NMath Reference Guide

## PLS |

Class PLS1NipalsAlgorithm encapsulates the Nonlinear Iterative PArtial Least
Squares (NIPALS) algorithm for computing partial least squares regression components.

Inheritance Hierarchy

Syntax

The PLS1NipalsAlgorithm type exposes the following members.

Constructors

Name | Description | |
---|---|---|

PLS1NipalsAlgorithm | Constructs an instance of the PLS1NipalsAlgorithm class. |

Properties

Name | Description | |
---|---|---|

IsGood |
Whether the most recent calculation was successful.
(Overrides IPLS1CalcIsGood) | |

Loadings |
Gets the loadings matrix for PredictorMatrix. The loadings matrix
is described in the class summary.
(Overrides IPLS1CalcLoadings) | |

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 IPLS1CalcMessage) | |

PredictorMean | Gets the vector of means for the predictor variables. | |

RegressionVector |
Gets the vector of regression, r, which can be used for making
predictions as follows:
Let ybar and xbar be the means of the response and predictor variables, respectively, used to create the model. Then the predicted response, yhat, for a predictor vector, z is given by the formula C# yhat = ybar + (z - xbar)'r | |

ResponseMean | Gets the vector of means for the response variables. | |

ResponseWeights | Gets the vector of response weights. The ith element of this vector corresponds to the regression coefficient calculated by ordinary linear regression of the response vector on the ith score vector. | |

Scores |
Gets the scores matrix for PredictorMatrix. The scores matrix
is described in the class summary.
(Overrides IPLS1CalcScores) | |

Weights | Returns the matrix of weights computed by the algorithm. |

Methods

Name | Description | |
---|---|---|

Calculate |
Calculates a partial least squares from the given data and number of
components.
(Overrides IPLS1CalcCalculate(DoubleMatrix, DoubleVector, Int32)) | |

Clone |
Creates a deep copy of this PLS1NipalsAlgorithm.
(Overrides IPLS1CalcClone) | |

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 IPLS1Calc) | |

OnDeserialized | Sets most of the attributes only if isGood_ | |

OnSerializing | Conditionally sets most of the values for serialization only if isGood_ | |

Predict(DoubleMatrix) |
Use the calculated model to predict the response values, ResponseVector,
from the given set of predictor variables.
(Overrides IPLS1CalcPredict(DoubleMatrix)) | |

Predict(DoubleVector) |
Use the calculated model to predict the response value, y, from
the given value for the predictor variable.
(Overrides IPLS1CalcPredict(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.
(Overrides IPLS1CalcQResiduals) |

Remarks

During the calculation the following model for PredictorMatrix
(independent variable values) is formed:
where is the number of components specified for the model.
T is called the scores matrix (the columns of T
are the scores), and P is called the loadings matrix. The
matrix Xg is called the residual matrix for
PredictorMatrix.

C#

PredictorMatrix = TP' + Xg

C#

g

See Also