Package 'vrnmf' reference manual

Title:	Volume-Regularized Structured Matrix Factorization
Description:	Implements a set of routines to perform structured matrix factorization with minimum volume constraints. The NMF procedure decomposes a matrix X into a product C * D. Given conditions such that the matrix C is non-negative and has sufficiently spread columns, then volume minimization of a matrix D delivers a correct and unique, up to a scale and permutation, solution (C, D). This package provides both an implementation of volume-regularized NMF and "anchor-free" NMF, whereby the standard NMF problem is reformulated in the covariance domain. This algorithm was applied in Vladimir B. Seplyarskiy Ruslan A. Soldatov, et al. "Population sequencing data reveal a compendium of mutational processes in the human germ line". Science, 12 Aug 2021. <doi:10.1126/science.aba7408>. This package interacts with data available through the 'simulatedNMF' package, which is available in a 'drat' repository. To access this data package, see the instructions at <https://github.com/kharchenkolab/vrnmf>. The size of the 'simulatedNMF' package is approximately 8 MB.
Authors:	Ruslan Soldatov [aut], Peter Kharchenko [aut], Viktor Petukhov [aut], Evan Biederstedt [cre, aut]
Maintainer:	Evan Biederstedt <[email protected]>
License:	GPL-3
Version:	1.0.2
Built:	2024-11-02 02:56:20 UTC
Source:	https://github.com/kharchenkolab/vrnmf

Non-negative tri-factorization of co-occurence matrix using minimum volume approach.

Description

AnchorFree method tri-factorizes (co-occurence) matrix in a product $P ~ C*E*t(C)$ of non-negative matrices $C$ and $E$ such that matrix $E$ has mininum volume and columns of matrix $C$ equal to 1.

Usage

AnchorFree(
  vol,
  n.comp = 3,
  init = NULL,
  init.type = "diag",
  n.iter = 30,
  err.cut = 1e-30,
  verbose = FALSE
)
AnchorFree(
  vol,
  n.comp = 3,
  init = NULL,
  init.type = "diag",
  n.iter = 30,
  err.cut = 1e-30,
  verbose = FALSE
)

Arguments

`vol`	An output object of vol_preprocess(). The method factorizes co-occurence matrix `vol$P`.
`n.comp`	An integer. Number of components to extract (by default 3). Defines number of columns in matrix $C$ . (default=3)
`init`	A numeric matrix. Initial matrix `M`. (default=3)
`init.type`	A character. A strategy to randomly initialize matrix `M`. (default="diag") Options are to 1) generate diagonal unit matrix ("diag"), 2) use ICA solution as initialization ("ica", "ica.pos"). or sample entries from: 3) uniform distribution `[0,1]` ("unif.pos"), 4) unform distribution `[-1,1]`, 5) uniform distribution `[0.9,1.1]` ("similar"), 6) normal distribution `N(0,1)`.
`n.iter`	An integer. Number of iterations. (default=30)
`err.cut`	A numeric. Relative error in determinant between iterations to stop algorithm (now is not used). (default=1e-30)
`verbose`	A boolean. Print per-iteration information (default=FALSE)

Details

Implementation closely follows (Fu X et al., IEEE Trans Pattern Anal Mach Intell., 2019).

Value

List of objects:

C, E Factorization matrices.

Pest Estimate of vol$P co-occurence matrix $Pest = C*E*t(C)$ .

M, detM auxiliary matrix M and its determinant.

init.type type of initialization of matrix M that was used.

Examples

small_example <- sim_factors(5, 5, 5)
vol <- vol_preprocess(t(small_example$X))
vol.anchor <- AnchorFree(vol)

small_example <- sim_factors(5, 5, 5)
vol <- vol_preprocess(t(small_example$X))
vol.anchor <- AnchorFree(vol)

Infer a matrix of non-negative intensities in NMF with offset/nmf-offset.

