Version: 1.0.4
Date: 2021-11-20
Title: Multi-Class Discriminant Analysis using Binary Predictors
Author: Sebastian Gibb and Korbinian Strimmer.
Maintainer: Korbinian Strimmer <strimmerlab@gmail.com>
Depends: R (≥ 3.0.2), entropy (≥ 1.3.1)
Imports: graphics, stats, utils
Suggests: crossval
Description: Implements functions for multi-class discriminant analysis using binary predictors, for corresponding variable selection, and for dichotomizing continuous data.
License: GPL (≥ 3)
URL: https://strimmerlab.github.io/software/binda/
NeedsCompilation: no
Packaged: 2021-11-20 17:17:54 UTC; strimmer
Repository: CRAN
Date/Publication: 2021-11-20 18:00:02 UTC

The binda Package

Description

The "binda" package implements functions for multi-class discriminant analysis using binary predictors, for corresponding variable selection, and for dichotomizing continuous data.

Author(s)

Sebastian Gibb and Korbinian Strimmer (https://strimmerlab.github.io/)

References

Gibb, S., and K. Strimmer. 2015. Differential protein expression and peak selection in mass spectrometry data by binary discriminant analysis. Bioinformatics 31:3156-3162. <DOI:10.1093/bioinformatics/btv334>

Website: https://strimmerlab.github.io/software/binda/

See Also

binda, binda.ranking, dichotomize, chances.

Binary Discriminant Analysis: Model Fit and Class Prediction

Description

binda trains a diagonal multivariate Bernoulli model. predict.binda performs corresponding class prediction.

Usage

binda(Xtrain, L, lambda.freqs, verbose=TRUE)
## S3 method for class 'binda'
predict(object, Xtest, verbose=TRUE, ...)

Arguments

Xtrain

A matrix containing the training data set. Note that the rows correspond to observations and the columns to variables.

L

A factor with the class labels of the training samples.

lambda.freqs

Shrinkage intensity for the frequencies. If not specified it is estimated from the data. lambda.freqs=0 implies no shrinkage (i.e. empirical frequencies) and lambda.freqs=1 complete shrinkage (i.e. uniform frequencies).

verbose

Report shrinkage intensities (binda) and number of used features (predict.binda).

object

An binda fit object obtained from the function binda.

Xtest

A matrix containing the test data set. Note that the rows correspond to observations and the columns to variables.

...

Additional arguments for generic predict.

Details

For detailed description of binary discriminant analysis as implented in binda see Gibb and Strimmer (2015).

Value

predict.binda predicts class probabilities for each test sample and returns a list with two components:

class

a factor with the most probable class assignment for each test sample, and

posterior

a matrix containing the respective class posterior probabilities.

Author(s)

Sebastian Gibb and Korbinian Strimmer (https://strimmerlab.github.io).

References

Gibb, S., and K. Strimmer. 2015. Differential protein expression and peak selection in mass spectrometry data by binary discriminant analysis. Bioinformatics 31:3156-3162. <DOI:10.1093/bioinformatics/btv334>

See Also

binda.ranking.

Examples

# load "binda" library
library("binda")

# training data set with labels
Xtrain = matrix(c(1, 1, 0, 1, 0, 0,
             1, 1, 1, 1, 0, 0,
             1, 0, 0, 0, 1, 1,
             1, 0, 0, 0, 1, 1), nrow=4, byrow=TRUE)
colnames(Xtrain) = paste0("V", 1:ncol(Xtrain))
is.binaryMatrix(Xtrain) # TRUE
L = factor(c("Treatment", "Treatment", "Control", "Control") )

# learn predictor
binda.fit = binda(Xtrain, L)

# predict classes using new test data
Xtest = matrix(c(1, 1, 0, 1, 1, 1,
                 1, 0, 0, 0, 1, 1), nrow=2, byrow=TRUE)
colnames(Xtest) = paste0("V", 1:ncol(Xtest))

predict(binda.fit, Xtest)

Internal binda Functions

Description

Internal binda functions.

Note

These are not to be called by the user (or in some cases are just waiting for proper documentation to be written).

Binary Discriminant Analysis: Variable Ranking

Description

binda.ranking determines a ranking of predictors by computing corresponding t-scores between the group means and the pooled mean.

plot.binda.ranking provides a graphical visualization of the top ranking variables

Usage

binda.ranking(Xtrain, L, lambda.freqs, verbose=TRUE)
## S3 method for class 'binda.ranking'
plot(x, top=40, arrow.col="blue", zeroaxis.col="red", ylab="Variables", main, ...)

