Package 'RcppPlanc'

Title: Parallel Low-Rank Approximation with Nonnegativity Constraints
Description: 'Rcpp' bindings for 'PLANC', a highly parallel and extensible NMF/NTF (Non-negative Matrix/Tensor Factorization) library. Wraps algorithms described in Kannan et. al (2018) <doi:10.1109/TKDE.2017.2767592> and Eswar et. al (2021) <doi:10.1145/3432185>. Implements algorithms described in Welch et al. (2019) <doi:10.1016/j.cell.2019.05.006>, Gao et al. (2021) <doi:10.1038/s41587-021-00867-x>, and Kriebel & Welch (2022) <doi:10.1038/s41467-022-28431-4>.
Authors: Andrew Robbins [aut, cre], Yichen Wang [aut], Joshua Welch [cph], Ramakrishnan Kannan [cph] (The original PLANC code), UT-Batelle [cph] (The original PLANC code)
Maintainer: Andrew Robbins <[email protected]>
License: GPL (>= 2)
Version: 1.0.0
Built: 2024-06-13 17:38:32 UTC
Source: https://github.com/welch-lab/RcppPlanc

Help Index


Block Principal Pivoted Non-Negative Least Squares

Description

Use the BPP algorithm to get the nonnegative least squares solution. Regular NNLS problem is described as optimizing minx0CXBF2\min_{x\ge0}||CX - B||_F^2 where CC and BB are given and XX is to be solved. bppnnls takes CC and BB as input. bppnnls_prod takes CTCC^\mathsf{T}C and CTBC^\mathsf{T}B as input to directly go for the intermediate step of BPP algorithm. This can be useful when the dimensionality of CC and BB is large while pre-calculating CTCC^\mathsf{T}C and CTBC^\mathsf{T}B is cheap.

Usage

bppnnls(C, B, nCores = 2L)

bppnnls_prod(CtC, CtB, nCores = 2L)

Arguments

C

Input dense CC matrix

B

Input BB matrix of either dense or sparse form

nCores

The number of parallel tasks that will be spawned. Default 2

CtC

The CTCC^\mathsf{T}C matrix, see description.

CtB

The CTBC^\mathsf{T}B matrix, see description.

Value

The calculated solution matrix in dense form.

Examples

set.seed(1)
C <- matrix(rnorm(250), nrow = 25)
B <- matrix(rnorm(375), nrow = 25)
res1 <- bppnnls(C, B)
dim(res1)
res2 <- bppnnls_prod(t(C) %*% C, t(C) %*% B)
all.equal(res1, res2)

Example single-cell transcriptomic data in sparse form

Description

The two datasets, namingly ctrl.sparse and stim.sparse, are single-cell transcriptomic data preprocessed and subsampled from the study of Hyun Min Kang and et al., Nat Biotech., 2018. The raw datasets were two sparse matrices of integer values indicating the counts of genes (rows) per cell (columns). We normalized each column of both matrices by its library size (sum), and selected common variable genes across the datasets. Finally, we scaled the genes without centering them, in order to keep the non-negativity. The processed datasets were then randomly subsampled for a minimal example.

Usage

ctrl.sparse

stim.sparse

Format

An object of class dgCMatrix with 173 rows and 300 columns.

An object of class dgCMatrix with 173 rows and 300 columns.

Source

https://www.nature.com/articles/nbt.4042


Retrieve the dimension of H5SpMat argument list

Description

Retrieve the dimension of H5SpMat argument list

Usage

## S3 method for class 'H5SpMat'
dim(x)

## S3 replacement method for class 'H5SpMat'
dim(x) <- value

Arguments

x

H5SpMat argument list object

value

Numeric vector of two, for number of rows and number of columns.

Value

Retriever returns a vector of two (nrow and ncol), setter sets the value of that in the argument list.

Examples

h <- H5SpMat(system.file("extdata/ctrl_sparse.h5", package = "RcppPlanc"),
             "data", "indices", "indptr", 173, 300)
dim(h)
nrow(h)
ncol(h)
dim(h) <- c(200, 200)
h

Prepare character information of a H5Mat object

Description

Prepare character information of a H5Mat object

Usage

## S3 method for class 'H5Mat'
format(x, ...)

Arguments

x

H5Mat argument list object

...

Not used.