Description

factor_intensities estimates a non-negative matrix D that optimizes the objective function $F = ||X - C*D - offset||^2$ , where offset is either column-specific offset or a "1-rank nmf term": product of row vector and column vector

Usage

factor_intensities(
  C,
  X,
  fit.nmf = TRUE,
  fit.factor = FALSE,
  qp.exact = FALSE,
  n.iter = 200,
  qp.iter = 10,
  rel.error.cutoff = 1e-05,
  extrapolate = TRUE,
  extrapolate.const = TRUE,
  extrapolate.convex = FALSE,
  q.factor = 1,
  verbose = TRUE,
  n.cores = 1
)
factor_intensities(
  C,
  X,
  fit.nmf = TRUE,
  fit.factor = FALSE,
  qp.exact = FALSE,
  n.iter = 200,
  qp.iter = 10,
  rel.error.cutoff = 1e-05,
  extrapolate = TRUE,
  extrapolate.const = TRUE,
  extrapolate.convex = FALSE,
  q.factor = 1,
  verbose = TRUE,
  n.cores = 1
)

Arguments

`C`	Numeric matrices.
`X`	Numeric matrices.
`fit.nmf`	A boolean. Fit both intensities and spectrum of the offset residuals.
`fit.factor`	A boolean. Fit only spectrum of the offset residuals (keep intensities constant across samples).
`qp.exact`	A boolean. Estimate intensities using exact quadratic programming (qp.exact = TRUE) or inexact QP via gradient decent with extrapolation (qp.exact = FALSE).
`n.iter`	An integer. Number of iterations.
`qp.iter`	= 1e+1 An integer. Number of iterations of inexact QP.
`rel.error.cutoff`	A numeric. Relative error cutoff between iterations to stop iterations.
`extrapolate`	A boolean. Use Nesterov-like extrapolation at each iteration.
`extrapolate.const`	A boolean. Use extrapolation scheme that adds a constant extrapolation q.factor (described below) at each iteration.
`extrapolate.convex`	A boolean. Use Nesterov extrapolation scheme.
`q.factor`	A numeric. Specification of a a constant extrapolation factor used in case of extrapolate.const = T.
`verbose`	A boolean. Print per-iteration information (by default TRUE).
`n.cores`	An integer. Number of cores to use.

Value

Fitted matrix D.

Infer a matrix of non-negative intensities in NMF

Description

infer_intensities estimates a non-negative matrix D that optimizes the objective function $F = ||X - C*D||^2$ using per-row quadratic programming.

Usage

infer_intensities(C, X, esign = "pos", n.cores = 1)
infer_intensities(C, X, esign = "pos", n.cores = 1)

Arguments

`C`	Numeric matrices.
`X`	Numeric matrices.
`esign`	A character. Keep elements of matrix `D` non-negative ("pos") or not ("all). (default="pos")
`n.cores`	An integer. Number of cores to use. (default=1)

Value

Fitted matrix D.

Project vector onto a probabilistic simplex.

Description

projection_onto_simplex projects a vector unproj onto a probabilistic simplex of sum bound.

Usage

projection_onto_simplex(unproj, bound)
projection_onto_simplex(unproj, bound)

Arguments

`unproj`	A numeric vector. An unprojected vector
`bound`	A numeric. Sum of projected vector elements.

Value

A projected vector.

Simulate matrices to explores `vrnmf`

Description

sim_factors simulates non-negative factorization matrices C and D under a variaty of conditions to explore factorization $X = C*D + noise$ .

Usage

sim_factors(
  m,
  n,
  r,
  simplex = "col",
  distr = "unif",
  frac.zeros = 0.4,
  condition = FALSE,
  noise = 0
)
sim_factors(
  m,
  n,
  r,
  simplex = "col",
  distr = "unif",
  frac.zeros = 0.4,
  condition = FALSE,
  noise = 0
)

