BERT (Batch-Effect Removal with Trees) offers flexible and efficient batch effect correction of omics data, while providing maximum tolerance to missing values. Tested on multiple datasets from proteomic analyses, BERT offered a typical 5-10x runtime improvement over existing methods, while retaining more numeric values and preserving batch effect reduction quality.
As such, BERT is a valuable preprocessing tool for data analysis workflows, in particular for proteomic data. By providing BERT via Bioconductor, we make this tool available to a wider research community. An accompanying research paper is currently under preparation and will be made public soon.
BERT addresses the same fundamental data integration challenges than the [HarmonizR][https://github.com/HSU-HPC/HarmonizR] package, which is released on Bioconductor in November 2023. However, various algorithmic modications and optimizations of BERT provide better execution time and better data coverage than HarmonizR. Moreover, BERT offers a more user-friendly design and a less error-prone input format.
Please note that our package BERT is neither affiliated with nor related to Bidirectional Encoder Representations from Transformers as published by Google.
Please report any questions and issues in the GitHub forum, the BioConductor forum or directly contact the authors,
Please download and install a current version of R (Windows binaries). You might want to consider installing a development environment as well, e.g. RStudio. Finally, BERT can be installed via Bioconductor using
if (!require("BiocManager", quietly = TRUE)){
install.packages("BiocManager")
}
BiocManager::install("BERT")which will install all required dependencies. To install the development version of BERT, you can use devtools as follows
which may require the manual installation of the dependencies
sva and limma.
As input, BERT requires a dataframe1 with samples in rows
and features in columns. For each sample, the respective batch should be
indicated by an integer or string in a corresponding column labelled
Batch. Missing values should be labelled as NA. A
valid example dataframe could look like this:
example = data.frame(feature_1 = stats::rnorm(5), feature_2 = stats::rnorm(5), Batch=c(1,1,2,2,2))
example
#> feature_1 feature_2 Batch
#> 1 0.06440718 -0.2917951 1
#> 2 -0.79107671 -0.9596097 1
#> 3 -0.24007155 -0.9133434 2
#> 4 -0.07670759 -1.8330606 2
#> 5 -0.85650121 -1.0975937 2Note that each batch should contain at least two samples. Optional columns that can be passed are
Label A column with integers or strings indicating
the (known) class for each sample. NA is not allowed. BERT
may use this columns and Batch to compute quality metrics
after batch effect correction.
Sample A sample name. This column is ignored by BERT
and can be used to provide meta-information for further
processing.
Cov_1, Cov_2, …, Cov_x:
One or multiple columns with integers, indicating one or several
covariate levels. NA is not allowed. If this(these)
column(s) is present, BERT will pass them as covariates to the the
underlying batch effect correction method. As an example, this
functionality can be used to preserve differences between
healthy/tumorous samples, if some of the batches exhibit strongly
variable class distributions. Note that BERT requires at least two
numeric values per batch and unique covariate level to adjust a feature.
Features that don’t satisfy this condition in a specific batch are set
to NA for that batch.
Reference A column with integers or strings from
\(\mathbb{N}_0\) that indicate, whether
a sample should be used for “learning” the transformation for batch
effect correction or whether the sample should be co-adjusted using the
learned transformation from the other samples.NA is not
allowed. This feature can be used, if some batches contain unique
classes or samples with unknown classes which would prohibit the usage
of covariate columns. If the column contains a 0 for a
sample, this sample will be co-adjusted. Otherwise, the sample should
contain the respective class (encoded as integer or string). Note that
BERT requires at least two references of common class per adjustment
step and that the Reference column is mutually exclusive
with covariate columns.
Note that BERT tries to find all metadata information for a
SummarizedExperiment, including the mandatory batch
information, using colData. For instance, a valid
SummarizedExperiment might be defined as
nrows <- 200
ncols <- 8
expr_values <- matrix(runif(nrows * ncols, 1, 1e4), nrows)
# colData also takes all other metadata information, such as Label, Sample,
# Covariables etc.
colData <- data.frame(Batch=c(1,1,1,1,2,2,2,2), Reference=c(1,1,0,0,1,1,0,0))
dataset_raw = SummarizedExperiment::SummarizedExperiment(assays=list(expr=expr_values), colData=colData)BERT can be invoked by importing the BERT library and
calling the BERT function. The batch effect corrected data
is returned as a dataframe that mirrors the input dataframe2.
library(BERT)
# generate test data with 10% missing values as provided by the BERT library
dataset_raw <- generate_dataset(features=60, batches=10, samplesperbatch=10, mvstmt=0.1, classes=2)
# apply BERT
dataset_adjusted <- BERT(dataset_raw)
#> 2026-05-21 10:35:52.869023 INFO::Formatting Data.
