nmf class methods

Given an NMF model in the form $A = wdh$, project projects w onto A to solve for h.

Usage

# S4 method for class 'nmf'
subset(x, i, ...)

# S4 method for class 'nmf,ANY,ANY,ANY'
x[i]

# S4 method for class 'nmf'
head(x, n = getOption("digits"), ...)

# S4 method for class 'nmf'
show(object)

# S4 method for class 'nmf'
dimnames(x)

# S4 method for class 'nmf'
dim(x)

# S4 method for class 'nmf'
t(x)

# S4 method for class 'nmf'
sort(x, decreasing = TRUE, ...)

# S4 method for class 'nmf'
prod(x, ..., na.rm = FALSE)

# S4 method for class 'nmf'
x$name

# S4 method for class 'nmf,list'
coerce(from, to)

# S4 method for class 'nmf'
x[[i]]

# S4 method for class 'nmf'
predict(
  object,
  data,
  L1 = NULL,
  L2 = NULL,
  mask = NULL,
  upper_bound = NULL,
  threads = 0,
  verbose = FALSE,
  ...
)

Arguments

x: object of class nmf.
i: indices
...: arguments passed to or from other methods
n: number of rows/columns to show
object: fitted model, class nmf, generally the result of calling nmf, with models of equal dimensions as data
decreasing: logical. Should the sort be increasing or decreasing?
na.rm: remove na values
name: name of nmf class slot
from: class which the coerce method should perform coercion from
to: class which the coerce method should perform coercion to
data: dense or sparse matrix of features in rows and samples in columns. Prefer matrix or Matrix::dgCMatrix, respectively. Also accepts a file path (character string) which will be auto-loaded based on extension.
L1: a single LASSO penalty in the range (0, 1]
L2: a single Ridge penalty greater than zero
mask: missing data mask. Accepts: NULL (no masking), "zeros" (mask zeros), "NA" (mask NAs), a dgCMatrix/matrix (custom mask), or list("zeros", <matrix>) to mask zeros and use a custom mask simultaneously.
upper_bound: maximum value permitted in least squares solutions, essentially a bounded-variable least squares problem between 0 and upper_bound
threads: number of threads for OpenMP parallelization (default 0 = all available)
verbose: print progress information (default FALSE)

Value

An nmf object subsetted to the specified factors.

Invisibly returns the nmf object.

A list of length two: row names of w and column names of h.

An integer vector of length 3: number of features, number of samples, and rank.

An nmf object with transposed factorization (w and h swapped and transposed).

An nmf object with factors reordered by decreasing (or increasing) d.

A dense matrix equal to w %*% diag(d) %*% h.

Contents of the named slot (w, d, h, or misc), or the named element from misc.

A named list with elements w, d, h, and misc.

The element from the misc list at the given name or index.

An nmf object containing the projected model (with updated h matrix).

Details

For the alternating least squares matrix factorization update problem $A = wh$, the updates (or projection) of $h$ is given by the equation: $$w^Twh = wA_j$$ which is in the form $ax = b$ where $a = w^Tw$ $x = h$ and $b = wA_j$ for all columns $j$ in $A$.

Any L1 penalty is subtracted from $b$ and should generally be scaled to max(b), where $b = WA_j$ for all columns $j$ in $A$. An easy way to properly scale an L1 penalty is to normalize all columns in $w$ to sum to the same value (e.g. 1). No scaling is applied in this function. Such scaling guarantees that L1 = 1 gives a completely sparse solution.

There are specializations for dense and sparse input matrices, symmetric input matrices, and for rank-1 and rank-2 projections. See documentation for nmf for theoretical details and guidance.

References

DeBruine, ZJ, Melcher, K, and Triche, TJ. (2021). "High-performance non-negative matrix factorization for large single-cell data." BioRXiv.

Author

Zach DeBruine

Examples

# \donttest{
library(Matrix)
w <- matrix(runif(1000 * 10), 1000, 10)
h_true <- matrix(runif(10 * 100), 10, 100)
# A is the crossproduct of "w" and "h" with 10% signal dropout
mask <- rsparsematrix(1000, 100, density = 0.1)
A <- (w %*% h_true) * (mask != 0)
h <- nnls(w = w, A = A)
cor(as.vector(h_true), as.vector(h))
#> [1] 0.3003039

# alternating projections refine solution (like NMF)
h <- nnls(w = w, A = A)
w <- nnls(h = h, A = A)
h <- nnls(w = w, A = A)
w <- nnls(h = h, A = A)
h <- nnls(w = w, A = A)
w <- nnls(h = h, A = A)
# }