Arguments

`m`	Integers. Size of matrices. Matrix `C` has a size of `mr` and matrix `D` has a size of `rn`.
`n`	Integers. Size of matrices. Matrix `C` has a size of `mr` and matrix `D` has a size of `rn`.
`r`	Integers. Size of matrices. Matrix `C` has a size of `mr` and matrix `D` has a size of `rn`.
`simplex`	A character. Either columns ("col") or rows ("row") of matrix `C` are projected onto unit simplex. (default="col")
`distr`	A character. Distribution to simulate matrix entries: "unif" for uniform and "exp" for exponential distributions. (default="unif")
`frac.zeros`	A numeric. Fraction of zeros in matrix `C`. It promotes sufficient scattering of matrix column/row vectors. (default=0.4)
`condition`	A boolean. Generate more well-conditioned matrix `R`. (default=FALSE)
`noise`	A numeric. Standard deviation of gaussian noise to add. (default=0e-4)

Value

List of simulated matrices:

X.noise, X - noisy and original matrix X to decompose.

C, D - factorization matrices.

Preprocess the data for downstream volume analysis.

Description

vol_preprocess Routine normalizes the data (as requested), estimates covariance and SVD decomposition.

Usage

vol_preprocess(X, col.norm = "sd", row.norm = NULL, pfactor = NULL)
vol_preprocess(X, col.norm = "sd", row.norm = NULL, pfactor = NULL)

Arguments

`X`	A numeric matrix. Covariance is estimated for column vectors of `X`.
`col.norm`	A character. Specifies column normalization strategy (by default "sd"). NULL to avoid normalization.
`row.norm`	A character. Specifies row normalization strategy (by default NULL).
`pfactor`	A numeric A factor to normalize co-occurence matrix (by default NULL). Row normalization follows column normalization. NULL to avoid normalization.

Value

A list of objects that include normalized matrix X.process, row and column normalization factors row.factors and col.factors, covariance matrix P0, covariance matrix P normalized to maximum value pfactor, orthonormal basis U and vector of eigenvalues eigens.

Examples

small_example <- sim_factors(5, 5, 5)
vol <- vol_preprocess(t(small_example$X))

small_example <- sim_factors(5, 5, 5)
vol <- vol_preprocess(t(small_example$X))

Update volume-regularized matrix `R` using det volume approximation

Description

volnmf_det finds matrix R that minimizes objective ||X-C*R||^2 + w.vol*det(R)

Usage

volnmf_det(
  C,
  X,
  R,
  posit = FALSE,
  w.vol = 0.1,
  eigen.cut = 1e-16,
  err.cut = 0.001,
  n.iter = 1000
)
volnmf_det(
  C,
  X,
  R,
  posit = FALSE,
  w.vol = 0.1,
  eigen.cut = 1e-16,
  err.cut = 0.001,
  n.iter = 1000
)

Arguments

`C`	Numeric Matrices. Matrices involved in objective function. Matrix R serves as initialization.
`X`	Numeric Matrices. Matrices involved in objective function. Matrix R serves as initialization.
`R`	Numeric Matrices. Matrices involved in objective function. Matrix R serves as initialization.
`posit`	A boolean. Set up (TRUE) or not (FALSE) non-negative constraints on matrix `R`. (default=TRUE)
`w.vol`	A numeric. Volume (det) weight in objective function. (default=0.1)
`eigen.cut`	A numeric. Threshold on eigenvalue of SVD eigenvectors. (default=1e-16)
`err.cut`	A numeric. Stop algorithm if relative erro in R between iteration is less than `err.cut`. (default=1e-3)
`n.iter`	An integer. Number of iterations. (default=1e+3)

Value

An updated matrix R.

Alternating optimization of volume-regularized NMF

Description

volnmf_estimate provides alternating optimization of volume-regularized factorization of a matrix B using the following objective function: $F = ||B*Q - C*R||^2 + w.vol*volume(R)$ . Matrix C is required to be non-negative and having either column or row vectors on the simplex. Matrix R can optionally have non-negativity constraint. Matrix Q can optionally be identity matrix or any unitary.