#> 2026-05-21 10:35:52.876177 INFO::Replacing NaNs with NAs.
#> 2026-05-21 10:35:52.883103 INFO::Removing potential empty rows and columns
#> 2026-05-21 10:35:53.419421 INFO::Found 600 missing values.
#> 2026-05-21 10:35:53.430395 INFO::Introduced 0 missing values due to singular proteins at batch/covariate level.
#> 2026-05-21 10:35:53.43091 INFO::Done
#> 2026-05-21 10:35:53.431333 INFO::Acquiring quality metrics before batch effect correction.
#> 2026-05-21 10:35:53.441388 INFO::Starting hierarchical adjustment
#> 2026-05-21 10:35:53.442107 INFO::Found 10 batches.
#> 2026-05-21 10:35:53.442542 INFO::Cores argument is not defined or BPPARAM has been specified. Argument corereduction will not be used.
#> 2026-05-21 10:35:55.09439 INFO::Using default BPPARAM
#> 2026-05-21 10:35:55.094928 INFO::Processing subtree level 1
#> 2026-05-21 10:35:56.46628 INFO::Processing subtree level 2
#> 2026-05-21 10:35:57.916456 INFO::Adjusting the last 1 batches sequentially
#> 2026-05-21 10:35:57.918269 INFO::Done
#> 2026-05-21 10:35:57.918924 INFO::Acquiring quality metrics after batch effect correction.
#> 2026-05-21 10:35:57.923914 INFO::ASW Batch was 0.552013043245698 prior to batch effect correction and is now -0.135436099847324 .
#> 2026-05-21 10:35:57.924576 INFO::ASW Label was 0.296496655615574 prior to batch effect correction and is now 0.753182545857864 .
#> 2026-05-21 10:35:57.925659 INFO::Total function execution time is 5.07497596740723 s and adjustment time is 4.47637224197388 s ( 88.2 )BERT uses the logging library to convey live information
to the user during the adjustment procedure. The algorithm first
verifies the shape and suitability of the input dataframe (lines 1-6)
before continuing with the actual batch effect correction (lines 8-14).
BERT measure batch effects before and after the correction step by means
of the average silhouette score (ASW) with respect to batch and labels
(lines 7 and 15). The ASW Label should increase in a successful batch
effect correction, whereas low values (\(\leq
0\)) are desireable for the ASW Batch3. Finally, BERT prints
the total function execution time (including the computation time for
the quality metrics).
BERT offers a large number of parameters to customize the batch effect adjustment. The full function call, including all defaults is
BERT(data, cores = NULL, combatmode = 1, corereduction=2, stopParBatches=2, backend="default", method="ComBat", qualitycontrol=TRUE, verify=TRUE, labelname="Label", batchname="Batch", referencename="Reference", samplename="Sample", covariatename=NULL, BPPARAM=NULL, assayname=NULL)In the following, we list the respective meaning of each parameter: -
data: The input dataframe/matrix/SummarizedExperiment to
adjust. See Data Preparation for
detailed formatting instructions. - data The data for
batch-effect correction. Must contain at least two samples per batch and
2 features.
cores: BERT uses BiocParallel
for parallelization. If the user specifies a value cores,
BERT internally creates and uses a new instance of
BiocParallelParam, which is however not exhibited to the
user. Setting this parameter can speed up the batch effect adjustment
considerably, in particular for large datasets and on unix-based
operating systems. A value between \(2\) and \(4\) is a reasonable choice for typical
commodity hardware. Multi-node computations are not supported as of now.
