| Title: | BiCluster Algorithms |
|---|---|
| Description: | The main function biclust() provides several algorithms to find biclusters in two-dimensional data: Cheng and Church (2000, ISBN:1-57735-115-0), spectral (2003) <doi:10.1101/gr.648603>, plaid model (2005) <doi:10.1016/j.csda.2004.02.003>, xmotifs (2003) <doi:10.1142/9789812776303_0008> and bimax (2006) <doi:10.1093/bioinformatics/btl060>. In addition, the package provides methods for data preprocessing (normalization and discretisation), visualisation, and validation of bicluster solutions. |
| Authors: | Sebastian Kaiser, Rodrigo Santamaria, Tatsiana Khamiakova, Martin Sill, Roberto Theron, Luis Quintales, Friedrich Leisch, Ewoud De Troyer and Sami Leon. |
| Maintainer: | Sebastian Kaiser <[email protected]> |
| License: | GPL-3 |
| Version: | 2.0.3.1 |
| Built: | 2024-08-28 06:36:50 UTC |
| Source: | CRAN |
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.
## 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)## 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)
x |
A logical matrix which represents the data. |
method |
Here BCBimax, to perform Bimax algorithm |
minr |
Minimum row size of resulting bicluster. |
minc |
Minimum column size of resulting bicluster. |
number |
Number of Bicluster to be found. |
maxc |
Maximum column size of resulting bicluster. |
Returns an object of class Biclust.
Sebastian Kaiser [email protected]
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
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) restest <- 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
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.
## S4 method for signature 'matrix,BCCC' biclust(x, method=BCCC(), delta = 1.0, alpha=1.5, number=100)## S4 method for signature 'matrix,BCCC' biclust(x, method=BCCC(), delta = 1.0, alpha=1.5, number=100)
x |
Data matrix. |
method |
Here BCCC, to perform CC algorithm |
delta |
Maximum of accepted score. |
alpha |
Scaling factor. |
number |
Number of bicluster to be found. |
Returns an object of class Biclust.
Sebastian Kaiser [email protected]
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
test <- matrix(rbinom(400, 50, 0.4), 20, 20) res <- biclust(test, method=BCCC(), delta=1.5, alpha=1, number=10) restest <- matrix(rbinom(400, 50, 0.4), 20, 20) res <- biclust(test, method=BCCC(), delta=1.5, alpha=1, number=10) res
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.
## 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)## 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)
x |
The data matrix where biclusters have to be found |
method |
Here BCPlaid, to perform Plaid algorithm |
cluster |
'r', 'c' or 'b', to cluster rows, columns or both (default 'b') |
fit.model |
Model (formula) to fit each layer. Usually, a linear model is used, that estimates three parameters: m (constant for all elements in the bicluster), a(contant for all rows in the bicluster) and b (constant for all columns). Thus, default is: y ~ m + a + b. |
background |
If 'TRUE' the method will consider that a background layer (constant for all rows and columns) is present in the data matrix. |
background.layer |
If background='TRUE' a own background layer (Matrix with dimension of x) can be specified. |
background.df |
Degrees of Freedom of backround layer if background.layer is specified. |
shuffle |
Before a layer is added, it's statistical significance is compared against a number of layers obtained by random defined by this parameter. Default is 3, higher numbers could affect time performance. |
iter.startup |
Number of iterations to find starting values |
iter.layer |
Number of iterations to find each layer |
back.fit |
After a layer is added, additional iterations can be done to refine the fitting of the layer (default set to 0) |
row.release |
Scalar in [0,1](with interval recommended [0.5-0.7]) used as threshold to prune rows in the layers depending on row homogeneity |
col.release |
As above, with columns |
max.layers |
Maximum number of layer to include in the model |
verbose |
If 'TRUE' prints extra information on progress. |
Returns an Biclust object.
Adaptation of original code from Heather Turner from Rodrigo Santamaria [email protected]. [email protected]
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.