Value

A character scalar of the displayed message

Examples

h <- H5Mat(system.file("extdata/ctrl_dense.h5", package = "RcppPlanc"),
           "data")
format(h)

prepare character information of a H5SpMat object

Description

prepare character information of a H5SpMat object

Usage

## S3 method for class 'H5SpMat'
format(x, ...)

Arguments

x

H5SpMat argument list object

...

Not used.

Value

A character scalar of the displayed message

Examples

h <- H5SpMat(system.file("extdata/ctrl_sparse.h5", package = "RcppPlanc"),
             "data", "indices", "indptr", 173, 300)
format(h)

Argument list object for using a dense matrix stored in HDF5 file

Description

For running inmf, onlineINMF or uinmf with dense matrix stored in HDF5 file, users will need to construct an argument list for the filename of the HDF5 file as well as the path in the file storing the matrix. H5Mat is provided as an instructed constructor. Meanwhile, since the INMF functions require that all datasets should be of the same type, as.H5Mat is provided for writing in-memory data into a new HDF5 file on disk and returning the constructed argument list.

Usage

H5Mat(filename, dataPath)

as.H5Mat(x, filename, dataPath = "data", overwrite = FALSE, ...)

## S3 method for class 'matrix'
as.H5Mat(x, filename, dataPath = "data", overwrite = FALSE, ...)

## S3 method for class 'dgCMatrix'
as.H5Mat(x, filename, dataPath = "data", overwrite = FALSE, ...)

## Default S3 method:
as.H5Mat(x, filename, dataPath = "data", overwrite = FALSE, ...)

Arguments

filename

Filename of the HDF5 file

dataPath

Path in the HDF5 file that points to a 2D dense matrix. Default "data" when using as.H5Mat.

x

For as.H5Mat, matrix of either dense or sparse type to be written; for print, a H5Mat argument list object

overwrite

Logical, whether to overwrite the file if already exists at the given path. Default FALSE.

...

not used

Value

H5Mat object, indeed a list object.

Examples

if (require("withr")) {
H5MatEx <- function(){
withr::local_dir(withr::local_tempdir())
h <- H5Mat(system.file("extdata/ctrl_dense.h5", package = "RcppPlanc"),
           "data")
print(h)

library(Matrix)
ctrl.dense <- as.matrix(ctrl.sparse)
h1 <- as.H5Mat(ctrl.dense, "ctrl_from_dense_to_dense.h5",
               dataPath = "data")
h1
h2 <- as.H5Mat(ctrl.sparse, "ctrl_from_sparse_to_dense.h5",
               dataPath = "data")
}
H5MatEx()
}

Argument list object for using a sparse matrix stored in HDF5 file

Description

For running inmf, onlineINMF or uinmf with sparse matrix stored in HDF5 file, users will need to construct an argument list for the filename of the HDF5 file as well as the paths in the file storing the arrays that construct the CSC (compressed sparse column) matrix. H5SpMat is provided as an instructed constructor. Meanwhile, since the INMF functions require that all datasets should be of the same type, as.H5SpMat is provided for writing in-memory data into a new HDF5 file on disk and returning the constructed argument list.

Usage

H5SpMat(filename, valuePath, rowindPath, colptrPath, nrow, ncol)

as.H5SpMat(
  x,
  filename,
  valuePath = "data",
  rowindPath = "indices",
  colptrPath = "indptr",
  overwrite = FALSE,
  ...
)

## S3 method for class 'matrix'
as.H5SpMat(
  x,
  filename,
  valuePath = "data",
  rowindPath = "indices",
  colptrPath = "indptr",
  overwrite = FALSE,
  ...
)

## S3 method for class 'dgCMatrix'
as.H5SpMat(
  x,
  filename,
  valuePath = "data",
  rowindPath = "indices",
  colptrPath = "indptr",
  overwrite = FALSE,
  ...
)

## Default S3 method:
as.H5SpMat(
  x,
  filename,
  valuePath = "data",
  rowindPath = "indices",
  colptrPath = "indptr",
  overwrite = FALSE,
  ...
)

Arguments

filename

Filename of the HDF5 file

valuePath

Path in the HDF5 file that points to a 1D array storing the non-zero values of the sparse matrix. Default "data" when using as.H5SpMat.

rowindPath

Path in the HDF5 file that points to a 1D integer array storing the row indices of non-zero values in each column of the sparse matrix. Default "indices" when using as.H5SpMat.

colptrPath

Path in the HDF5 file that points to a 1D integer array storing the number of non-zero values in each column of the sparse matrix. Default "indptr" when using as.H5SpMat.

nrow, ncol

Integer, the true dimensionality of the sparse matrix.

x

For as.H5SpMat, matrix of either dense or sparse type to be written; for print, a H5SpMat argument list object.

overwrite

Logical, whether to overwrite the file if already exists at the given path. Default FALSE.

