NonNegativeMatrixFactorizationT Class

public sealed class NonNegativeMatrixFactorization<T> : Decomposition<T>

Public NotInheritable Class NonNegativeMatrixFactorization(Of T)
	Inherits Decomposition(Of T)

generic<typename T>
public ref class NonNegativeMatrixFactorization sealed : public Decomposition<T>

[<SealedAttribute>]
type NonNegativeMatrixFactorization<'T> =  
    class
        inherit Decomposition<'T>
    end

Type Parameters

T

The NonNegativeMatrixFactorizationT type exposes the following members.

	Name	Description
	NonNegativeMatrixFactorizationT	Constructs a new NonNegativeMatrixFactorizationT object.,

	Name	Description
	BaseMatrix	Gets the underlying matrix of the decomposition. (Inherited from DecompositionT.)
	ColumnCount	Gets the number of columns in the matrix. (Inherited from LinearOperatorT.)
	ColumnIndex	Gets or sets the index of labels for the columns of the matrix. (Inherited from LinearOperatorT.)
	ElementType	Gets the element type of the matrix. (Inherited from LinearOperatorT.)
	Factors	Gets a collection of the matrix factors that make up the decomposition. (Overrides DecompositionTFactors.)
	LeftFactor	Gets the left component of the factorization.
	Overwrite	Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition. (Inherited from DecompositionT.)
	RightFactor	Gets the right component of the factorization.
	RowCount	Gets the number of rows in the matrix. (Inherited from LinearOperatorT.)
	RowIndex	Gets or sets the index of labels for the rows of the matrix. (Inherited from LinearOperatorT.)

	Name	Description
	AddProductToVector	Obsolete. Multiplies a VectorT by this instance and stores the result in a second vector of type DenseVectorT. (Inherited from LinearOperatorT.)
	Decompose	Performs the actual LU decomposition. (Overrides DecompositionTDecompose.)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	EstimateConditionNumber	Calculates an estimate for the condition number of a matrix. (Overrides LinearOperatorTEstimateConditionNumber.)
	GetDeterminant	Calculates the determinant of a matrix. (Overrides LinearOperatorTGetDeterminant.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetInverse	Calculates the inverse matrix.. (Inherited from LinearOperatorT.)
	GetInverse(Boolean)	Calculates the inverse of the factorized matrix. (Overrides LinearOperatorTGetInverse(Boolean).)
	GetObjectData	Populates a SerializationInfo with the data needed to serialize the target object. (Inherited from LinearOperatorT.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	IsSingular	Gets a value indicating whether the BaseMatrix of this decomposition is singular. (Inherited from DecompositionT.)
	LeastSquaresSolve(MatrixT)	Solves the system of linear equations for the specified right-hand side matrix in the least squares sense. (Inherited from LinearOperatorT.)
	LeastSquaresSolve(VectorT)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperatorT.)
	LeastSquaresSolve(DenseMatrixT, Boolean)	Solves the system of linear equations for the specified right-hand side dense matrix in the least squares sense and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	LeastSquaresSolve(DenseVectorT, Boolean)	Solves the system of linear equations for the specified right-hand side dense vector in the least squares sense and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	LeastSquaresSolveInto(MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides in the least squares sense. (Inherited from LinearOperatorT.)
	LeastSquaresSolveInto(VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side in the least squares sense. (Inherited from DecompositionT.)
	Multiply(MatrixT)	Applies the linear operator to a matrix. (Inherited from LinearOperatorT.)
	Multiply(VectorT)	Applies the linear operator to a vector. (Inherited from LinearOperatorT.)
	Multiply(TransposeOperation, MatrixT)	Obsolete. Multiplies a matrix on the left by this matrix. (Inherited from LinearOperatorT.)
	Multiply(TransposeOperation, VectorT)	Obsolete. Multiplies a vector on the left by this vector. (Inherited from LinearOperatorT.)
	MultiplyTranspose(MatrixT)	Applies the transpose of the linear operator to a matrix. (Inherited from LinearOperatorT.)
	MultiplyTranspose(VectorT)	Applies the (conjugate) transpose of the linear operator to a vector. (Inherited from LinearOperatorT.)
	Rank	Returns the numerical rank of a matrix. (Inherited from LinearOperatorT.)
	Rank(T)	Returns the numerical rank of a matrix using the specified tolerance. (Overrides LinearOperatorTRank(T).)
	Solve(MatrixT)	Solves the system of linear equations for the specified right-hand side matrix. (Inherited from LinearOperatorT.)
	Solve(VectorT)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperatorT.)
	Solve(DenseMatrixT, Boolean)	Solves the system of linear equations for the specified right-hand side dense matrix and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	Solve(DenseVectorT, Boolean)	Solves the system of linear equations for the specified right-hand side dense vector and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	SolveInto(MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Inherited from LinearOperatorT.)
	SolveInto(VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side. (Inherited from LinearOperatorT.)
	SolveInto(TransposeOperation, MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Inherited from LinearOperatorT.)
	SolveInto(TransposeOperation, VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side. (Overrides LinearOperatorTSolveInto(TransposeOperation, VectorT, VectorT).)
	SolveTranspose(MatrixT)	Solves the transposed system of linear equations for the specified right-hand side matrix. (Inherited from LinearOperatorT.)
	SolveTranspose(VectorT)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperatorT.)
	SolveTranspose(DenseMatrixT, Boolean)	Solves the transposed system of linear equations for the specified right-hand side dense matrix and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	SolveTranspose(DenseVectorT, Boolean)	Solves the transposed system of linear equations for the specified right-hand side dense vector and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	SolveTransposeInto(MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Inherited from LinearOperatorT.)
	SolveTransposeInto(VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side. (Inherited from LinearOperatorT.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)

Use the NonNegativeMatrixFactorizationT class to compute an approximate factorization of a Matrix into matrices with only positive components. In other words, it rewrites a matrix X as a product

X = WH

where W and H have only zero or positive components. The inner dimension of the product (the number of columns of W and the number of rows of H) may be less than the rank of X. In this case, the factorization is only an approximation to the original matrix. This is actually very common, since the Non-Negative Matrix Factorization is often used to reduce the dimensionality of data.

The constructor NonNegativeMatrixFactorizationT takes two arguments. The first is the matrix that is to be factorized. The second is the inner dimension of the product. The Decompose method performs the actual calculation using an alternating least squares method. The resulting factors are then available as the LeftFactor and RightFactor properties.

Reference