#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#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
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.
## 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)## 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)
x |
Data Matrix. |
method |
Here BCQuest, to perform Questmotif algorithm |
ns |
Number of questions choosen. |
nd |
Number of repetitions. |
sd |
Sample size in repetitions. |
alpha |
Scaling factor for column result. |
number |
Number of bicluster to be found. |
d |
Half margin of intervall question values should be in (Intervall is mean-d,mean+d). |
quant |
Which quantile to use on metric data |
vari |
Which varianz to use for metric data |
Returns an object of class Biclust.
Class "BiclustMethod", directly.
Sebastian Kaiser [email protected]
Murali, T. & Kasif, S. Extracting Conserved Gene Expression Motifs from Gene Expression Data Pacific Symposium on Biocomputing, sullivan.bu.edu, 2003, 8, 77-88
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).
## 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)## 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)
x |
The data matrix where biclusters are to be found |
method |
Here BCSpectral, to perform Spectral algorithm |
normalization |
Normalization method to apply to mat. Three methods are allowed as described by Kluger et al.: "log" (Logarithmic normalization), "irrc" (Independent Rescaling of Rows and Columns) and "bistochastization". If "log" normalization is used, be sure you can apply logarithm to elements in data matrix, if there are values under 1, it automatically will sum to each element in mat (1+abs(min(mat))) Default is "log", as recommended by Kluger et al. |
numberOfEigenvalues |
the number of eigenValues considered to find biclusters. Each row (gene) eigenVector will be combined with all column (condition) eigenVectors for the first numberOfEigenValues eigenvalues. Note that a high number could increase dramatically time performance. Usually, only the first eigenvectors are used. With "irrc" and "bistochastization" methods, first eigenvalue contains background (irrelevant) information, so it is ignored. |
minr |
minimum number of rows that biclusters must have. The algorithm will not consider smaller biclusters. |
minc |
minimum number of columns that biclusters must have. The algorithm will not consider smaller biclusters. |
withinVar |
maximum within variation allowed. Since spectral biclustering outputs a checkerboard structure despite of relevance of individual cells, a filtering of only relevant cells is necessary by means of this within variation threshold. |
n_clusters |
vector with first element the number of row clusters and second element the number of column clusters. If |
n_best |
number of eigenvectors to which the data is projected for the final clustering step, recommended values are 2 or 3. |
Returns an object of class Biclust.
Sami Leon [email protected]
Rodrigo Santamaria [email protected]
Kluger et al., "Spectral Biclustering of Microarray Data: Coclustering Genes and Conditions", Genome Research, 2003, vol. 13, pages 703-716
# 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)])# 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)])
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.
## S4 method for signature 'matrix,BCXmotifs' biclust(x, method=BCXmotifs(), ns=10, nd=10, sd=5, alpha=0.05, number=100)## S4 method for signature 'matrix,BCXmotifs' biclust(x, method=BCXmotifs(), ns=10, nd=10, sd=5, alpha=0.05, number=100)
x |
Data Matrix. |
method |
Here BCXmotifs, to perform Xmotifs algorithm |
ns |
Number of columns choosen. |
nd |
Number of repetitions. |
sd |
Sample size in repetitions. |
alpha |
Scaling factor for column result. |
number |
Number of bicluster to be found. |
Returns an object of class Biclust.
Class "BiclustMethod", directly.
Sebastian Kaiser [email protected]
Murali, T. & Kasif, S. Extracting Conserved Gene Expression Motifs from Gene Expression Data Pacific Symposium on Biocomputing, sullivan.bu.edu, 2003, 8, 77-88
data(BicatYeast) x<-discretize(BicatYeast) res <- biclust(x, method=BCXmotifs(), ns=20, nd=20, sd=5, alpha=0.01, number=10) resdata(BicatYeast) x<-discretize(BicatYeast) res <- biclust(x, method=BCXmotifs(), ns=20, nd=20, sd=5, alpha=0.01, number=10) res
Microarray data matrix for 80 experiments with Saccharomyces Cerevisiae organism extracted from BicAT example data set.
data(BicatYeast)data(BicatYeast)
Data structure with information about the expression levels of 419 probesets over 70 conditions Row names follow Affymetrix probeset notation
BicAT datasets at http://www.tik.ee.ethz.ch/sop/bicat/
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.