...

not used

Value

H5SpMat object, indeed a list object.

Examples

if (require("withr")) {
H5SpMatEx <- function(){
withr::local_dir(withr::local_tempdir())
h <- H5SpMat(system.file("extdata/ctrl_sparse.h5", package = "RcppPlanc"),
             "data", "indices", "indptr", 173, 300)
dim(h)

library(Matrix)
ctrl.dense <- as.matrix(ctrl.sparse)
h1 <- as.H5SpMat(ctrl.sparse, "ctrl_from_sparse_to_sparse.h5",
                 valuePath = "data", rowindPath = "indices",
                 colptrPath = "indptr", nrow = nrow(ctrl.sparse),
                 ncol = ncol(ctrl.sparse))
h1
h2 <- as.H5SpMat(ctrl.dense, "ctrl_from_dense_to_sparse.h5",
                 valuePath = "data", rowindPath = "indices",
                 colptrPath = "indptr", nrow = nrow(ctrl.sparse),
                 ncol = ncol(ctrl.sparse))
h2
}
H5SpMatEx()
}

Perform Integrative Non-negative Matrix Factorization

Description

Performs integrative non-negative matrix factorization (iNMF) (J.D. Welch, 2019) to return factorized HH, WW, and VV matrices. The objective function is stated as

argminH0,W0,V0idEi(W+Vi)HiF2+λidViHiF2\arg\min_{H\ge0,W\ge0,V\ge0}\sum_{i}^{d}||E_i-(W+V_i)Hi||^2_F+ \lambda\sum_{i}^{d}||V_iH_i||_F^2

where EiE_i is the input non-negative matrix of the ii'th dataset, dd is the total number of datasets. EiE_i is of size m×nim \times n_i for mm features and nin_i sample points, HiH_i is of size k×nik \times n_i, ViV_i is of size m×km \times k, and WW is of size m×km \times k.

inmf optimizes the objective with ANLS strategy, while onlineINMF optimizes the same objective with an online learning strategy.

Usage

inmf(
  objectList,
  k = 20,
  lambda = 5,
  niter = 30,
  nCores = 2,
  Hinit = NULL,
  Vinit = NULL,
  Winit = NULL,
  verbose = FALSE
)

Arguments

objectList

list of input datasets. List elements should all be of the same class. Viable classes include: matrix, dgCMatrix, H5Mat, H5SpMat.

k

Integer. Inner dimensionality to factorize the datasets into. Default 20.

lambda

Regularization parameter. Larger values penalize dataset-specific effects more strongly (i.e. alignment should increase as lambda increases). Default 5.

niter

Integer. Total number of block coordinate descent iterations to perform. Default 30.

nCores

The number of parallel tasks that will be spawned. Default 2

Hinit

Initial values to use for HH matrices. A list object where each element is the initial HH matrix of each dataset. Each should be dense matrix of size ni×kn_i \times k. Default NULL.

Vinit

Similar to Hinit, but each should be of size m×km \times k.

Winit

Initial values to use for WW matrix. A matrix object of size m×km \times k. Default NULL.

verbose

Logical scalar. Whether to show information and progress. Default FALSE.

Value

A list of the following elements:

  • H - a list of result HiH_i matrices of size ni×kn_i \times k

  • V - a list of result ViV_i matrices

  • W - the result WW matrix

  • objErr - the final objective error value.

Author(s)

Yichen Wang

References

Joshua D. Welch and et al., Single-Cell Multi-omic Integration Compares and Contrasts Features of Brain Cell Identity, Cell, 2019

Examples

library(Matrix)
set.seed(1)
result <- inmf(list(ctrl.sparse, stim.sparse), k = 10, niter = 10)

Perform Non-negative Matrix Factorization

Description

Regularly, Non-negative Matrix Factorization (NMF) is factorizes input matrix XX into low rank matrices WW and HH, so that XWHX \approx WH. The objective function can be stated as argminW0,H0XWHF2\arg\min_{W\ge0,H\ge0}||X-WH||_F^2. In practice, XX is usually regarded as a matrix of mm features by nn sample points. And the result matrix WW should have the dimensionality of m×km \times k and H with n×kn \times k (transposed). This function wraps the algorithms implemented in PLANC library to solve NMF problems. Algorithms includes Alternating Non-negative Least Squares with Block Principal Pivoting (ANLS-BPP), Alternating Direction Method of Multipliers (ADMM), Hierarchical Alternating Least Squares (HALS), and Multiplicative Update (MU).

