Rescaling NMF Models

Description

Rescales an NMF model keeping the fitted target matrix identical.

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).

Value

an NMF object

Details

Standard NMF models are identifiable modulo a scaling factor, meaning that the basis components and basis profiles can be rescaled without changing the fitted values:

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] 4.821564 4.774258 5.044443

colSums(basis(scale(x)))

## [1] 1 1 1

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

## [1] 10 10 10

rowSums(coef(rx))

## [1] 0.712381 1.167180 1.600620

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

## [1] 1.477490 2.444735 3.173035

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] 0.712381 1.167180 1.600620

# 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: 0.7950857"