C# Class Accord.Math.Decompositions.NonnegativeFactorization

Nonnegative Matrix Factorization.

For a nonnegative n-by-m matrix A, the Nonnegative Matrix Factorization is given by a n-by-k matrix of nonnegative factors W and a k-by-m matrix of nonnegative factor coefficients H. The factorization is not exact, as W * H is a lower-rank approximation to A. The factors W and H are chosen to minimize the root-mean-squared residual U between A and W * H.

References: http://en.wikipedia.org/wiki/Non-negative_matrix_factorization http://www.mathworks.com/help/toolbox/stats/nnmf.html

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Public Methods

Method	Description
NonnegativeFactorization ( double value ) : System	Constructs a new non-negative matrix factorization.
NonnegativeFactorization ( double value, double h0, double w0 ) : System	Constructs a new non-negative matrix factorization.
NonnegativeFactorization ( double value, double h0, double w0, NonnegativeFactorizationAlgorithm algorithm ) : System	Constructs a new non-negative matrix factorization.
NonnegativeFactorization ( double value, double h0, double w0, NonnegativeFactorizationAlgorithm algorithm, int attempts, int maxIterations, double errorTolerance, double changeTolerance ) : System	Constructs a new non-negative matrix factorization.
NonnegativeFactorization ( double value, int k ) : System	Constructs a new non-negative matrix factorization.
NonnegativeFactorization ( double value, int k, NonnegativeFactorizationAlgorithm algorithm ) : System	Constructs a new non-negative matrix factorization.
NonnegativeFactorization ( double value, int k, NonnegativeFactorizationAlgorithm algorithm, int attempts, int maxIterations, double errorTolerance, double changeTolerance ) : System	Constructs a new non-negative matrix factorization.
NonnegativeFactorization ( double value, int k, int attempts ) : System	Constructs a new non-negative matrix factorization.

Private Methods

Method	Description
init ( double value, int k, NonnegativeFactorizationAlgorithm algorithm, double h0, double w0, int attempts, int maxIterations, double errorTolerance, double changeTolerance ) : void	Constructs a new non-negative matrix factorization.
makepositive ( double value ) : void	Enforces a matrix to contain only positive values.
maxabs ( double value ) : double	Max absolute value
maxdiff ( double matrixA, double matrixB ) : double	Max absolute difference
nnmf ( double value, double &w0, double &h0, NonnegativeFactorizationAlgorithm alg, int maxIterations, double normChangeThreshold, double maxFactorChangeThreshold ) : double	Single non-negative matrix factorization.
normdiff ( double matrixA, double matrixB ) : double	Norm of differences

Method Details

NonnegativeFactorization() public method

Constructs a new non-negative matrix factorization.

public NonnegativeFactorization ( double value ) : System
value	double	The matrix to be factorized.
return	System

NonnegativeFactorization() public method

Constructs a new non-negative matrix factorization.

public NonnegativeFactorization ( double value, double h0, double w0 ) : System
value	double	The matrix to be factorized.
h0	double	Initial approximation to the coefficient matrix H. /// Default is .
w0	double	Initial approximation to the weight matrix W. /// Default is .
return	System

NonnegativeFactorization() public method

Constructs a new non-negative matrix factorization.

public NonnegativeFactorization ( double value, double h0, double w0, NonnegativeFactorizationAlgorithm algorithm ) : System
value	double	The matrix to be factorized.
h0	double	Initial approximation to the coefficient matrix H.
w0	double	Initial approximation to the weight matrix W.
algorithm	NonnegativeFactorizationAlgorithm	The algorithm to be used in the factorization. /// Please see for details. /// Default is .
return	System

NonnegativeFactorization() public method

Constructs a new non-negative matrix factorization.

public NonnegativeFactorization ( double value, double h0, double w0, NonnegativeFactorizationAlgorithm algorithm, int attempts, int maxIterations, double errorTolerance, double changeTolerance ) : System
value	double	The matrix to be factorized.
h0	double	Initial approximation to the coefficient matrix H.
w0	double	Initial approximation to the weight matrix W.
algorithm	NonnegativeFactorizationAlgorithm	The algorithm to be used in the factorization. /// Please see for details. /// Default is .
attempts	int	How many repetitions of the method should be /// performed to avoid arriving at a poor local solution minima. Default /// value is 1.
maxIterations	int	The maximum number of iterations to perform.
errorTolerance	double	The minimum change in error to use as convergence criteria.
changeTolerance	double	The maximum absolute factor change to use as convergence criteria.
return	System

NonnegativeFactorization() public method

Constructs a new non-negative matrix factorization.

public NonnegativeFactorization ( double value, int k ) : System
value	double	The matrix to be factorized.
k	int	The desired approximation rank.
return	System

NonnegativeFactorization() public method

Constructs a new non-negative matrix factorization.

public NonnegativeFactorization ( double value, int k, NonnegativeFactorizationAlgorithm algorithm ) : System
value	double	The matrix to be factorized.
k	int	The desired approximation rank.
algorithm	NonnegativeFactorizationAlgorithm	The algorithm to be used in the factorization. /// Please see for details. /// Default is .
return	System

NonnegativeFactorization() public method

Constructs a new non-negative matrix factorization.

public NonnegativeFactorization ( double value, int k, NonnegativeFactorizationAlgorithm algorithm, int attempts, int maxIterations, double errorTolerance, double changeTolerance ) : System
value	double	The matrix to be factorized.
k	int	The desired approximation rank.
algorithm	NonnegativeFactorizationAlgorithm	The algorithm to be used in the factorization. /// Please see for details. /// Default is .
attempts	int	How many repetitions of the method should be /// performed to avoid arriving at a poor local solution minima. Default /// value is 1.
maxIterations	int	The maximum number of iterations to perform.
errorTolerance	double	The minimum change in error to use as convergence criteria.
changeTolerance	double	The maximum absolute factor change to use as convergence criteria.
return	System

NonnegativeFactorization() public method

Constructs a new non-negative matrix factorization.

public NonnegativeFactorization ( double value, int k, int attempts ) : System
value	double	The matrix to be factorized.
k	int	The desired approximation rank.
attempts	int	How many repetitions of the method should be /// performed to avoid arriving at a poor local solution minima. Default /// value is 1.
return	System