## S4 method for signature 'matrix,BiclustMethod' biclust(x,method,...) ## S4 method for signature 'matrix,character' biclust(x,method,...)## S4 method for signature 'matrix,BiclustMethod' biclust(x,method,...) ## S4 method for signature 'matrix,character' biclust(x,method,...)
x |
Data matrix. |
method |
An object of class |
... |
Additional Parameters of the |
Returns an object of class Biclust.
Sebastian Kaiser [email protected]
Biclust-class, BCCC, BCXmotifs, BCPlaid, BCSpectral, BCBimax, BCQuest, BiclustMethod-class
test <- matrix(rbinom(400, 50, 0.4), 20, 20) res1 <- biclust(test, method=BCCC(), delta=1.5, alpha=1, number=10)test <- matrix(rbinom(400, 50, 0.4), 20, 20) res1 <- biclust(test, method=BCCC(), delta=1.5, alpha=1, number=10)
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 can be created by performing a bicluster algorithm via the biclust() function.
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
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.
Sebastian Kaiser [email protected]
Draws a barchart for a Bicluster result representing the columns
biclustbarchart(x, Bicres, which=NULL, ...)biclustbarchart(x, Bicres, which=NULL, ...)
x |
The data matrix |
Bicres |
BiclustResult object with a bicluster result set. If this value is set to NULL, the data matrix is drawn as a heatmap, without any reordering. Default NULL. |
which |
If specified gives the ploting order of the columns from bottom to top |
... |
Additional plot options passed to barchart |
Sebastian Kaiser [email protected]
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.
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)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)
Function to extract the bicluster or the row and column numbers from a given bicluster result
bicluster(x, BicRes, number= 1:BicRes@Number) biclusternumber(BicRes, number= 1:BicRes@Number)bicluster(x, BicRes, number= 1:BicRes@Number) biclusternumber(BicRes, number= 1:BicRes@Number)
x |
The data matrix |
BicRes |
BiclustResult object |
number |
Which bicluster to be extracted |
Returns a list containing all extracted bicluster
Sebastian Kaiser [email protected]
writeclust,writeBiclusterResults
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)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)
Draws a membership graph cluster x columns
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)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)
x |
The data matrix |
bicResult |
BiclustResult object with a bicluster result set. |
res |
Cluster Result (is converted into a kcca object) |
mid |
If TRUE, shows the value of the remaining objects inside the cluster value, else shows both aside each other. |
cl_label |
Ticks of x-axis |
which |
If specified gives the ploting order of the columns from bottom to top |
main |
Gives the title of the plot |
xlab |
Label of x-axis |
color |
Range of colors for the plot |
... |
Additional plot options or if neccessary option for as.kcca |
cols |
If TRUE orders the column by appearance in the bicluster, else orders the rows. |
rev |
If TRUE reverses the order |
Sebastian Kaiser [email protected]
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.
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)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)
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.
