","NormSim"))

#Plot Distributions
diagnosticPlot2(out,number=1)

## End(Not run)

Testing Procedure for Bicluster Diagnostics

Description

Calculate the statistical value of the row, column and multiplicative effect based on discovered biclusters in the data. Additionally multiple sampling methods are available to compute the statistical significance through p-values.

Usage

diagnosticTest(BCresult, data, number = 1:BCresult@Number, verbose = TRUE,
  statistics = c("F", "Tukey"), sampling = TRUE, samplingtypes = NULL,
  nSim = 1000, alpha = 0.05, save_F = FALSE)

Arguments

Details

Due to the uncertainty of discovering the true bicluster(s) in the data, it's often advisable to not rely on the theoretical p-values but instead retrieve the p-values through a sampling procedure.

Available p-values/sampling types for each statistical method:

• "F": "Theoretical" and "Permutation" for both row and column effect.

• "Tukey": "Theoretical", "SemiparPerm" and "SemiparBoot".

• "ModTukey": "Theoretical", "SemiparPerm", "SemiparBoot", "PermutationCor" and "SamplingCor".

• "Tusell": "SemiparPerm", "SemiparBoot" and "NormSim".

• "Mandel": "Theoretical", "SemiparPerm" and "SemiparBoot".

• "LBI": "SemiparPerm", "SemiparBoot" and "NormSim".

• "JandG": "SemiparPerm", "SemiparBoot" and "NormSim".

More info on the sampling types can be found in the secion below. If available, the "Theoretical" will always be computed. By default when sampling=TRUE, a sampling method without replacement is chosen, namely "Permutation" and "SemiparPerm".

When save_F=TRUE, the null distributions of the statistics can be visualised with diagnosticPlot2.

Disclaimer: While their functionality did not change, some functions of the additivityTests package were altered in order to be able to return the permuted/bootstrapped statistics and p-values.

Value

Returns a list with length(number) elements. Each element corresponds with the requested biclusters and is a list containing:

• table: a data frame where each row is statistics and samplingtypes (including Theoretical) combination. The data frame contains the Method, Type (p-value type), StatVal (statistical value), CritVal (critical value), pVal and Sign (0/1 significance indicator based on alpha).

• save_F: if save_F=TRUE, a (nSim x number of permuted/bootstrapped p-values) matrix contained the sampled statistics.

Sampling Types

For each sampling type a permuted/bootstrapped BC is created as following:

• "Permutation": Sample a BC from the entire dataset with replacement.

• "SemiparPerm": A semi-parametric permutation procedure. Two-way ANOVA is applied on the original BC and the residual matrix extracted. A new residual matrix is created by sampling without replacement from the original residual matrix. The sampled BC is then generated by adding this sampled residual matrix on top the mean, row and column effect of the ANOVA procedure of the original BC.

• "SemiparBoot": A semi-parametric bootstrapping procedure. Two-way ANOVA is applied on the original BC and the residual matrix extracted. A new residual matrix is created by sampling with replacement from the original residual matrix. The sampled BC is then generated by adding this sampled residual matrix on top the mean, row and column effect of the ANOVA procedure of the original BC.

• "PermutationCor": See correction=1 parameter of mtukey.test. More info in Simecek and Simeckova (2012).

• "SamplingCor": See correction=2 parameter of mtukey.test. More info in Simecek and Simeckova (2012).

• "NormSim": Sample a BC from a standard normal distribution. This sampling procedure is used for some methods in the additivityTests package.

Author(s)

Ewoud De Troyer

References

Tukey, J.W.: One Degree of Freedom for Non-additivity, Biometrics 5, pp. 232-242, 1949.

Simecek, Petr, and Simeckova, Marie. "Modification of Tukey's additivity test." Journal of Statistical Planning and Inference, 2012.

Examples

## Not run: 
#Random matrix with embedded bicluster (with multiplicative effect)
test <- matrix(rnorm(5000),100,50)
roweff <- sample(1:5,10,replace=TRUE)
coleff <- sample(1:5,10,replace=TRUE)
test[11:20,11:20] <- test[11:20,11:20] +
  matrix(coleff,nrow=10,ncol=10,byrow=TRUE) +
  matrix(roweff,nrow=10,ncol=10) +
  roweff %*% t(coleff)


#Apply Plaid Biclustering
res <- biclust(test, method=BCPlaid())

#Apply default diagnosticTest
out <- diagnosticTest(BCresult=res, data=test, save_F=TRUE, number=1,
                      statistics=c("F","Tukey","ModTukey","Tusell","Mandel","LBI","JandG"),
                      samplingtypes=c("Permutation","SemiparPerm","SemiparBoot",
                      "PermutationCor","SamplingCor","NormSim"))

out[[1]]$table

## End(Not run)

Create a discret matrix

Description

Some biclusteralgorithms need a discret matrix to perform well. This function delivers a discret matrix with either a given number of levels of equally spaced intervals from minimum to maximum, or levels of same size using the quantiles.