Usage

volnmf_estimate(
  B,
  C,
  R,
  Q,
  domain = "covariance",
  volf = "logdet",
  R.majorate = FALSE,
  wvol = NULL,
  delta = 1e-08,
  n.iter = 10000,
  err.cut = 1e-08,
  vol.iter = 100,
  c.iter = 100,
  extrapolate = TRUE,
  accelerate = TRUE,
  acc.C = 4/5,
  acc.R = 3/4,
  C.constraint = "col",
  C.bound = 1,
  R.constraint = "pos",
  verbose = TRUE,
  record = 100,
  Canchor = NULL,
  Ctrue = NULL,
  mutation.run = FALSE
)
volnmf_estimate(
  B,
  C,
  R,
  Q,
  domain = "covariance",
  volf = "logdet",
  R.majorate = FALSE,
  wvol = NULL,
  delta = 1e-08,
  n.iter = 10000,
  err.cut = 1e-08,
  vol.iter = 100,
  c.iter = 100,
  extrapolate = TRUE,
  accelerate = TRUE,
  acc.C = 4/5,
  acc.R = 3/4,
  C.constraint = "col",
  C.bound = 1,
  R.constraint = "pos",
  verbose = TRUE,
  record = 100,
  Canchor = NULL,
  Ctrue = NULL,
  mutation.run = FALSE
)

Arguments

`B`	A numeric matrix. A matrix to factorize (by default NULL). If not given than matrix `B` is taken to be a square root decomposition of $P = B*t(B)$ .
`C`	Numeric matrices. Initial matrices for optimiztion.
`R`	Numeric matrices. Initial matrices for optimiztion.
`Q`	Numeric matrices. Initial matrices for optimiztion.
`domain`	A character. Optimize unitary rotation matrix `Q` ("covariance") or keep it as identity matrix (as in standard NMF). By default "covariance".
`volf`	A character. Function that approximate volume. Can have values of "logdet" or "det" (by default "logdet").
`R.majorate`	A boolean. Majorate logdet each iteration of `volnmf_logdet()` (by default FALSE).
`wvol`	A numeric. A weight of volume-regularized term `volume(R)`.
`delta`	A numeric. Logdet regularization term `log(det(R) + delta)` (by default 1e-8).
`n.iter`	An integer. Number of iterations (by default `1,000`).
`err.cut`	A numeric. Relative error in determinant between iterations to stop algorithm (by default `1e-8`).
`vol.iter`	An integer. Number of iterations to update volume-regularized matrix `R` at each alternating step.
`c.iter`	An integer. Number of iterations to update simplex matrix `C` at each alternating step.
`extrapolate`	A numeric. Do Nesterov extrapolation inside blocks of R and C optimization (by default TRUE).
`accelerate`	A numeric. Do acceleration each update after R and C blocks estimated via Nesterov-like extrapolation.
`acc.C`	A numeric. Acceleration parameter of matrix C.
`acc.R`	A numeric. Acceleration parameter of matrix R.
`C.constraint`	A character. Constraint either sum of columns ("col") or sum of rows ("row) to be equal to `C.bound` (By default "col").
`C.bound`	A numeric. A simplex constraint on matrix C vectors.
`R.constraint`	A character. Set up non-negativity ("pos") constraint on elements of `R` (by default "pos", alternative "no").
`verbose`	A boolean. Print per-iteration information (by default FALSE)
`record`	A numeric. Record parameters every 'record' iterations (by default `NULL`).
`Canchor`	A matrix. A matrix of anchor components (unused currently). (default=NULL)
`Ctrue`	A matrix. Correct matrix C if known. Useful for benchmark.
`mutation.run`	A boolean. Assess goodness of solution using reflection test if mutation.run=TRUE (applicable only to analysis of mutation patterns). (default=FALSE)

Value

List of objects:

C, R, Q, E Factorization matrices.

iter, err Number of iterations and relative per-iteration error err in matrix C.

info.record a list of objects that record and store state of matrices each record iterations.

Update volume-regularized matrix `R` using logdet volume approximation.

Description

volnmf_logdet finds matrix R that minimizes objective ||X-C*R||^2 + w.vol*log(det(R)+delta).