Currently 6 classes inherit from BiclustMethod:
BCCC, BCXmotifs, BCPlaid, BCSpectral, BCBimax, BCQuest
Sebastian Kaiser [email protected]
biclust, Biclust-class, BCCC, BCXmotifs, BCPlaid, BCSpectral, BCBimax, BCQuest, BiclustMethod-class
Generates a list containing parameter settings for the ensemble algorithm.
bimax.grid(method = "BCBimax", minr = c(10, 11), minc = c(10, 11), number = 10)bimax.grid(method = "BCBimax", minr = c(10, 11), minc = c(10, 11), number = 10)
method |
Here BCBimax, to perform Bimax algorithm |
minr |
Minimum row size of resulting bicluster. |
minc |
Minimum column size of resulting bicluster. |
number |
Number of Bicluster to be found. |
A list containing parameter settings
Sebastian Kaiser [email protected]
bimax.grid()bimax.grid()
Methods to convert a real matrix to a binary matrix.
binarize(x, threshold=NA) binarizeByPercentage(x,percentage, error=0.2, gap=0.1) densityOnes(x)binarize(x, threshold=NA) binarizeByPercentage(x,percentage, error=0.2, gap=0.1) densityOnes(x)
x |
The data matrix to be binarized. |
threshold |
Threshold used to binarize. Values over threshold will be set to 1, the rest to 0. If threshold is NA, median is used as threshold. Default NA. |
percentage |
Percentage of ones against zeros desired in the binary matrix. |
error |
Percentage of ones against zeros in the final matrix will be in [percentage-error, percentage+error]. Default 0.2 |
gap |
Value used for incremental search of threshold. Default 0.1 |
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
Rodrigo Santamaria [email protected]
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)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)
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.
bubbleplot(x, bicResult1, bicResult2=NULL, bicResult3=NULL, projection="mean", showLabels=FALSE)bubbleplot(x, bicResult1, bicResult2=NULL, bicResult3=NULL, projection="mean", showLabels=FALSE)
x |
The data matrix from which biclusters were identified. |
bicResult1 |
BiclustResult object with a bicluster result set whose biclusters will be drawn in green. |
bicResult2 |
BiclustResult object with an optional second bicluster result set. Will be drawn in red (default NULL) |
bicResult3 |
BiclustResult object with an optional third bicluster result set. Will be drawn in blue (default NULL) |
projection |
Projection algorithm used to position bubbles. Allowed projections are 'mean', 'isomds' and 'cmdscale' (default 'mean'). See details section for a broader explanation. |
showLabels |
If 'TRUE', puts a label over each bubble that tells the number within the corresponding bicluster result (default 'FALSE'). |
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)
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.
Rodrigo Santamaria [email protected]
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.
#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)#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)
Function computing scores as described in the paper of Chia and Karuturi (2010)
ChiaKaruturi(x, bicResult, number)ChiaKaruturi(x, bicResult, number)
x |
Data Matrix |
bicResult |
|
number |
Number of bicluster in the output for computing the scores |
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.
Data.Frame with 6 slots: T, B scores for within and outside bicluster, SB and TS scores
Tatsiana KHAMIAKOVA [email protected]
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.
diagnosticPlot, computeObservedFstat, diagnoseColRow
#---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)#---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)
Different preliminary measures of how much constant or (additive, multiplicative, sign) coherent a bicluster is, following Madeira and Oliveira classification of biclusters.
constantVariance(x, resultSet, number, dimension="both") additiveVariance(x, resultSet, number, dimension="both") multiplicativeVariance(x, resultSet, number, dimension="both") signVariance(x, resultSet, number, dimension="both")constantVariance(x, resultSet, number, dimension="both") additiveVariance(x, resultSet, number, dimension="both") multiplicativeVariance(x, resultSet, number, dimension="both") signVariance(x, resultSet, number, dimension="both")
x |
The data matrix from which biclusters were identified |
resultSet |
BiclustResult object with a bicluster result set where is the bicluster to measure |
number |
Number of the bicluster withing the result set |
dimension |
"both" for determining overall variance, "row" for gene variance and "col" for column variance. Default "both" |
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.
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.
Rodrigo Santamaria [email protected]
#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")#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")
Functions for obtaining F statistics within bicluster and the significance levels. The main effects considered are row, column and interaction effect.
computeObservedFstat(x, bicResult, number)computeObservedFstat(x, bicResult, number)
x |
Data Matrix |
bicResult |
|
number |
Number of bicluster in the output for computing observed statistics |
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.