If, however, cores is not specified, BERT will default to
BiocParallel::bpparam(), which may have been set by the
user or the system. Additionally, the user can directly specify a
specific instance of BiocParallelParam to be used via the
BPPARAM argument.combatmode An integer that encodes the parameters to
use for ComBat.| Value | par.prior | mean.only |
|---|---|---|
| 1 | TRUE | FALSE |
| 2 | TRUE | TRUE |
| 3 | FALSE | FALSE |
| 4 | FALSE | TRUE |
The value of this parameter will be ignored, if
method!="ComBat".
corereduction Positive integer indicating the factor
by which the number of processes should be reduced, once no further
adjustment is possible for the current number of batches.4 This parameter is used
only, if the user specified a custom value for parameter
cores.
stopParBatches Positive integer indicating the
minimum number of batches required at a hierarchy level to proceed with
parallelized adjustment. If the number of batches is smaller, adjustment
will be performed sequentially to avoid communication
overheads.
backend: The backend to use for inter-process
communication. Possible choices are default and
file, where the former refers to the default communication
backend of the requested parallelization mode and the latter will create
temporary .rds files for data communication. ‘default’ is
usually faster for small to medium sized datasets.
method: The method to use for the underlying batch
effect correction steps. Should be either ComBat,
limma for limma::removeBatchEffects or
ref for adjustment using specified references (cf. Data Preparation). The underlying batch
effect adjustment method for ref is a modified version of
the limma method.
qualitycontrol: A boolean to (de)activate the ASW
computation. Deactivating the ASW computations accelerates the
computations.
verify: A boolean to (de)activate the initial format
check of the input data. Deactivating this verification step accelerates
the computations.
labelname: A string containing the name of the
column to use as class labels. The default is “Label”.
batchname: A string containing the name of the
column to use as batch labels. The default is “Batch”.
referencename: A string containing the name of the
column to use as reference labels. The default is “Reference”.
covariatename: A vector containing the names of
columns with categorical covariables.The default is NULL, in which case
all column names are matched agains the pattern “Cov”.
BPPARAM: An instance of
BiocParallelParam that will be used for parallelization.
The default is null, in which case the value of cores
determines the behaviour of BERT.
assayname: If the user chooses to pass a
SummarizedExperiment object, they need to specify the name
of the assay that they want to apply BERT to here. BERT then returns the
input SummarizedExperiment with an additional assay labeled
assayname_BERTcorrected.
BERT utilizes the logging package for output. The user
can easily specify the verbosity of BERT by setting the global logging
level in the script. For instance
BERT exhibits a large number of parameters for parallelisation as to provide users with maximum flexibility. For typical scenarios, however, the default parameters are well suited. For very large experiments (\(>15\) batches), we recommend to increase the number of cores (a reasonable value is \(4\) but larger values may be possible on your hardware). Most users should leave all parameters to their respective default.
In the following, we present simple cookbook examples for BERT usage. Note that ASWs (and runtime) will most likely differ on your machine, since the data generating process involves multiple random choices.
Here, BERT uses limma as underlying batch effect correction algorithm
(method='limma') and performs all computations on a single
process (cores parameter is left on default).
# import BERT
library(BERT)
# generate data with 30 batches, 60 features, 15 samples per batch, 15% missing values and 2 classes
dataset_raw <- generate_dataset(features=60, batches=20, samplesperbatch=15, mvstmt=0.15, classes=2)
# BERT
dataset_adjusted <- BERT(dataset_raw, method="limma")
#> 2026-05-21 10:35:57.969941 INFO::Formatting Data.
#> 2026-05-21 10:35:57.970579 INFO::Replacing NaNs with NAs.
#> 2026-05-21 10:35:57.971406 INFO::Removing potential empty rows and columns
#> 2026-05-21 10:35:57.973354 INFO::Found 2700 missing values.
#> 2026-05-21 10:35:57.992392 INFO::Introduced 0 missing values due to singular proteins at batch/covariate level.
#> 2026-05-21 10:35:57.992841 INFO::Done
#> 2026-05-21 10:35:57.993228 INFO::Acquiring quality metrics before batch effect correction.
#> 2026-05-21 10:35:58.001697 INFO::Starting hierarchical adjustment
#> 2026-05-21 10:35:58.002264 INFO::Found 20 batches.
#> 2026-05-21 10:35:58.002647 INFO::Cores argument is not defined or BPPARAM has been specified. Argument corereduction will not be used.