Usage

volnmf_logdet(
  C,
  X,
  R,
  R.constraint = "pos",
  majorate = FALSE,
  extrapolate = TRUE,
  qmax = 100,
  w.vol = 0.1,
  delta = 1,
  err.cut = 0.001,
  n.iter = 1000
)
volnmf_logdet(
  C,
  X,
  R,
  R.constraint = "pos",
  majorate = FALSE,
  extrapolate = TRUE,
  qmax = 100,
  w.vol = 0.1,
  delta = 1,
  err.cut = 0.001,
  n.iter = 1000
)

Arguments

`C`	Numeric Matrices. Matrices involved in objective function.Matrix R serves as initialization.
`X`	Numeric Matrices. Matrices involved in objective function.Matrix R serves as initialization.
`R`	Numeric Matrices. Matrices involved in objective function.Matrix R serves as initialization.
`R.constraint`	A character. Set up ('pos') or not ('no') non-negative constraints on matrix `R` (by default 'pos').
`majorate`	A boolean. Majorate logdet each iteration (by default FALSE).
`extrapolate`	A boolean. Use Nesterov acceleration (by default FALSE, currently is not supported).
`qmax`	A numeric. Maximum asymptotic (1 - 1/qmax) of extrapolation step.
`w.vol`	A numeric. Volume (logdet) weight in objective function.
`delta`	A numeric. Determinant pseudocount in objective function.
`err.cut`	A numeric. Stop algorithm if relative erro in R between iteration is less than `err.cut`.
`n.iter`	An integer. Number of iterations.

Value

An updated matrix R.

Volume-regularized NMF

Description

volnmf_main enables volume-regularized factorization of a matrix B using the following objective function: $F = ||B*Q - C*R||^2 + w.vol*volume(R)$ . Matrix C is required to be non-negative and having either column or row vectors on the simplex. Matrix R can optionally have non-negativity constraint. Matrix Q can optionally be identity matrix or any unitary. The latter option is used to decompose co-occurence matrix vol_P.

Usage

volnmf_main(
  vol,
  B = NULL,
  volnmf = NULL,
  n.comp = 3,
  n.reduce = n.comp,
  do.nmf = TRUE,
  iter.nmf = 100,
  seed = NULL,
  domain = "covariance",
  volf = "logdet",
  wvol = NULL,
  delta = 1e-08,
  n.iter = 500,
  err.cut = 1e-16,
  vol.iter = 20,
  c.iter = 20,
  extrapolate = TRUE,
  accelerate = FALSE,
  acc.C = 4/5,
  acc.R = 3/4,
  C.constraint = "col",
  C.bound = 1,
  R.constraint = "pos",
  R.majorate = FALSE,
  C.init = NULL,
  R.init = NULL,
  Q.init = NULL,
  anchor = NULL,
  Ctrue = NULL,
  verbose = TRUE,
  record = 100,
  verbose.nmf = FALSE,
  record.nmf = NULL,
  mutation.run = FALSE
)
volnmf_main(
  vol,
  B = NULL,
  volnmf = NULL,
  n.comp = 3,
  n.reduce = n.comp,
  do.nmf = TRUE,
  iter.nmf = 100,
  seed = NULL,
  domain = "covariance",
  volf = "logdet",
  wvol = NULL,
  delta = 1e-08,
  n.iter = 500,
  err.cut = 1e-16,
  vol.iter = 20,
  c.iter = 20,
  extrapolate = TRUE,
  accelerate = FALSE,
  acc.C = 4/5,
  acc.R = 3/4,
  C.constraint = "col",
  C.bound = 1,
  R.constraint = "pos",
  R.majorate = FALSE,
  C.init = NULL,
  R.init = NULL,
  Q.init = NULL,
  anchor = NULL,
  Ctrue = NULL,
  verbose = TRUE,
  record = 100,
  verbose.nmf = FALSE,
  record.nmf = NULL,
  mutation.run = FALSE
)