Data frame with three rows ("Row Effect", "Column Effect", "Tukey test") and 2 columns for corresponding statistics (Fstat) and their p-values (PValue). 2
Tatsiana KHAMIAKOVA [email protected]
diagnosticTest, diagnosticPlot2, ChiaKaruturi, diagnoseColRow
#---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)#---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)
Calculate the significance of the discovered patter in the data based on the bootstrapping procedure.
diagnoseColRow(x, bicResult, number, nResamplings, replace = TRUE)diagnoseColRow(x, bicResult, number, nResamplings, replace = TRUE)
x |
data matrix, which |
bicResult |
object of class |
number |
number of bicluster from the output for the diagnostics |
nResamplings |
number of bootstrap replicates |
replace |
logical flag for bootstrap (TRUE), or sampling without replacement (FALSE) |
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
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.
bootstrapFstats |
matrix with two columns, containing values of bootstrap F-statistics. The first column corresponds to row, the second column corresponds to column. |
observedFstatRow |
observed F-statistics for the row effect |
observedFstatCol |
observed F-statistics for the column effect |
bootstrapPvalueRow |
bootstrap p value for row effect |
bootstrapPvalueCol |
bootstrap p value for column effect |
Tatsiana KHAMIAKOVA [email protected]
diagnosticTest, diagnosticPlot2, diagnosticPlot, computeObservedFstat, ChiaKaruturi
#---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#---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
Plots distributions of bootstrap replicates of F-statistics for row and column effect and highlights the observed statistics
diagnosticPlot(bootstrapOutput)diagnosticPlot(bootstrapOutput)
bootstrapOutput |
output of |
No value is returned. The plot is constructed in a current device.
Tatsiana KHAMIAKOVA [email protected]
diagnoseColRow, computeObservedFstat
#---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)#---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)
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.
diagnosticPlot2(diagnosticTest, number = 1, StatVal = TRUE, binwidth = NULL)diagnosticPlot2(diagnosticTest, number = 1, StatVal = TRUE, binwidth = NULL)
diagnosticTest |
output of |
number |
Number of which BC to plot. This needs to be one of the Biclusters requested in in |
StatVal |
Boolean value to draw the observed statistic on the distribution plots. |
binwidth |
The width of the bins. |
Returns a ggplot object.
Ewoud De Troyer
## 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)## 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)
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.
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)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)
BCresult |
An object of class |
data |
data matrix, which |
number |
Vector of bicluster numbers of which the diagnostics should be calculated. (default = all available biclusters) |
verbose |
Boolean value to print progression of computed statistics. |
statistics |
Vector select which statistics to compute. (default =
|
sampling |
Boolean value to apply sampling methods to compute statistical significance (default= |
samplingtypes |
Vector of sampling methods for
See Details for more info. |
nSim |
Number of permutations/bootstraps. |
alpha |
Significance level (default=0.05) |
save_F |
Option to save the permuted/bootstraped statistics. This is necessary for |
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.
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.
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.
Ewoud De Troyer
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.
## 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]]$table ## End(Not run)## Not run: #Random matrix with embedded bicluster (with multiplicative effect) test <- matrix(rnorm(5000),100,50) roweff <- sample(1:5,10,replace=TRUE) coleff <- sample(1:5,10,replace=TRUE) test[11:20,11:20] <- test[11:20,11:20] + matrix(coleff,nrow=10,ncol=10,byrow=TRUE) + matrix(roweff,nrow=10,ncol=10) + roweff %*% t(coleff) #Apply Plaid Biclustering res <- biclust(test, method=BCPlaid()) #Apply default diagnosticTest out <- diagnosticTest(BCresult=res, data=test, save_F=TRUE, number=1, statistics=c("F","Tukey","ModTukey","Tusell","Mandel","LBI","JandG"), samplingtypes=c("Permutation","SemiparPerm","SemiparBoot", "PermutationCor","SamplingCor","NormSim")) out[[1]]$table ## End(Not run)
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.