Usage

nmf(
  x,
  k,
  niter = 30L,
  algo = "anlsbpp",
  nCores = 2L,
  Winit = NULL,
  Hinit = NULL
)

Arguments

x

Input matrix for factorization. Can be either dense or sparse.

k

Integer. Factor matrix rank.

niter

Integer. Maximum number of NMF interations.

algo

Algorithm to perform the factorization, choose from "anlsbpp", "admm", "hals" or "mu". See detailed sections.

nCores

The number of parallel tasks that will be spawned. Only applies to anlsbpp. Default 2

Winit

Initial left-hand factor matrix, must be of size m x k.

Hinit

Initial right-hand factor matrix, must be of size n x k.

Value

A list with the following elements:

  • W - the result left-hand factor matrix

  • H - the result right hand matrix.

  • objErr - the objective error of the factorization.

References

Ramakrishnan Kannan and et al., A High-Performance Parallel Algorithm for Nonnegative Matrix Factorization, PPoPP '16, 2016, 10.1145/2851141.2851152


Perform Integrative Non-negative Matrix Factorization Using Online Learning

Description

Performs integrative non-negative matrix factorization (iNMF) (J.D. Welch, 2019, C. Gao, 2021) using online learning approach to return factorized HH, WW, and VV matrices. The objective function is stated as

argminH0,W0,V0idEi(W+Vi)HiF2+λidViHiF2\arg\min_{H\ge0,W\ge0,V\ge0}\sum_{i}^{d}||E_i-(W+V_i)Hi||^2_F+ \lambda\sum_{i}^{d}||V_iH_i||_F^2

where EiE_i is the input non-negative matrix of the ii'th dataset, dd is the total number of datasets. EiE_i is of size m×nim \times n_i for mm features and nin_i sample points, HiH_i is of size k×nik \times n_i, ViV_i is of size m×km \times k, and WW is of size m×km \times k.

Different from inmf which optimizes the objective with ANLS approach, onlineINMF optimizes the same objective with online learning strategy, where it updates mini-batches of HiH_i solving the NNLS problem, and updates ViV_i and WW with HALS multiplicative method.

This function allows online learning in 3 scenarios:

  1. Fully observed datasets;

  2. Iterative refinement using continually arriving datasets;

  3. Projection of new datasets without updating the existing factorization

Usage

onlineINMF(
  objectList,
  newDatasets = NULL,
  project = FALSE,
  k = 20,
  lambda = 5,
  maxEpoch = 5,
  minibatchSize = 5000,
  maxHALSIter = 1,
  nCores = 2,
  Vinit = NULL,
  Winit = NULL,
  Ainit = NULL,
  Binit = NULL,
  verbose = FALSE
)

Arguments

objectList

list of input datasets. List elements should all be of the same class. Viable classes include: matrix, dgCMatrix, H5Mat, H5SpMat.

newDatasets

Same requirements as for new arriving datasets. Default NULL for scenario 1, specify for scenario 2 or 3.

project

Logical scalar, whether to run scenario 3. See description. Default FALSE.

k

Integer. Inner dimensionality to factorize the datasets into. Default 20.

lambda

Regularization parameter. Larger values penalize dataset-specific effects more strongly (i.e. alignment should increase as lambda increases). Default 5.

maxEpoch

The number of epochs to iterate through. Default 5.

minibatchSize

Total number of cells in each mini-batch. Default 5000.

maxHALSIter

Maximum number of block coordinate descent (HALS algorithm) iterations to perform for each update of WW and VV. Default 1. Changing this parameter is not recommended.

nCores

The number of parallel tasks that will be spawned. Default 2

Vinit, Winit, Ainit, Binit

Pass the previous factorization result for datasets existing in objectList, in order to run scenario 2 or 3. All should have length(objectList) matrices inside. See description for dimensionality of ViV_i and WiW_i. AiA_i should be of size k×kk \times k and BiB_i should be of size m×km \times k

verbose

Logical scalar. Whether to show information and progress. Default FALSE.

