Pcatrans object (Multivariate Analysis Toolbox for Matlab®)

This object represents principal component analysis. Here, the factors are named principal components, and their maximal number is p. The user can specify that he would like to have less components, d <= p, which is normally the case.

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Each field can be accessed by the dot (.) operation, or by the GET function. The GET function can work on multiple instances simultaneously. Most fields, except for those that are Dependent, can be modified using the dot (.) operation, or by the SET function.

		Field	Description	Type	Default	Dedicated Get/Set Function
		algorithm	Description of the algorithm used for the computations.	string	''
		ortho_constraints	orthogonality contraints. Each constraint is a column vector.	double matrix	[]
		name	Inherited from lintrans. name of object, should be short and used as identifier. This field will never be empty.	string	'unnamed'
		description	Inherited from lintrans. verbal description of the class content.	string	''
		source	Inherited from lintrans. verbal description of the source of information.	string	''
		type	Inherited from lintrans. type of linear transformation.	string	''
		U	Inherited from lintrans. Transformation matrix.	vvmatrix	[]
		eigvals	Inherited from lintrans. eigenvalues associated with the solution.	double vector	[]
		f_eigvals	Inherited from lintrans. fractional importance of each eigenvalue.	double vector	[]
		no_samples	Inherited from lintrans. number of samples in the original data.	integer	[]	nosamples
		preprocess	Inherited from lintrans. preprocessing of the data matrix. Should be applied to any data before operating with the linear transformation.	vector of preprocess structures	[]
		scores	Inherited from lintrans. the data projected into the new variables (factors).	vsmatrix	[]
	Dependent	no_factors	Inherited from lintrans. number of new factors.	integer scalar	0	nofactors
	Dependent	no_variables	Inherited from lintrans. number of original variables.	integer scalar	0	novariables

Empty instance (scalar)

an empty pcatrans instance, with all fields initialized to their default values.

syntax: pc = pcatrans;

Empty instance (matrix)

an array of empty pcatrans instances.

syntax: pc = pcatrans(size);

Copy constructor

one pcatrans instance is copied into another.

syntax: pc_destination = pcatrans(pc_origin);

Construction by field names

an instance is formed by directly providing field values. Any field which is not dependent is permitted.

syntax: pc = pcatrans(field_name, field_value, ...);

Computing from a vsmatrix

Computing factors from an input in the form of a sample-variable matrix.

syntax: pc = pcatrans(vsm, opt_name, opt_val, ...);

Computing from a covmatrix

Computing factors from an input in the form of a correlation/covariance matrix.

syntax: pc = pcatrans(cvm, opt_name, opt_val, ...);

Display functions:

show

displays class content. Source: lintrans.

Inference:

cieigvals

computes confidence intervals for the eigenvalues.

ciexclusion

computes upper CI for excluding last principal components.

stdeigvals

computes the standard deviations of the PCA eigenvalues.

stdeigvecs

computes the standard deviates of the PCA eigenvectors.

testpcs

tests whether the PCs fit a predefined form.

testredundancy

tests the redundancy hypothesis.

testsphericity

tests the sphericity hypothesis.

vareigvals

computes the variance of the PCA eigenvalues.

vareigvecs

computes the variance of the PCA eigenvectors.

Operators:

mtimes

operating with the linear transformation Source: lintrans.

SET/GET functions:

eigvals

retrieves the eigenvalues of the linear transformation. Source: lintrans.

factornames

retrieves the names of the factors. Source: lintrans.

factors

retrieves the factors of the linear transformation. Source: lintrans.

get

get method

nofactors

retrieves the number of factors. Source: lintrans.

nosamples

retrieves the number of samples. Source: lintrans.

novariables

retrieves the number of original variables. Source: lintrans.

set

set method

variablenames

retrieves the names of the original variables. Source: lintrans.

Transformations:

deletefactors

excludes certain factors. Source: lintrans.

invertsign

inverts the signs of selected factors. Source: lintrans.

Visualization:

loadings

plots the loadings of the linear transformation. Source: lintrans.

scatter

plots factors versus factors for all data samples Source: lintrans.

scree

plots a scree diagram of the transformation eigenvalues. Source: lintrans.