discretize(x,nof=10,quant=FALSE)discretize(x,nof=10,quant=FALSE)
x |
The data matrix from which should be dicretized |
nof |
Number of levels |
quant |
If TRUE using the quantiles, else using equally spaced levels |
Sebastian Kaiser [email protected]
#Discretize yeast microarray data data(BicatYeast) discretize(BicatYeast[1:10,1:10])#Discretize yeast microarray data data(BicatYeast) discretize(BicatYeast[1:10,1:10])
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.
drawHeatmap(x,bicResult=NULL,number=NA,local=TRUE, beamercolor=FALSE,paleta,...) drawHeatmap2(x,bicResult=NULL,number=NA,plotAll=FALSE)drawHeatmap(x,bicResult=NULL,number=NA,local=TRUE, beamercolor=FALSE,paleta,...) drawHeatmap2(x,bicResult=NULL,number=NA,plotAll=FALSE)
x |
The data matrix where the bicluster is to be drawn. |
bicResult |
BiclustResult object with a bicluster result set. If this value is set to NULL, the data matrix is drawn as a heatmap, without any reordering. Default NULL. |
number |
Bicluster to be drawn from the result set 'bicResult'. If bicResult is set to NULL, this value is ignored. Default NA |
local |
If TRUE, only rows and columns of the bicluster were drawn. |
plotAll |
If TRUE, all Bicluster of result set 'bicResult' were drawn. |
beamercolor |
If TRUE, palete colors are used. |
paleta |
Colors |
... |
Additional plot options |
'plotAll' only works if there is a exclusive rows and column Result!
Rodrigo Santamaria [email protected], Sebastian Kaiser
bubbleplot for simultaneous representation of biclusters.\
parallelCoordinatesfor single representation of biclusters as lines of gene or condition profiles.
#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)#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)
Microarray data matrix for 80 experiments with Saccharomyces Cerevisiae organism by Eisen Lab.
data(EisenYeast)data(EisenYeast)
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.
Eisen Lab at http://rana.lbl.gov/EisenData.htm
Calculates an ensemble of biclusters from different parameter setting of possible different bicluster algorithms.
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, ...)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, ...)
x |
Data Matrix |
confs |
Matrix containing parameter sets |
rep |
Number of repetitions for each parameter set |
maxNum |
Maximum number of biclusters taken from each run |
similar |
Function to produce a similarity matrix of bicluster |
thr |
Threshold for similarity |
simthr |
Proportion of row column combinations in bicluster |
subs |
Vector of proportion of rows and columns for subsampling. Default c(1,1) means no subsampling. |
bootstrap |
Should bootstrap sampling be used (logical: replace=bootstrap). |
support |
Which proportion of the runs must contain the bicluster to have enough support to report it (between 0 and 1). |
combine |
Function to combine the single bicluster only firstcome and hcl for hierarchical clustering are possible at the moment. |
... |
Arguments past to the combine function. |
Two different kinds (or both combined) of ensembling is possible. Ensemble of repeated runs or ensemble of runs on subsamples.
Return an object of class Biclust
Sebastian Kaiser [email protected]
Biclust-class, plaid.grid, bimax.grid
## 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)## 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)
Other than drawHeatmap this function plots all or a chosen number of bicluster in one plot even if they were overlapping.
heatmapBC(x, bicResult, number = 0, local = TRUE, order = FALSE, outside = FALSE, ...)heatmapBC(x, bicResult, number = 0, local = TRUE, order = FALSE, outside = FALSE, ...)
x |
The data matrix where the bicluster is to be drawn. |
bicResult |
BiclustResult object with a bicluster result set. |
number |
Number of bicluster to be drawn from the result set 'bicResult'. If the default 0 is chosen all bicluster of the bicResult are drawn. |
local |
If |
order |
If |
outside |
If |
... |
Additional plot options |
Overlap plotting only works for two neighbor bicluster defined by the order in the number slot.
