PLS2SimplsAlgorithm Class

Class PLS2SimplsAlgorithm encapsulates the Straightforward IMplementation of Partial Least Squares, or SIMPLS, algorithm (de Jong, 1993) for computing partial least squares regression components.

Inheritance Hierarchy

SystemObject
CenterSpace.NMath.CoreIPLS2Calc
CenterSpace.NMath.CorePLS2SimplsAlgorithm

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4

Syntax

C++

Copy

[SerializableAttribute]
public class PLS2SimplsAlgorithm : IPLS2Calc

<SerializableAttribute>
Public Class PLS2SimplsAlgorithm
	Inherits IPLS2Calc

[SerializableAttribute]
public ref class PLS2SimplsAlgorithm : public IPLS2Calc

[<SerializableAttribute>]
type PLS2SimplsAlgorithm = 
    class
        inherit IPLS2Calc
    end

The PLS2SimplsAlgorithm type exposes the following members.

Constructors

	Name	Description
	PLS2SimplsAlgorithm	Constructs an PLS2SimplsAlgorithm instance. The maximum number of iterations and convergence tolerance used in the power method to compute the dominant eigenvector at each iteration of the SIMPLS algorithm are set to their default values.
	PLS2SimplsAlgorithm(Int32, Double)	Constructs an instance of the PLS2SimplsAlgorithm class with the specified values for the maximum number of iterations and tolerance to be used in the power method algorithm used for computing dominant eigenvectors.

Top

Properties

	Name	Description
	Coefficients	Gets the regression coefficients matrix, B, for the PLS2 calculation. B satisifies the relationship C# Copy ResponseVector = XB + E where X and ResponseVector are, respectively, the centered independent and dependent variables values, and E is a noise term for the model. (Overrides IPLS2CalcCoefficients)
	DefaultMaxPowerIteration	Gets and sets the default value for the maximum number of iterations to be performed when use the power method for computing dominant eigenvectors and eigenvalues needed by the SIMPLS algorithm.
	DefaultPowerMethodTolerance	Gets and sets the default value for the tolerance used to determine convergence of the power method for computing dominant eigenvectors and eigenvalues needed by the SIMPLS algorithm.
	IsGood	Whether the most recent calculation was successful. (Overrides IPLS2CalcIsGood)
	MaxIterations	Gets and sets the maximum number of iterations to be performed when using the iterative power method to find dominant eigenvectors.
	Message	Gets any message that may have been generated by the algorithm. For example, if the calculation is unsuccessful, the message indicates the reason. (Overrides IPLS2CalcMessage)
	OrthogonalLoadings	Gets the matrix of orthogonal loadings, the basis for the predictor loadings matrix.
	PredictorLoadings	Gets the matrix of predictor loadings. The matrix of predictor loadings, P, is defined by C# Copy P = X'T where X' is the transpose of the predictor matrix and T is the predictor score matrix. (Overrides IPLS2CalcPredictorLoadings)
	PredictorMean	Gets the vector of means for the predictor variables.
	PredictorScores	Gets the matrix of predictor scores. (Overrides IPLS2CalcPredictorScores)
	PredictorWeights	Gets the matrix of predictor weights.
	ResponseLoadings	Gets the matrix of response loadings. The matrix of response loadings, Q, is defined by C# Copy Q = Y'T where Y' is the transpose of the response matrix and T is the predictor score matrix.
	ResponseMean	Gets the vector of means for the response variables.
	ResponseScores	Gets the matrix of response scores.
	Tolerance	Gets and sets the tolerance to be used in the iterative power method that is used to compute dominant eigenvectors. The power method converges if changes in the normalized eigenvector, with respect to the infinity norm, is less than this specified tolerance.

Top

Methods

	Name	Description
	Calculate	Calculates the PLS2 for the given predictor and response matrices and the given number of components. (Overrides IPLS2CalcCalculate(DoubleMatrix, DoubleMatrix, Int32))
	Clone	Creates a deep copy of this PLS2SimplsAlgorithm. (Overrides IPLS2CalcClone)
	HotellingsT2	Calculaties Hotelling's T2 statistic for each sample. T2 can be viewed as the squared distance from a samples projection into the subspace to the centroid of the subspace, or, more simply, the variation of the sample point within the model. (Inherited from IPLS2Calc)
	Predict(DoubleMatrix)	Predicts the responses for a set of predictor values. (Overrides IPLS2CalcPredict(DoubleMatrix))
	Predict(DoubleVector)	Predicts the response for the given predictor value. (Overrides IPLS2CalcPredict(DoubleVector))
	QResiduals	Calculates the Q residuals for in sample in the model. The Q residual for a given sample is the distance between the sample and its projection in the subspace of the model. (Inherited from IPLS2Calc)

Top

Remarks

The SIMPLS is used to find a predictive linear model of the form Y = XB, where Y is a matrix of response variables, X is a matrix of predictor variables, and B is the matrix of regression coefficients. This is achieved by compressing the predictor data matrix

Copy

X = [x1, x2,..., xp]

that contains the p values of n samples, into a set of c latent variable or factor scores

Copy

T = [t1, t2,...,tc]

These factor scores are then used to fit a set of n observations to m response variables

Copy

Y = [y1, y2,...,ym]

The relationship between the X and T is T = XR, where R is the matrix of predictor weights. Factor scores U and weights Q for the response variable Y are also computed and satisfy U = Y0Q, where Y0 is the matrix of centered response data.

The algorithm requires the computation of a dominant eigenvector at each iteration. The iterative Power Method is used to calculate this eigenvector and the maximum number of iterations and convergance tolerance may be specified for instances of this class through either through the contructor or properties.

Reference

CenterSpace.NMath.Core Namespace