PrincipalComponents Class

public class PrincipalComponents : PrincipalProjections

Public Class PrincipalComponents
	Inherits PrincipalProjections

public ref class PrincipalComponents : public PrincipalProjections

type PrincipalComponents = 
    class
        inherit PrincipalProjections
    end

Inheritance

Object    PrincipalProjections    PrincipalComponents

Rows of the data matrix correspond to individuals, columns to variables. Each row is interpreted as the coordinates of a multidimensional point with respect to a given basis, where the dimension is the number of possibly correlated variables observed for each individual. The analysis of the principal components aims to project the given cloud of points in a space having a reduced dimension, in which the new coordinates form uncorrelated variables which are selected by maximizing their variances, so that the projection retains as much of the variability of the initial variables as possible.

Class PrincipalComponents inherits from class PrincipalProjections. Check its documentation for a thorough explanation of the statistical methods underlying a Principal Component analysis.

Instantiation

New instances of class PrincipalComponents can be initialized by calling one of the overloaded methods Analyze(DoubleMatrix) or one of its overloaded versions. The simple overload Analyze takes a data matrix as the coordinates of the cloud with respect to the standard basis, and assigns uniform weights to each individual. Nonuniform weights can be specified through the overload Analyze, which again refers the coordinates to the standard basis.

The more complex overload Analyze takes the coordinates matrix, the individual weights, and a sequence of coefficients assigned to variables. Such variable coefficients are used to refer the coordinates to a basis other than the standard one. More thoroughly, given the sequence of coefficients , then the Basis is chosen so that its matrix is as follows:

Reference

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