Sebastian Kaiser
drawHeatmap,parallelCoordinates
set.seed(1234) data(BicatYeast) resplaid <- biclust(BicatYeast, BCPlaid(), verbose = FALSE) heatmapBC(x = BicatYeast, bicResult = resplaid)set.seed(1234) data(BicatYeast) resplaid <- biclust(BicatYeast, BCPlaid(), verbose = FALSE) heatmapBC(x = BicatYeast, bicResult = resplaid)
Checks if Biclusterresult includes overlapping rows or columns
isoverlapp(bicResult)isoverlapp(bicResult)
bicResult |
Result of biclust function |
Overlapping |
Is there overlapping |
Max.bicluster.Rows |
Maximal number of bicluster a single row is in |
Max.bicluster.Cols |
Maximal number of bicluster a single col is in |
Sebastian Kaiser [email protected]
An adaption of the Jaccard Index for clustering is calculated.
jaccardind(bicres1,bicres2) jaccard2(Rows, Cols)jaccardind(bicres1,bicres2) jaccard2(Rows, Cols)
bicres1 |
A object of class Biclust |
bicres2 |
A object of class Biclust |
Rows |
Matrix containing rows of biclusters |
Cols |
Matrix containing cols of biclusters |
The function calculates the percentage of datapoints in the same bicluster structure from all datapoints at least included in one bicluster.
jaccardind calculates the Jaccard index
jaccard2 returns a similarity matrix containing the Jaccard
index between all biclusters (upper triangle matrix)
Sebastian Kaiser [email protected]
## 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)## 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)
Represents expression levels through gene and/or condition profiles in a bicluster as lines.
parallelCoordinates(x, bicResult, number, plotBoth = FALSE, plotcol = TRUE, compare = TRUE, info = F, bothlab = c("Rows", "Columns"), order = FALSE, order2 = 0,ylab = "Value" , col=1,...)parallelCoordinates(x, bicResult, number, plotBoth = FALSE, plotcol = TRUE, compare = TRUE, info = F, bothlab = c("Rows", "Columns"), order = FALSE, order2 = 0,ylab = "Value" , col=1,...)
x |
The data matrix of the bicluster to be drawn |
bicResult |
BiclustResult object with a bicluster result set |
number |
Bicluster to be drawn from the result set 'bicResult' |
plotBoth |
If 'TRUE', Parallel Coordinates of rows (Genes) and columns (Conditions) were drawn one below the other. |
plotcol |
If 'TRUE', columns profiles are drawn, so each line represents one of the columns in the bicluster. Otherwise, row profiles are drawn. Default 'TRUE' |
compare |
If 'TRUE', values of the complete data matrix are considered and drawn as shaded lines. Default 'TRUE' |
info |
If 'TRUE', a prepared Title is drawn |
bothlab |
Names of the x Axis if PlotBoth |
order |
Rows and/or Columns are in increasing order. |
order2 |
Which ordering. |
ylab |
ylab |
col |
col |
... |
Plot Parameters |
Rodrigo Santamaria, Martin Sill and Sebastian Kaiser [email protected]
drawHeatmap for alternative representation of biclusters and bubbleplot for simultaneous representation of biclusters.
#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)#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)
Generates a list containing parameter settings for the ensemble algorithm.