Arguments

`vol`	An output object of vol_preprocess().
`B`	A numeric matrix. A matrix to factorize (by default NULL). If not given than matrix `B` is taken to be a square root decomposition of $P = B*t(B)$ .
`volnmf`	An output object of `volnmf.main`. An option is useful to re-estimate solution using different parameters (by default NULL).
`n.comp`	An integer. Number of components to extract (by default 3). Defines number of columns in matrix $C$ .
`n.reduce`	An integer. Dimensional reduction of matrix B (number of columns) if taken as a square root decomposition of `volP` (by default equal to `n.comp`).
`do.nmf`	A boolean. Estimate standard solution with `w.vol=0` as initialization before applying volume regularization (by default `TRUE`).
`iter.nmf`	An integer. Number of iterations to get solution with `w.vol=0` if the former requested (by default `1,000`).
`seed`	An integer. Fix seed.
`domain`	A character. Optimize unitary rotation matrix `Q` ("covariance") or keep it as identity matrix (as in standard NMF). By default "covariance".
`volf`	A character. Function that approximate volume. Can have values of "logdet" or "det" (by default "logdet").
`wvol`	A numeric. A weight of volume-regularized term `volume(R)`.
`delta`	A numeric. Logdet regularization term `log(det(R) + delta)` (by default 1e-8).
`n.iter`	An integer. Number of iterations (by default `1,000`).
`err.cut`	A numeric. Relative error in determinant between iterations to stop algorithm (by default `1e-8`).
`vol.iter`	An integer. Number of iterations to update volume-regularized matrix `R` at each alternating step.
`c.iter`	An integer. Number of iterations to update simplex matrix `C` at each alternating step.
`extrapolate`	A numeric. Do Nesterov extrapolation inside blocks of R and C optimization (by default TRUE).
`accelerate`	A numeric. Do acceleration each update after R and C blocks estimated via Nesterov-like extrapolation.
`acc.C`	A numeric. Acceleration parameter of matrix C.
`acc.R`	A numeric. Acceleration parameter of matrix R.
`C.constraint`	A character. Constraint either sum of columns ("col") or sum of rows ("row) to be equal to `C.bound` (By default "col").
`C.bound`	A numeric. A simplex constraint on matrix C vectors.
`R.constraint`	A character. Set up non-negativity ("pos") constraint on elements of `R` (by default "pos", alternative "no").
`R.majorate`	A boolean. Majorate logdet each iteration of `volnmf_logdet()` (by default FALSE).
`C.init`	Numeric matrices. Initialization of matrices `C, R, Q` (by default `NULL`).
`R.init`	Numeric matrices. Initialization of matrices `C, R, Q` (by default `NULL`).
`Q.init`	Numeric matrices. Initialization of matrices `C, R, Q` (by default `NULL`).
`anchor`	An output object of `AnchorFree()`. Object is used optionally to initialize matrices (by default `NULL`).
`Ctrue`	A matrix. Correct matrix C if known. Useful for benchmark.
`verbose`	A boolean. Print per-iteration information (by default FALSE).
`record`	A numeric. Record parameters every 'record' iterations (by default `NULL`).
`verbose.nmf`	A boolean. Print per-iteration information for standard NMF (by default FALSE).
`record.nmf`	A numeric. Record parameters every 'record' iterations for standard NMF (by default `NULL`).
`mutation.run`	A boolean. Assess goodness of solution using reflection test if mutation.run=TRUE (applicable only to analysis of mutation patterns).

Value

List of objects:

C, R, Q Factorization matrices.

C.init, R.init, Q.init Initialization matrices for volume-regularized optimization.

C.rand, R.rand, Q.rand Random initialization matrices for NMF optimization (w.vol=0).

rec a list of objects that record and store state of matrices each record iterations.

Procrustes algorithm estimates orthonormal transformation between two matrices.

