# rmatrix: Generating Random Matrices In NMF: Algorithms and Framework for Nonnegative Matrix Factorization (NMF)

 rmatrix R Documentation

## Generating Random Matrices

### Description

The S4 generic `rmatrix` generates a random matrix from a given object. Methods are provided to generate matrices with entries drawn from any given random distribution function, e.g. `runif` or `rnorm`.

### Usage

```  rmatrix(x, ...)

## S4 method for signature 'numeric'
rmatrix(x, y = NULL, dist = runif,
byrow = FALSE, dimnames = NULL, ...)
```

### Arguments

 `x` object from which to generate a random matrix `y` optional specification of number of columns `dist` a random distribution function or a numeric seed (see details of method `rmatrix,numeric`) `byrow` a logical passed in the internal call to the function `matrix` `dimnames` `NULL` or a `list` passed in the internal call to the function `matrix` `...` extra arguments passed to the distribution function `dist`.

### Methods

rmatrix

`signature(x = "numeric")`: Generates a random matrix of given dimensions, whose entries are drawn using the distribution function `dist`.

This is the workhorse method that is eventually called by all other methods. It returns a matrix with:

• `x` rows and `y` columns if `y` is not missing and not `NULL`;

• dimension `x` x `x` if `x` has at least two elements;

• dimension `x` (i.e. a square matrix) otherwise.

The default is to draw its entries from the standard uniform distribution using the base function `runif`, but any other function that generates random numeric vectors of a given length may be specified in argument `dist`. All arguments in `...` are passed to the function specified in `dist`.

The only requirement is that the function in `dist` is of the following form:

function(n, ...){ # return vector of length n ... }

This is the case of all base random draw function such as `rnorm`, `rgamma`, etc...

rmatrix

`signature(x = "ANY")`: Default method which calls `rmatrix,vector` on the dimensions of `x` that is assumed to be returned by a suitable `dim` method: it is equivalent to `rmatrix(dim(x), y=NULL, ...)`.

rmatrix

`signature(x = "NMF")`: Returns the target matrix estimate of the NMF model `x`, perturbated by adding a random matrix generated using the default method of `rmatrix`: it is a equivalent to `fitted(x) + rmatrix(fitted(x), ...)`.

This method can be used to generate random target matrices that depart from a known NMF model to a controlled extend. This is useful to test the robustness of NMF algorithms to the presence of certain types of noise in the data.

### Examples

```

#----------
# rmatrix,numeric-method
#----------
## Generate a random matrix of a given size
rmatrix(5, 3)

## Generate a random matrix of the same dimension of a template matrix
a <- matrix(1, 3, 4)
rmatrix(a)

## Specificy the distribution to use

# the default is uniform
a <- rmatrix(1000, 50)
## Not run:  hist(a)

# use normal ditribution
a <- rmatrix(1000, 50, rnorm)
## Not run:  hist(a)

# extra arguments can be passed to the random variate generation function
a <- rmatrix(1000, 50, rnorm, mean=2, sd=0.5)
## Not run:  hist(a)

#----------
# rmatrix,ANY-method
#----------
# random matrix of the same dimension as another matrix
x <- matrix(3,4)
dim(rmatrix(x))

#----------
# rmatrix,NMF-method
#----------
# generate noisy fitted target from an NMF model (the true model)
gr <- as.numeric(mapply(rep, 1:3, 3))
h <- outer(1:3, gr, '==') + 0
x <- rnmf(10, H=h)
y <- rmatrix(x)
## Not run:
# show heatmap of the noisy target matrix: block patterns should be clear
aheatmap(y)

## End(Not run)

# test NMF algorithm on noisy data
# add some noise to the true model (drawn from uniform [0,1])
res <- nmf(rmatrix(x), 3)
summary(res)

# add more noise to the true model (drawn from uniform [0,10])
res <- nmf(rmatrix(x, max=10), 3)
summary(res)
```

NMF documentation built on March 30, 2022, 1:05 a.m.