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)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)
method |
Here BCPlaid, to perform Plaid algorithm |
cluster |
'r', 'c' or 'b', to cluster rows, columns or both (default 'b') |
fit.model |
Model (formula) to fit each layer. Usually, a linear model is used, that estimates three parameters: m (constant for all elements in the bicluster), a(contant for all rows in the bicluster) and b (constant for all columns). Thus, default is: y ~ m + a + b. |
background |
If 'TRUE' the method will consider that a background layer (constant for all rows and columns) is present in the data matrix. |
background.layer |
If background='TRUE' a own background layer (Matrix with dimension of x) can be specified. |
background.df |
Degrees of Freedom of backround layer if background.layer is specified. |
shuffle |
Before a layer is added, it's statistical significance is compared against a number of layers obtained by random defined by this parameter. Default is 3, higher numbers could affect time performance. |
iter.startup |
Number of iterations to find starting values |
iter.layer |
Number of iterations to find each layer |
back.fit |
After a layer is added, additional iterations can be done to refine the fitting of the layer (default set to 0) |
row.release |
Scalar in [0,1](with interval recommended [0.5-0.7]) used as threshold to prune rows in the layers depending on row homogeneity |
col.release |
As above, with columns |
max.layers |
Maximum number of layer to include in the model |
verbose |
If 'TRUE' prints extra information on progress. |
A list containing parameter settings
Sebastian Kaiser [email protected]
plaid.grid()plaid.grid()
Draws a graph to compare the values inside the diffrent biclusters with the values outside the bicluster
plotclust(res,x,bicluster=TRUE,legende=FALSE,noC=5,wyld=3,Titel="Plotclust",...)plotclust(res,x,bicluster=TRUE,legende=FALSE,noC=5,wyld=3,Titel="Plotclust",...)
x |
The data matrix |
res |
BiclustResult object if bicluster=TRUE else a normal kcca object. |
bicluster |
If TRUE,res is treated as a BiclustResult object |
legende |
Draws a legend. |
noC |
Number of Clusters drawn |
wyld |
Gives the distance between plot and axis. |
Titel |
Gives the title of the plot. |
... |
Additional plot options |
Sebastian Kaiser [email protected]
bubbleplot for simultaneous representation of biclusters.
parallelCoordinatesfor single representation of biclusters as lines of gene or condition profiles.
drawHeatmapfor Heatmap representation of biclusters.
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)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)
Predicts cluster membership for new data rows given a BCrepBimax Result
predictBimax(BCrepBimax, x)predictBimax(BCrepBimax, x)
BCrepBimax |
Result of biclust function with method BCrepBimax |
x |
The data matrix which clustermembership should be predicted |
Returns a vector with clustermembership of data x of class.
Sebastian Kaiser [email protected]
Synthetic microarray data matrix generated by Syntren for 20 experiments using 200 genes from Transcription Regulatory Network of Shen-Orr et al. (2002).
data(SyntrenEcoli)data(SyntrenEcoli)
Data structure with information about the expression levels of 200 genes over 20 conditions. Conditions are named as C1... C20
SynTReN software can be downloaded at http://homes.esat.kuleuven.be/~kmarchal/SynTReN/index.html
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.
Write bicluster results to a file
writeBiclusterResults(fileName, bicResult, bicName, geneNames, arrayNames, append=FALSE, delimiter=" ")writeBiclusterResults(fileName, bicResult, bicName, geneNames, arrayNames, append=FALSE, delimiter=" ")
fileName |
Path to the file were biclusters are written. |
bicResult |
Biclusters results as a Biclust class. |
bicName |
Brief description for the biclustering algorithm used. |
geneNames |
Array of strings with gene (row) names in the analyzed data matrix |
arrayNames |
Array of strings with condition (column) names in the analyzed data matrix |
append |
If true, adds the bicluster results to previous information in the text file, if it exists. Default false. |
delimiter |
delimiter string between gene and condition names. Default " ". |
Rodrigo Santamaria [email protected]
## 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)## 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)
Draws a graph to compare the values inside the diffrent biclusters with the values outside the bicluster
writeclust(Biclusterresult,row=TRUE,noC=10)writeclust(Biclusterresult,row=TRUE,noC=10)
Biclusterresult |
BiclustResult object |
row |
If TRUE, cluster of rows were written. |
noC |
Number of Clusters written |
Sebastian Kaiser [email protected]
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)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)