#> 2026-05-21 10:35:58.003144 INFO::Using default BPPARAM
#> 2026-05-21 10:35:58.003525 INFO::Processing subtree level 1
#> 2026-05-21 10:35:58.336421 INFO::Processing subtree level 2
#> 2026-05-21 10:35:58.651141 INFO::Processing subtree level 3
#> 2026-05-21 10:35:58.977316 INFO::Adjusting the last 1 batches sequentially
#> 2026-05-21 10:35:58.978874 INFO::Done
#> 2026-05-21 10:35:58.979346 INFO::Acquiring quality metrics after batch effect correction.
#> 2026-05-21 10:35:58.987701 INFO::ASW Batch was 0.44333744407675 prior to batch effect correction and is now -0.120773518237797 .
#> 2026-05-21 10:35:58.988191 INFO::ASW Label was 0.35121474120411 prior to batch effect correction and is now 0.799121787356751 .
#> 2026-05-21 10:35:58.988902 INFO::Total function execution time is 1.01900815963745 s and adjustment time is 0.976713418960571 s ( 95.85 )Here, BERT uses ComBat as underlying batch effect correction
algorithm (method is left on default) and performs all
computations on a 2 processes (cores=2).
# import BERT
library(BERT)
# generate data with 30 batches, 60 features, 15 samples per batch, 15% missing values and 2 classes
dataset_raw <- generate_dataset(features=60, batches=20, samplesperbatch=15, mvstmt=0.15, classes=2)
# BERT
dataset_adjusted <- BERT(dataset_raw, cores=2)
#> 2026-05-21 10:35:59.016407 INFO::Formatting Data.
#> 2026-05-21 10:35:59.017006 INFO::Replacing NaNs with NAs.
#> 2026-05-21 10:35:59.017821 INFO::Removing potential empty rows and columns
#> 2026-05-21 10:35:59.019699 INFO::Found 2700 missing values.
#> 2026-05-21 10:35:59.041606 INFO::Introduced 0 missing values due to singular proteins at batch/covariate level.
#> 2026-05-21 10:35:59.042104 INFO::Done
#> 2026-05-21 10:35:59.042516 INFO::Acquiring quality metrics before batch effect correction.
#> 2026-05-21 10:35:59.051332 INFO::Starting hierarchical adjustment
#> 2026-05-21 10:35:59.051927 INFO::Found 20 batches.
#> 2026-05-21 10:35:59.530298 INFO::Set up parallel execution backend with 2 workers
#> 2026-05-21 10:35:59.531256 INFO::Processing subtree level 1 with 20 batches using 2 cores.
#> 2026-05-21 10:36:01.6045 INFO::Adjusting the last 2 batches sequentially
#> 2026-05-21 10:36:01.605501 INFO::Adjusting sequential tree level 1 with 2 batches
#> 2026-05-21 10:36:02.739258 INFO::Done
#> 2026-05-21 10:36:02.739715 INFO::Acquiring quality metrics after batch effect correction.
#> 2026-05-21 10:36:02.747213 INFO::ASW Batch was 0.479801647315673 prior to batch effect correction and is now -0.134992600611331 .
#> 2026-05-21 10:36:02.747622 INFO::ASW Label was 0.302644119827161 prior to batch effect correction and is now 0.856179180300236 .
#> 2026-05-21 10:36:02.74814 INFO::Total function execution time is 3.73179054260254 s and adjustment time is 3.68724942207336 s ( 98.81 )Here, BERT takes the input data using a
SummarizedExperiment instead. Batch effect correction is
then performed using ComBat as underlying algorithm (method
is left on default) and all computations are performed on a single
process (cores parameter is left on default).
nrows <- 200
ncols <- 8
# SummarizedExperiments store samples in columns and features in rows (in contrast to BERT).
# BERT will automatically account for this.
expr_values <- matrix(runif(nrows * ncols, 1, 1e4), nrows)
# colData also takes further metadata information, such as Label, Sample,
# Reference or Covariables
colData <- data.frame("Batch"=c(1,1,1,1,2,2,2,2), "Label"=c(1,2,1,2,1,2,1,2), "Sample"=c(1,2,3,4,5,6,7,8))
dataset_raw = SummarizedExperiment::SummarizedExperiment(assays=list(expr=expr_values), colData=colData)
dataset_adjusted = BERT(dataset_raw, assayname = "expr")
#> 2026-05-21 10:36:02.786679 INFO::Formatting Data.
