NMFNonsmoothUpdate Class 
Namespace: CenterSpace.NMath.Core
The NMFNonsmoothUpdate type exposes the following members.
Name  Description  

NMFNonsmoothUpdate 
Constructs a NMFNonsmoothUpdate instance with smoothing parameter theta
equal to zero.
 
NMFNonsmoothUpdate(Double) 
Constructs a NMFNonsmoothUpdate instance with the specified smoothing parameter.

Name  Description  

SmoothingMatrix 
Gets the smoothing matrix.
The smoothing matrix is a positive
symmetric matrix S defined as:
S = (1  theta)I + (theta/q)11'where I is the identity matrix, 1 is a vector of ones and the parameter t is between 0 and 1, inclusive. See class description.  
Theta 
The Nonsmooth Nonnegative Matrix Factorization is defined as
V = WSHwhere V, W, and H are the same as in the original NMF model. The positive symmetric matrix S is a "smoothing" matrix defined as: S = (1  theta)I + (theta/q)11' 
Name  Description  

Clone 
Returns a deep copy of self.
 
Cost 
Returns the value of the cost function for the nonnegative
factorization of V = WH. The cost function is minimized by
the factorization.
 
InitialFactors 
Provides the initial factors for the iteration process that
computes W and H in the nonnegative matrix factorization
V = WH.
 
IterationStep 
Updates the factors W and H in the nonnegative matrix factorization
V = WH.

V = WSHwhere V, W, and H are the same as in the original NMF model. The positive symmetric matrix S is a "smoothing" matrix defined as:
S = (1  theta)I + (theta/q)11'where I is the identity matrix, 1 is a vector of ones and the parameter theta is between 0 and 1, inclusive. The interpretation of theta as a smoothing parameter is as follows: If x is a positive, nonzero, vector and y = Sx, then y = x when theta = 0 and there is no smoothing. As theta > 1, the vector y tends to the constant vector with all elements equal to the average of the elements of x. This is the smoothest possible vector in the sense of nonsparseness because all the entries are equal to the same nonzero value, instead of having values close to zero and others clearly not zero. See the paper Nonsmooth Nonnegative Matrix Factorization (nsNMF) Alberto PascualMontano, J.M Carazo, Kieko Kochi, Dietrich Lehmann, and Roberto D. PascualMarui IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 28, No. 3, March 2006.