Smoothing Matrix in Nonsmooth NMF Models

Description

The function smoothing builds a smoothing matrix for using in Nonsmooth NMF models.

Usage

smoothing(x, theta = x@theta, ...)

Arguments

x: a object of class NMFns.
theta: the smoothing parameter (numeric) between 0 and 1.
...: extra arguments to allow extension (not used)

Value

if x estimates a r-rank NMF, then the result is a r \times r square matrix.

Details

For a r-rank NMF, the smoothing matrix of parameter \theta is built as follows:

S = (1-\theta)I + \frac{\theta}{r} 11^T ,
where I is the identity matrix and 1 is a vector of ones
(cf. NMFns-class for more details).

Examples



x <- nmfModel(3, model='NMFns')
smoothing(x)

##           [,1]      [,2]      [,3]
## [1,] 0.6666667 0.1666667 0.1666667
## [2,] 0.1666667 0.6666667 0.1666667
## [3,] 0.1666667 0.1666667 0.6666667

smoothing(x, 0.1)

##            [,1]       [,2]       [,3]
## [1,] 0.93333333 0.03333333 0.03333333
## [2,] 0.03333333 0.93333333 0.03333333
## [3,] 0.03333333 0.03333333 0.93333333