Usage

discretize(x,nof=10,quant=FALSE)

Arguments

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

Examples

  #Discretize yeast microarray data
  data(BicatYeast)
  discretize(BicatYeast[1:10,1:10])

  

Draw Heatmap

Description

Draws a microarray data matrix as a heatmap, with rows and colums reordered so the rows and columns of the input bicluster will be at top-left of the matrix.

Usage

drawHeatmap(x,bicResult=NULL,number=NA,local=TRUE, beamercolor=FALSE,paleta,...)
drawHeatmap2(x,bicResult=NULL,number=NA,plotAll=FALSE)

Arguments

Details

'plotAll' only works if there is a exclusive rows and column Result!

Author(s)

Rodrigo Santamaria rodri@usal.es, Sebastian Kaiser

See Also

bubbleplot for simultaneous representation of biclusters.\ parallelCoordinatesfor single representation of biclusters as lines of gene or condition profiles.

Examples

  #Random 100x50 matrix with a single, up-regulated 10x10 bicluster
  s2=matrix(rnorm(5000),100,50)
  s2[11:20,11:20]=rnorm(100,3,0.3)
  set.seed(1)
  bics <- biclust(s2,BCPlaid(), back.fit = 2, shuffle = 3, fit.model = ~m + a + b,
  iter.startup = 5, iter.layer = 30,  verbose = TRUE)
  drawHeatmap(s2,bics,1)

Ensemble Methods for Bicluster Algorithms

Description

Calculates an ensemble of biclusters from different parameter setting of possible different bicluster algorithms.

Usage

ensemble(x, confs, rep = 1, maxNum = 5, similar = jaccard2, thr = 0.8, simthr =0.7,
  subs = c(1, 1), bootstrap = FALSE, support = 0, combine=firstcome, ...)

Arguments

Details

Two different kinds (or both combined) of ensembling is possible. Ensemble of repeated runs or ensemble of runs on subsamples.

Value

Return an object of class Biclust

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

See Also

Biclust-class, plaid.grid, bimax.grid

Examples

## Not run: 
data(BicatYeast)
ensemble.plaid <- ensemble(BicatYeast,plaid.grid()[1:5],rep=1,maxNum=2, thr=0.5, subs = c(1,1))
ensemble.plaid
x <- binarize(BicatYeast)
ensemble.bimax <- ensemble(x,bimax.grid(),rep=10,maxNum=2,thr=0.5, subs = c(0.8,0.8))
ensemble.bimax

## End(Not run)

Overlapping Heatmap

Description

Other than drawHeatmap this function plots all or a chosen number of bicluster in one plot even if they were overlapping.

Usage

heatmapBC(x, bicResult, number = 0, local = TRUE, order = FALSE, 
          outside = FALSE, ...)

Arguments

Details

Overlap plotting only works for two neighbor bicluster defined by the order in the number slot.

Author(s)

Sebastian Kaiser

See Also

drawHeatmap,parallelCoordinates

Examples

  set.seed(1234)
  data(BicatYeast)
  resplaid <- biclust(BicatYeast, BCPlaid(), verbose = FALSE)
  heatmapBC(x = BicatYeast, bicResult = resplaid)

Is Bicresult overlapping?

Description

Checks if Biclusterresult includes overlapping rows or columns

Usage

isoverlapp(bicResult)

Arguments

Value

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

See Also

drawHeatmap

Jaccardind

Description

An adaption of the Jaccard Index for clustering is calculated.

Usage

jaccardind(bicres1,bicres2)
jaccard2(Rows, Cols)

Arguments

Details

The function calculates the percentage of datapoints in the same bicluster structure from all datapoints at least included in one bicluster.

Value

jaccardind calculates the Jaccard index jaccard2 returns a similarity matrix containing the Jaccard index between all biclusters (upper triangle matrix)

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

Examples

## Not run: 
data(BicatYeast)
res1<-biclust(BicatYeast, method=BCPlaid(), back.fit = 2, shuffle = 3,
  fit.model = ~m + a + b,iter.startup = 5, iter.layer = 30,  verbose = TRUE)
res2<-biclust(BicatYeast, method=BCCC())
jaccardind(res1,res2)


## End(Not run)

Parallel Coordinates

Description

Represents expression levels through gene and/or condition profiles in a bicluster as lines.

