Rescaling NMF Models

Usage

S3 (NMF)
`scale`(x, center = c("basis", "coef"), scale = 1)

Arguments

x

an NMF object

center

either a numeric normalising vector delta, or either 'basis' or 'coef', which respectively correspond to using the column sums of the basis matrix or the inverse of the row sums of the coefficient matrix as a normalising vector. If numeric, center should be a single value or a vector of length the rank of the NMF model, i.e. the number of columns in the basis matrix.

scale

scaling coefficient applied to D, i.e. the value of alpha, or, if center='coef', the value of 1/alpha (see section Details).

X = W
  H = (W D) (D^-1 H) with D= alpha * diag(1/delta_1, ...,
  1/delta_r)

  
      
The default call scale(object) rescales the basis
  NMF object so that each column of the basis matrix sums
  up to one.
  
    

Examples

# random 3-rank 10x5 NMF model
x <- rnmf(3, 10, 5)

# rescale based on basis
colSums(basis(x))

## [1] 4.822 4.774 5.044

colSums(basis(scale(x)))

## [1] 1 1 1

rx <- scale(x, 'basis', 10)
colSums(basis(rx))

## [1] 10 10 10

rowSums(coef(rx))

## [1] 0.7124 1.1672 1.6006

# rescale based on coef
rowSums(coef(x))

## [1] 1.477 2.445 3.173

rowSums(coef(scale(x, 'coef')))

## [1] 1 1 1

rx <- scale(x, 'coef', 10)
rowSums(coef(rx))

## [1] 10 10 10

colSums(basis(rx))

## [1] 0.7124 1.1672 1.6006

# fitted target matrix is identical but the factors have been rescaled
rx <- scale(x, 'basis')
all.equal(fitted(x), fitted(rx))

## [1] TRUE

all.equal(basis(x), basis(rx))

## [1] "Mean relative difference: 0.7951"