Arguments

Xtrain

A matrix containing the training data set. Note that the rows correspond to observations and the columns to variables.

L

A factor with the class labels of the training samples.

lambda.freqs

Shrinkage intensity for the class frequencies. If not specified it is estimated from the data. lambda.freqs=0 implies no shrinkage (i.e. empirical frequencies) and lambda.freqs=1 complete shrinkage (i.e. uniform frequencies).

verbose

Print out some info while computing.

x

A "binda.ranking" object – this is produced by the binda.ranking() function.

top

The number of top-ranking variables shown in the plot (default: 40).

arrow.col

Color of the arrows in the plot (default is "blue").

zeroaxis.col

Color for the center zero axis (default is "red").

ylab

Label written next to feature list (default is "Variables").

main

Main title (if missing, "The", top, "Top Ranking Variables" is used).

...

Other options passed on to generic plot().

Details

The overall ranking of a feature is determined by computing a weighted sum of the squared t-scores. This is approximately equivalent to the mutual information between the response and each variable. The same criterion is used in dichotomize. For precise details see Gibb and Strimmer (2015).

Value

binda.ranking returns a matrix with the following columns:

idx

original feature number

score

the score determining the overall ranking of a variable

t

for each group and feature the t-score of the class mean versus the pooled mean

Author(s)

Sebastian Gibb and Korbinian Strimmer (https://strimmerlab.github.io).

References

Gibb, S., and K. Strimmer. 2015. Differential protein expression and peak selection in mass spectrometry data by binary discriminant analysis. Bioinformatics 31:3156-3162. <DOI:10.1093/bioinformatics/btv334>

See Also

binda, predict.binda, dichotomize.

Examples

# load "binda" library
library("binda")

# training data set with labels
Xtrain = matrix(c(1, 1, 0, 1, 0, 0,
             1, 1, 1, 1, 0, 0,
             1, 0, 0, 0, 1, 1,
             1, 0, 0, 0, 1, 1), nrow=4, byrow=TRUE)
colnames(Xtrain) = paste0("V", 1:ncol(Xtrain))
is.binaryMatrix(Xtrain) # TRUE
L = factor(c("Treatment", "Treatment", "Control", "Control") )

# ranking variables
br = binda.ranking(Xtrain, L)
br
#   idx    score t.Control t.Treatment
#V2   2 4.000000 -2.000000    2.000000
#V4   4 4.000000 -2.000000    2.000000
#V5   5 4.000000  2.000000   -2.000000
#V6   6 4.000000  2.000000   -2.000000
#V3   3 1.333333 -1.154701    1.154701
#V1   1 0.000000  0.000000    0.000000
#attr(,"class")
#[1] "binda.ranking"
#attr(,"cl.count")
#[1] 2

# show plot
plot(br)

# result: variable V1 is irrelevant for distinguishing the two groups

Estimate Bernoulli Parameters from Binary Matrix with Class Labels

Description

chances estimates Bernoulli parameters (=chances) from a binary matrix and associated class labels.

Usage

chances(X, L, lambda.freqs, verbose=TRUE)

Arguments

X

data matrix (columns correspond to variables, rows to samples).

L

factor containing the class labels, one for each sample (row).

lambda.freqs

shrinkage parameter for class frequencies (if not specified it is estimated).

verbose

report shrinkage intensity and other information.

Details

The class-specific chances are estimated using the empirical means over the 0s and 1s in each class. For estimating the pooled mean the class-specific means are weighted using the estimated class frequencies. Class frequencies are estimated using freqs.shrink.

Value

chances returns a list with the following components:

samples: the samples in each class,

regularization: the shrinkage intensity used to estimate the class frequencies,

freqs: the estimated class frequencies,

means: the estimated chances (parameters of Bernoulli distribution, expectations of 1s) for each variable conditional on class, as well as the marginal changes (pooled means).

Author(s)

Sebastian Gibb and Korbinian Strimmer (https://strimmerlab.github.io).

See Also

is.binaryMatrix.