Usage

parallelCoordinates(x, bicResult, number, plotBoth = FALSE, plotcol = TRUE,
compare = TRUE, info = F, bothlab = c("Rows", "Columns"), order = FALSE,
order2 = 0,ylab = "Value" , col=1,...)

Arguments

Author(s)

Rodrigo Santamaria, Martin Sill and Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

See Also

drawHeatmap for alternative representation of biclusters and bubbleplot for simultaneous representation of biclusters.

Examples

  #Random 100x50 matrix with a single, up-regulated 10x10 bicluster
  s2=matrix(rnorm(5000),100,50)
  s2[11:20,11:20]=rnorm(100,3,0.3)
  set.seed(1)
  bics <- biclust(s2,BCPlaid(), back.fit = 2, shuffle = 3, fit.model = ~m + a + b,
  iter.startup = 5, iter.layer = 30,  verbose = TRUE)
  parallelCoordinates(x=s2,bicResult=bics,number=1, plotBoth=TRUE,
plotcol=TRUE, compare=TRUE, info=TRUE,bothlab=c("Genes Bicluster
1","Conditions Bicluster 1"), order =TRUE)
  parallelCoordinates(x=s2,bicResult=bics,number=1, plotBoth=FALSE, plotcol=TRUE, 
    compare=FALSE, info=TRUE)

Parameter Grid for BCPlaid Biclustering

Description

Generates a list containing parameter settings for the ensemble algorithm.

Usage

plaid.grid(method = "BCPlaid", cluster = "b", fit.model = y ~ m + a + b, 
  background = TRUE, background.layer = NA, background.df = 1, 
  row.release = c(0.5, 0.6, 0.7), col.release = c(0.5, 0.6, 0.7), 
  shuffle = 3, back.fit = 0, max.layers = 20, iter.startup = 5, 
  iter.layer = 10, verbose = FALSE)

Arguments

Value

A list containing parameter settings

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

See Also

ensemble, BCPlaid

Examples

plaid.grid()

Barplot of Bicluster

Description

Draws a graph to compare the values inside the diffrent biclusters with the values outside the bicluster

Usage

plotclust(res,x,bicluster=TRUE,legende=FALSE,noC=5,wyld=3,Titel="Plotclust",...)

Arguments

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

See Also

bubbleplot for simultaneous representation of biclusters. parallelCoordinatesfor single representation of biclusters as lines of gene or condition profiles. drawHeatmapfor Heatmap representation of biclusters.

Examples

  s2=matrix(rnorm(400),20,20)
  s2[12:16,12:16]=rnorm(25,3,0.3)
  set.seed(1)
  bics <- biclust(s2,BCPlaid(), back.fit = 2, shuffle = 3, fit.model = ~m + a + b,
  iter.startup = 5, iter.layer = 30,  verbose = TRUE)
  plotclust(bics,s2)

Predict from a BCrepBimax Result

Description

Predicts cluster membership for new data rows given a BCrepBimax Result

Usage

predictBimax(BCrepBimax, x)

Arguments

Value

Returns a vector with clustermembership of data x of class.

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

See Also

BCrepBimax

writeBiclusterResults

Description

Write bicluster results to a file

Usage

writeBiclusterResults(fileName, bicResult, bicName, geneNames, arrayNames,
  append=FALSE, delimiter=" ")

Arguments

Author(s)

Rodrigo Santamaria rodri@usal.es

Examples

## Not run: 
  data(BicatYeast)
  res <- biclust(BicatYeast, method=BCCC(), delta=1.5,  alpha=1, number=10)
  writeBiclusterResults("results.txt", res,"CC with delta 1.5", dimnames(BicatYeast)[1][[1]],
    dimnames(BicatYeast)[2][[1]])
  
## End(Not run)
  

Write a Bicluster as a Cluster Result

Description

Draws a graph to compare the values inside the diffrent biclusters with the values outside the bicluster

Usage

writeclust(Biclusterresult,row=TRUE,noC=10)

Arguments

Author(s)

Sebastian Kaiser sebastian.kaiser@stat.uni-muenchen.de

Examples

  s2=matrix(rnorm(400),20,20)
  s2[12:16,12:16]=rnorm(25,3,0.3)
  set.seed(1)
  bics <- biclust(s2,BCPlaid(), back.fit = 2, shuffle = 3, fit.model = ~m + a + b,
  iter.startup = 5, iter.layer = 30,  verbose = TRUE)
  writeclust(bics)