#> 2026-05-21 10:36:02.787169 INFO::Recognized SummarizedExperiment
#> 2026-05-21 10:36:02.787516 INFO::Typecasting input to dataframe.
#> 2026-05-21 10:36:02.811326 INFO::Replacing NaNs with NAs.
#> 2026-05-21 10:36:02.812036 INFO::Removing potential empty rows and columns
#> 2026-05-21 10:36:02.814219 INFO::Found 0 missing values.
#> 2026-05-21 10:36:02.818374 INFO::Introduced 0 missing values due to singular proteins at batch/covariate level.
#> 2026-05-21 10:36:02.818748 INFO::Done
#> 2026-05-21 10:36:02.819129 INFO::Acquiring quality metrics before batch effect correction.
#> 2026-05-21 10:36:02.8217 INFO::Starting hierarchical adjustment
#> 2026-05-21 10:36:02.822203 INFO::Found 2 batches.
#> 2026-05-21 10:36:02.822541 INFO::Cores argument is not defined or BPPARAM has been specified. Argument corereduction will not be used.
#> 2026-05-21 10:36:02.822962 INFO::Using default BPPARAM
#> 2026-05-21 10:36:02.82329 INFO::Adjusting the last 2 batches sequentially
#> 2026-05-21 10:36:02.823905 INFO::Adjusting sequential tree level 1 with 2 batches
#> 2026-05-21 10:36:02.853706 INFO::Done
#> 2026-05-21 10:36:02.854107 INFO::Acquiring quality metrics after batch effect correction.
#> 2026-05-21 10:36:02.856589 INFO::ASW Batch was -0.00301580557563385 prior to batch effect correction and is now -0.0918547469714993 .
#> 2026-05-21 10:36:02.857023 INFO::ASW Label was -0.0220248365476004 prior to batch effect correction and is now -0.011407177077379 .
#> 2026-05-21 10:36:02.857512 INFO::Total function execution time is 0.0708076953887939 s and adjustment time is 0.0315985679626465 s ( 44.63 )BERT can utilize categorical covariables that are specified in
columns Cov_1, Cov_2, .... These columns are automatically
detected and integrated into the batch effect correction process.
# import BERT
library(BERT)
# set seed for reproducibility
set.seed(1)
# generate data with 5 batches, 60 features, 30 samples per batch, 15% missing values and 2 classes
dataset_raw <- generate_dataset(features=60, batches=5, samplesperbatch=30, mvstmt=0.15, classes=2)
# create covariable column with 2 possible values, e.g. male/female condition
dataset_raw["Cov_1"] = sample(c(1,2), size=dim(dataset_raw)[1], replace=TRUE)
# BERT
dataset_adjusted <- BERT(dataset_raw)
#> 2026-05-21 10:36:02.882877 INFO::Formatting Data.
#> 2026-05-21 10:36:02.883368 INFO::Replacing NaNs with NAs.
#> 2026-05-21 10:36:02.884002 INFO::Removing potential empty rows and columns
#> 2026-05-21 10:36:02.885187 INFO::Found 1350 missing values.
#> 2026-05-21 10:36:02.885787 INFO::BERT requires at least 2 numeric values per batch/covariate level. This may reduce the number of adjustable features considerably, depending on the quantification technique.
#> 2026-05-21 10:36:02.897582 INFO::Introduced 0 missing values due to singular proteins at batch/covariate level.
#> 2026-05-21 10:36:02.897999 INFO::Done
#> 2026-05-21 10:36:02.898338 INFO::Acquiring quality metrics before batch effect correction.
#> 2026-05-21 10:36:02.901633 INFO::Starting hierarchical adjustment
#> 2026-05-21 10:36:02.902139 INFO::Found 5 batches.
#> 2026-05-21 10:36:02.902484 INFO::Cores argument is not defined or BPPARAM has been specified. Argument corereduction will not be used.