Value

A list of the following elements:

  • H - a list of result HiH_i matrices of size ni×kn_i \times k

  • V - a list of result ViV_i matrices

  • W - the result WW matrix

  • A - a list of result AiA_i matrices, k×kk \times k

  • B - a list of result BiB_i matrices, m×km \times k

  • objErr - the final objective error value.

Author(s)

Yichen Wang

References

Joshua D. Welch and et al., Single-Cell Multi-omic Integration Compares and Contrasts Features of Brain Cell Identity, Cell, 2019

Chao Gao and et al., Iterative single-cell multi-omic integration using online learning, Nat Biotechnol., 2021

Examples

library(Matrix)

# Scenario 1 with sparse matrices
set.seed(1)
res1 <- onlineINMF(list(ctrl.sparse, stim.sparse), 
                   minibatchSize = 50, k = 10)

# Scenario 2 with H5 dense matrices
h5dense1 <- H5Mat(filename = system.file("extdata", "ctrl_dense.h5",
                             package = "RcppPlanc", mustWork = TRUE),
                                          dataPath = "scaleData")
h5dense2 <- H5Mat(filename = system.file("extdata", "stim_dense.h5",
                             package = "RcppPlanc", mustWork = TRUE),
                                          dataPath = "scaleData")
res2 <- onlineINMF(list(ctrl = h5dense1), minibatchSize = 50, k = 10)
res3 <- onlineINMF(list(ctrl = h5dense1),
                   newDatasets = list(stim = h5dense2),
                   Vinit = res2$V, Winit = res2$W,
                   Ainit = res2$A, Binit = res2$B, 
                   minibatchSize = 50, k = 10)

# Scenario 3 with H5 sparse matrices
h5sparse1 <- H5SpMat(filename = system.file("extdata", "ctrl_sparse.h5",
                                package = "RcppPlanc", mustWork = TRUE),
                                valuePath = "scaleDataSparse/data",
                                rowindPath = "scaleDataSparse/indices",
                                colptrPath = "scaleDataSparse/indptr",
                                nrow = nrow(ctrl.sparse),
                                ncol = ncol(ctrl.sparse))
h5sparse2 <- H5SpMat(filename = system.file("extdata", "stim_sparse.h5",
                                package = "RcppPlanc", mustWork = TRUE),
                                valuePath = "scaleDataSparse/data",
                                rowindPath = "scaleDataSparse/indices",
                                colptrPath = "scaleDataSparse/indptr",
                                nrow = nrow(stim.sparse),
                                ncol = nrow(stim.sparse))
res4 <- onlineINMF(list(ctrl = h5sparse1), minibatchSize = 50, k = 10)
res5 <- onlineINMF(list(ctrl = h5sparse1),
                   newDatasets = list(stim = h5sparse2), project = TRUE,
                   Vinit = res4$V, Winit = res4$W,
                   Ainit = res4$A, Binit = res4$B, minibatchSize = 50, k = 10)

Show information of a H5Mat object

Description

Show information of a H5Mat object

Usage

## S3 method for class 'H5Mat'
print(x, ...)

Arguments

x

H5Mat argument list object

...

Not used.

Value

NULL. Information displayed.

Examples

h <- H5Mat(system.file("extdata/ctrl_dense.h5", package = "RcppPlanc"),
           "data")
print(h)

Show information of a H5SpMat object

Description

Show information of a H5SpMat object

Usage

## S3 method for class 'H5SpMat'
print(x, ...)

Arguments

x

H5SpMat argument list object

...

Not used.

Value

NULL. Information displayed.

Examples

h <- H5SpMat(system.file("extdata/ctrl_sparse.h5", package = "RcppPlanc"),
             "data", "indices", "indptr", 173, 300)
print(h)

Perform Symmetric Non-negative Matrix Factorization

Description

Symmetric input matrix XX of size n×nn \times n is required. Two approaches are provided. Alternating Non-negative Least Squares Block Principal Pivoting algorithm (ANLSBPP) with symmetric regularization, where the objective function is set to be argminH0,W0XWHF2+λWHF2\arg\min_{H\ge0,W\ge0}||X-WH||_F^2+ \lambda||W-H||_F^2, can be run with algo = "anlsbpp". Gaussian-Newton algorithm, where the objective function is set to be argminH0XHTHF2\arg\min_{H\ge0}||X-H^\mathsf{T}H||_F^2, can be run with algo = "gnsym". In the objectives, WW is of size n×kn \times k and HH is of size k×nk \times n. The returned results will all be n×kn \times k.

