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,] 0.6667 0.1667 0.1667
## [2,] 0.1667 0.6667 0.1667
## [3,] 0.1667 0.1667 0.6667

smoothing(x, 0.1)

##         [,1]    [,2]    [,3]
## [1,] 0.93333 0.03333 0.03333
## [2,] 0.03333 0.93333 0.03333
## [3,] 0.03333 0.03333 0.93333