#> 2026-05-21 10:36:02.902928 INFO::Using default BPPARAM
#> 2026-05-21 10:36:02.903287 INFO::Processing subtree level 1
#> 2026-05-21 10:36:03.122741 INFO::Adjusting the last 2 batches sequentially
#> 2026-05-21 10:36:03.12462 INFO::Adjusting sequential tree level 1 with 2 batches
#> 2026-05-21 10:36:03.168359 INFO::Done
#> 2026-05-21 10:36:03.168952 INFO::Acquiring quality metrics after batch effect correction.
#> 2026-05-21 10:36:03.173062 INFO::ASW Batch was 0.492773245691086 prior to batch effect correction and is now -0.0377157224767566 .
#> 2026-05-21 10:36:03.173524 INFO::ASW Label was 0.40854766060101 prior to batch effect correction and is now 0.895560693013661 .
#> 2026-05-21 10:36:03.174213 INFO::Total function execution time is 0.291405916213989 s and adjustment time is 0.26627516746521 s ( 91.38 )In rare cases, class distributions across experiments may be severely
skewed. In particular, a batch might contain classes that other batches
don’t contain. In these cases, samples of common conditions may serve as
references (bridges) between the batches
(method="ref"). BERT utilizes those samples as references
that have a condition specified in the “Reference” column of the input.
All other samples are co-adjusted. Please note, that this strategy
implicitly uses limma as underlying batch effect correction
algorithm.
# import BERT
library(BERT)
# generate data with 4 batches, 6 features, 15 samples per batch, 15% missing values and 2 classes
dataset_raw <- generate_dataset(features=6, batches=4, samplesperbatch=15, mvstmt=0.15, classes=2)
# create reference column with default value 0. The 0 indicates, that the respective sample should be co-adjusted only.
dataset_raw[, "Reference"] <- 0
# randomly select 2 references per batch and class - in practice, this choice will be determined by external requirements (e.g. class known for only these samples)
batches <- unique(dataset_raw$Batch) # all the batches
for(b in batches){ # iterate over all batches
# references from class 1
ref_idx = sample(which((dataset_raw$Batch==b)&(dataset_raw$Label==1)), size=2, replace=FALSE)
dataset_raw[ref_idx, "Reference"] <- 1
# references from class 2
ref_idx = sample(which((dataset_raw$Batch==b)&(dataset_raw$Label==2)), size=2, replace=FALSE)
dataset_raw[ref_idx, "Reference"] <- 2
}
# BERT
dataset_adjusted <- BERT(dataset_raw, method="ref")
#> 2026-05-21 10:36:03.252303 INFO::Formatting Data.
#> 2026-05-21 10:36:03.252923 INFO::Replacing NaNs with NAs.
#> 2026-05-21 10:36:03.253576 INFO::Removing potential empty rows and columns
#> 2026-05-21 10:36:03.254319 INFO::Found 60 missing values.
#> 2026-05-21 10:36:03.25701 INFO::Introduced 0 missing values due to singular proteins at batch/covariate level.
#> 2026-05-21 10:36:03.257409 INFO::Done
#> 2026-05-21 10:36:03.257791 INFO::Acquiring quality metrics before batch effect correction.
#> 2026-05-21 10:36:03.259819 INFO::Starting hierarchical adjustment
#> 2026-05-21 10:36:03.260327 INFO::Found 4 batches.
#> 2026-05-21 10:36:03.260704 INFO::Cores argument is not defined or BPPARAM has been specified. Argument corereduction will not be used.
#> 2026-05-21 10:36:03.261155 INFO::Using default BPPARAM
#> 2026-05-21 10:36:03.261517 INFO::Processing subtree level 1
#> 2026-05-21 10:36:03.343425 INFO::Adjusting the last 2 batches sequentially
#> 2026-05-21 10:36:03.345545 INFO::Adjusting sequential tree level 1 with 2 batches
#> 2026-05-21 10:36:03.367756 INFO::Done
#> 2026-05-21 10:36:03.368336 INFO::Acquiring quality metrics after batch effect correction.
#> 2026-05-21 10:36:03.370953 INFO::ASW Batch was 0.440355021914032 prior to batch effect correction and is now -0.087480278736629 .
#> 2026-05-21 10:36:03.3714 INFO::ASW Label was 0.373906827748893 prior to batch effect correction and is now 0.919791677398366 .