Examples

# load binda library
library("binda")

# example binary matrix with 6 variables (in columns) and 4 samples (in rows)
Xb = matrix(c(1, 1, 0, 1, 0, 0,
             1, 1, 1, 1, 0, 0,
             1, 0, 0, 0, 1, 1,
             1, 0, 0, 0, 1, 1), nrow=4, byrow=TRUE)
colnames(Xb) = paste0("V", 1:ncol(Xb))

# Test for binary matrix
is.binaryMatrix(Xb) # TRUE

L = factor(c("Treatment", "Treatment", "Control", "Control") )

chances(Xb, L)

Dichotomize Continuous Data Set With Labels

Description

dichotomize converts a matrix containing continous measurements into a binary matrix.

optimizeThreshold determines optimal thresholds for dichotomization.

Usage

dichotomize(X, thresh)
optimizeThreshold(X, L, lambda.freqs, verbose=FALSE)

Arguments

X

data matrix (columns correspond to variables, rows to samples).

thresh

vector of thresholds, one for each variable (column).

L

factor containing the class labels, one for each sample (row).

lambda.freqs

shrinkage parameter for class frequencies (if not specified it is estimated).

verbose

report shrinkage intensity and other information.

Details

dichotomize assigns 0 if a matrix entry is lower than given column-specific threshold, otherwise it assigns 1.

optimizeThreshold uses (approximate) mutual information to determine the optimal thresholds. Specifically, the thresholds are chosen to maximize the mutual information between response and each variable. The same criterion is also used in binda.ranking. For detailed description of the dichotomization procedure see Gibb and Strimmer (2015).

Class frequencies are estimated using freqs.shrink.

Value

dichotomize returns a binary matrix.

optimizeThreshold returns a vector containing the variable thresholds.

Author(s)

Sebastian Gibb and Korbinian Strimmer (https://strimmerlab.github.io).

References

Gibb, S., and K. Strimmer. 2015. Differential protein expression and peak selection in mass spectrometry data by binary discriminant analysis. Bioinformatics 31:3156-3162. <DOI:10.1093/bioinformatics/btv334>

See Also

binda.ranking, freqs.shrink, mi.plugin, is.binaryMatrix.

Examples

# load binda library
library("binda")

# example data with 6 variables (in columns) and 4 samples (in rows)
X = matrix(c(1, 1, 1, 1.75, 0.4,    0,
             1, 1, 2,    2, 0.4, 0.09,
             1, 0, 1,    1, 0.5,  0.1,
             1, 0, 1,  0.5, 0.6,  0.1), nrow=4, byrow=TRUE)
colnames(X) = paste0("V", 1:ncol(X))

# class labels
L = factor(c("Treatment", "Treatment", "Control", "Control") )
rownames(X) = paste0(L, rep(1:2, times=2))

X
#          V1 V2 V3   V4  V5   V6
#Treatment1  1  1  1 1.75 0.4 0.00
#Treatment2  1  1  2 2.00 0.4 0.09
#Control1    1  0  1 1.00 0.5 0.10
#Control2    1  0  1 0.50 0.6 0.10

# find optimal thresholds (one for each variable)
thr = optimizeThreshold(X, L)
thr
#  V1   V2   V3   V4   V5   V6 
#1.00 1.00 2.00 1.75 0.50 0.10

# convert into binary matrix
# if value is lower than threshold -> 0 otherwise -> 1
Xb = dichotomize(X, thr)
is.binaryMatrix(Xb) # TRUE
Xb
#          V1 V2 V3 V4 V5 V6
#Treatment1  1  1  0  1  0  0
#Treatment2  1  1  1  1  0  0
#Control1    1  0  0  0  1  1
#Control2    1  0  0  0  1  1
#attr(,"thresh")
#  V1   V2   V3   V4   V5   V6 
#1.00 1.00 2.00 1.75 0.50 0.10

Check For Binary Matrix

Description

is.binaryMatrix tests whether m is a matrix and whether it contains only 0s and 1s.

Note that functions like binda.ranking and binda require a binary matrix as input.

Usage

is.binaryMatrix(m)

Arguments

m

a matrix.

Value

is.binaryMatrix returns either TRUE or FALSE.

Author(s)

Sebastian Gibb and Korbinian Strimmer (https://strimmerlab.github.io).

Examples

# load binda library
library("binda")

# test matrix
m = matrix(c(1, 1, 0, 1, 0, 0,
             1, 1, 1, 1, 0, 0,
             1, 0, 0, 0, 1, 1,
             1, 0, 0, 0, 1, 1), nrow=4, byrow=TRUE)

# Test for binary matrix
is.binaryMatrix(m) # TRUE