| NMFNonsmoothUpdate Class |
Class NMFNonsmoothUpdate encapulates an NMF update algorithm which
minimizes a cost functional designed to explicitly represent sparseness,
in the form on nonsmoothness, which is controlled by a single parameter.
Inheritance Hierarchy Namespace: CenterSpace.NMath.CoreAssembly: NMath (in NMath.dll) Version: 7.4
Syntax [SerializableAttribute]
public class NMFNonsmoothUpdate : INMFUpdateAlgorithm,
ICloneable
<SerializableAttribute>
Public Class NMFNonsmoothUpdate
Implements INMFUpdateAlgorithm, ICloneable
[SerializableAttribute]
public ref class NMFNonsmoothUpdate : INMFUpdateAlgorithm,
ICloneable
[<SerializableAttribute>]
type NMFNonsmoothUpdate =
class
interface INMFUpdateAlgorithm
interface ICloneable
end
The NMFNonsmoothUpdate type exposes the following members.
Constructors Properties | 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 = WSH
where 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'
|
TopMethods | Name | Description |
---|
| Clone |
Returns a deep copy of self.
|
| Cost |
Returns the value of the cost function for the non-negative
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 non-negative matrix factorization
V = WH.
|
| IterationStep |
Updates the factors W and H in the non-negative matrix factorization
V = WH.
|
TopRemarks
The Nonsmooth Nonnegative Matrix Factorization is defined as
V = WSH
where 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 Pascual-Montano, J.M Carazo, Kieko Kochi, Dietrich Lehmann, and
Roberto D. Pascual-Marui
IEEE Transactions on Pattern Analysis and Machine Intelligence
Vol. 28, No. 3, March 2006.
See Also