Usage

symNMF(
  x,
  k,
  niter = 30L,
  lambda = 0,
  algo = "gnsym",
  nCores = 2L,
  Hinit = NULL
)

Arguments

x

Input matrix for factorization. Must be symmetric. Can be either dense or sparse.

k

Integer. Factor matrix rank.

niter

Integer. Maximum number of symNMF interations. Default 30

lambda

Symmetric regularization parameter. Must be non-negative. Default 0.0 uses the square of the maximum value in x.

algo

Algorithm to perform the factorization, choose from "gnsym" or "anlsbpp". Default "gnsym"

nCores

The number of parallel tasks that will be spawned. Only applies to anlsbpp. Default 2

Hinit

Initial right-hand factor matrix, must be of size n x k. Default NULL.

Value

A list with the following elements:

  • W - the result left-hand factor matrix, non-empty when using "anlsbpp"

  • H - the result right hand matrix.

  • objErr - the objective error of the factorization.

References

Srinivas Eswar and et al., Distributed-Memory Parallel Symmetric Nonnegative Matrix Factorization, SC '20, 2020, 10.5555/3433701.3433799


Perform Mosaic Integrative Non-negative Matrix Factorization with Unshared Features

Description

Performs mosaic integrative non-negative matrix factorization (UINMF) (A.R. Kriebel, 2022) to return factorized HH, WW, VV and UU matrices. The objective function is stated as

argminH0,W0,V0,U0id[EiPi]([W0]+[ViUi])HiF2+λiid[ViUi]HiF2\arg\min_{H\ge0,W\ge0,V\ge0,U\ge0}\sum_{i}^{d} ||\begin{bmatrix}E_i \\ P_i \end{bmatrix} - (\begin{bmatrix}W \\ 0 \end{bmatrix}+ \begin{bmatrix}V_i \\ U_i \end{bmatrix})Hi||^2_F+ \lambda_i\sum_{i}^{d}||\begin{bmatrix}V_i \\ U_i \end{bmatrix}H_i||_F^2

where EiE_i is the input non-negative matrix of the ii'th dataset, PiP_i is the input non-negative matrix for the unshared features, dd is the total number of datasets. EiE_i is of size m×nim \times n_i for mm shared features and nin_i sample points, PiP_i is of size ui×niu_i \times n_i for uiu_i unshared feaetures, HiH_i is of size k×nik \times n_i, ViV_i is of size m×km \times k, WW is of size m×km \times k and UiU_i is of size ui×ku_i \times k.

Similar to inmf, uinmf also optimizes the objective with ANLS algorithm.

Usage

uinmf(
  objectList,
  unsharedList,
  k = 20,
  lambda = 5,
  niter = 30,
  nCores = 2,
  verbose = FALSE
)

Arguments

objectList

list of input datasets. List elements should all be of the same class. Viable classes include: matrix, dgCMatrix, H5Mat, H5SpMat.

unsharedList

List of input unshared feature matrices, with the same requirement as objectList.

k

Integer. Inner dimensionality to factorize the datasets into. Default 20.

lambda

Regularization parameter. Use one number for all datasets or a vector to specify for each dataset. Larger values penalize dataset-specific effects more strongly (i.e. alignment should increase as lambda increases). Default 5.

niter

Integer. Total number of block coordinate descent iterations to perform. Default 30.

nCores

The number of parallel tasks that will be spawned. Default 2.

verbose

Logical scalar. Whether to show information and progress. Default FALSE.

Value

A list of the following elements:

  • H - a list of result HiH_i matrices of size ni×kn_i \times k

  • V - a list of result ViV_i matrices

  • W - the result WW matrix

  • U - a list of result AiA_i matrices

  • objErr - the final objective error value.

Author(s)

Yichen Wang

References

April R. Kriebel and Joshua D. Welch, UINMF performs mosaic integration of single-cell multi-omic datasets using nonnegative matrix factorization, Nat. Comm., 2022

Examples

# Fake matrices representing unshared features of the given datasets
# Real-life use should have features that are not presented in the 
# intersection of features of all datasets involved.
ctrl.unshared <- ctrl.sparse[1:10,]
stim.unshared <- stim.sparse[11:30,]
set.seed(1)
result <- uinmf(list(ctrl.sparse, stim.sparse), 
                list(ctrl.unshared, stim.unshared))