Description

volnmf_procrustes finds orthonormal matrix Q that minimizes objective ||A-B*Q||^2

Usage

volnmf_procrustes(A, B)
volnmf_procrustes(A, B)

Arguments

`A`	Numeric Matrices. Orthonormal transformation convert matrix `B` in matrix `A`.
`B`	Numeric Matrices. Orthonormal transformation convert matrix `B` in matrix `A`.

Value

An optimal orthonormal tranformation matrix Q.

Update of a matrix in NMF with equality contstraints on columns.

Description

volnmf_simplex_col finds non-negative matrix C that minimizes the objective ||X-C*R||^2 under constraints that columns of C equal to 1 using local approximation with extrapolation.

Usage

volnmf_simplex_col(
  X,
  R,
  C.prev = NULL,
  bound = 1,
  extrapolate = TRUE,
  err.cut = 1e-10,
  n.iter = 10000,
  qmax = 100
)
volnmf_simplex_col(
  X,
  R,
  C.prev = NULL,
  bound = 1,
  extrapolate = TRUE,
  err.cut = 1e-10,
  n.iter = 10000,
  qmax = 100
)

Arguments

`X`	Numeric Matrices. Matrices involved in the objective function.
`R`	Numeric Matrices. Matrices involved in the objective function.
`C.prev`	Numeric Matrices. Matrices involved in the objective function. Matrix `C.prev` serves as initialization. (default=NULL)
`bound`	A numeric. Equality constraint on columns of matrix `C`. (default=1)
`extrapolate`	A boolean. Use extrapolation after local approximation. (default=TRUE)
`err.cut`	A numeric. Stop iterations if relative error between iterations is less than `err.cut` (parameter is not active now). (default=1e-10)
`n.iter`	An integer. Number of iterations. (default=1000)
`qmax`	A numeric. Maximum asymptotic (1 - 1/qmax) of extrapolation step.

Value

An updated matrix C.

Update of a matrix in NMF with equality contstraints on rows.

Description

volnmf_simplex_row finds non-negative matrix C that minimizes the objective ||X-C*R||^2 under constraints that rows of C equal to 1 using per-row quadratic programming.

Usage

volnmf_simplex_row(X, R, C.prev = NULL, meq = 1)
volnmf_simplex_row(X, R, C.prev = NULL, meq = 1)

Arguments

`X`	Numeric Matrices. Matrices involved in the objective function.
`R`	Numeric Matrices. Matrices involved in the objective function.
`C.prev`	Numeric Matrices. Matrices involved in the objective function. Matrix `C.prev` serves as initialization. (default=NULL)
`meq`	An integer 0 or 1. Require equality (`meq=1`) or inequality (`meq=0`) constratint on rows (by default 1).

Value

An updated matrix C.

Package 'vrnmf'

Help Index

Non-negative tri-factorization of co-occurence matrix using minimum volume approach.

Description

Usage

Arguments

Details

Value

Examples

Infer a matrix of non-negative intensities in NMF with offset/nmf-offset.

Description

Usage

Arguments

Value

Infer a matrix of non-negative intensities in NMF

Description

Usage

Arguments

Value

Project vector onto a probabilistic simplex.

Description

Usage

Arguments

Value

Simulate matrices to explores vrnmf

Description

Usage

Arguments

Value

Preprocess the data for downstream volume analysis.

Description

Usage

Arguments

Value

Examples

Update volume-regularized matrix R using det volume approximation

Description

Usage

Arguments

Value

Alternating optimization of volume-regularized NMF

Description

Usage

Arguments

Value

Update volume-regularized matrix R using logdet volume approximation.

Description

Usage

Arguments

Value

Volume-regularized NMF

Description

Usage

Arguments

Value

Procrustes algorithm estimates orthonormal transformation between two matrices.

Description

Usage

Arguments

Value

Update of a matrix in NMF with equality contstraints on columns.

Description

Usage

Arguments

Value

Update of a matrix in NMF with equality contstraints on rows.

Description

Usage

Arguments

Value

Simulate matrices to explores `vrnmf`

Update volume-regularized matrix `R` using det volume approximation

Update volume-regularized matrix `R` using logdet volume approximation.