#> 2026-05-21 10:36:03.372032 INFO::Total function execution time is 0.119756937026978 s and adjustment time is 0.107522964477539 s ( 89.78 )Issues can be reported in the GitHub forum, the BioConductor forum or directly to the authors.
This code is published under the GPLv3.0 License and is available for non-commercial academic purposes.
Please cite our manuscript, if you use BERT for your research: Schumann Y, Gocke A, Neumann J (2024). Computational Methods for Data Integration and Imputation of Missing Values in Omics Datasets. PROTEOMICS. ISSN 1615-9861, doi:10.1002/pmic.202400100
sessionInfo()
#> R version 4.6.0 (2026-04-24)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.4 LTS
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#> Matrix products: default
#> BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
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#> locale:
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#> tzcode source: system (glibc)
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] BERT_1.9.0 BiocStyle_2.41.0
#>
#> loaded via a namespace (and not attached):
#> [1] KEGGREST_1.53.0 SummarizedExperiment_1.43.0
#> [3] xfun_0.57 bslib_0.11.0
#> [5] Biobase_2.73.1 lattice_0.22-9
#> [7] vctrs_0.7.3 tools_4.6.0
#> [9] generics_0.1.4 stats4_4.6.0
#> [11] parallel_4.6.0 AnnotationDbi_1.75.0
#> [13] RSQLite_3.52.0 cluster_2.1.8.2
#> [15] blob_1.3.0 logging_0.10-108
#> [17] Matrix_1.7-5 S4Vectors_0.51.2
#> [19] lifecycle_1.0.5 compiler_4.6.0
#> [21] stringr_1.6.0 Biostrings_2.81.1
#> [23] statmod_1.5.2 janitor_2.2.1
#> [25] Seqinfo_1.3.0 codetools_0.2-20
#> [27] snakecase_0.11.1 htmltools_0.5.9
#> [29] sys_3.4.3 buildtools_1.0.0
#> [31] sass_0.4.10 yaml_2.3.12
#> [33] crayon_1.5.3 jquerylib_0.1.4
#> [35] comprehenr_0.6.10 BiocParallel_1.47.0
#> [37] limma_3.69.1 DelayedArray_0.39.2
#> [39] cachem_1.1.0 iterators_1.0.14
#> [41] abind_1.4-8 foreach_1.5.2
#> [43] nlme_3.1-169 sva_3.59.0
#> [45] genefilter_1.95.0 locfit_1.5-9.12
#> [47] tidyselect_1.2.1 digest_0.6.39
#> [49] stringi_1.8.7 splines_4.6.0
#> [51] maketools_1.3.2 fastmap_1.2.0
#> [53] grid_4.6.0 cli_3.6.6
#> [55] invgamma_1.2 SparseArray_1.13.2
#> [57] magrittr_2.0.5 S4Arrays_1.13.0
#> [59] survival_3.8-6 XML_3.99-0.23
#> [61] edgeR_4.11.0 bit64_4.8.2
#> [63] lubridate_1.9.5 timechange_0.4.0
#> [65] rmarkdown_2.31 XVector_0.53.0
#> [67] httr_1.4.8 matrixStats_1.5.0
#> [69] bit_4.6.0 png_0.1-9
#> [71] memoise_2.0.1 evaluate_1.0.5
#> [73] knitr_1.51 GenomicRanges_1.65.0
#> [75] IRanges_2.47.1 mgcv_1.9-4
#> [77] rlang_1.2.0 xtable_1.8-8
#> [79] glue_1.8.1 DBI_1.3.0
#> [81] BiocManager_1.30.27 BiocGenerics_0.59.2
#> [83] annotate_1.91.0 jsonlite_2.0.0
#> [85] R6_2.6.1 MatrixGenerics_1.25.0Matrices and SummarizedExperiments work as well, but will automatically be converted to dataframes.↩︎
In particular, the row and column names are in the same order and the optional columns are preserved.↩︎
The optimum of ASW Label is 1, which is typically however not achieved on real-world datasets. Also, the optimum of ASW Batch can vary, depending on the class distributions of the batches.↩︎
E.g. consider a BERT call with 8 batches and 8
processes. Further adjustment is not possible with this number of
processes, since batches are always processed in pairs. With
corereduction=2, the number of processes for the following
adjustment steps would be set to \(8/2=4\), which is the maximum number of
usable processes for this example.↩︎