Lintrans object (Multivariate Analysis Toolbox for Matlab®)

Dimensionality reduction of data is often times achieved by means of linear transformation. This object is meant to define a framework for such techniques, from which specific algorithms are derived using inheritance. In particular, this toolbox implements principal component analysis (pcatrans), Fisher linear transformation (fishtrans), and weighted-principal component analysis (wpcatrans).

Let X be the original p-by-n matrix, with p the number of variables, and n the number of samples. Linear dimensionality reduction is achieved by a p-by-d matrix U, with d <= p, such that U^TX is a d-by-n matrix, usually called the scores matrix, describing the new data in a reduced-dimensional space. Each column in U is called a factor.

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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
		name	name of object, should be short and used as identifier. This field will never be empty.	string	'unnamed'
		description	verbal description of the class content.	string	''
		source	verbal description of the source of information.	string	''
		type	type of linear transformation.	string	''
		U	Transformation matrix.	vvmatrix	[]
		eigvals	eigenvalues associated with the solution.	double vector	[]
		f_eigvals	fractional importance of each eigenvalue.	double vector	[]
		no_samples	number of samples in the original data.	integer	[]	nosamples
		preprocess	preprocessing of the data matrix. Should be applied to any data before operating with the linear transformation.	vector of preprocess structures	[]
		scores	the data projected into the new variables (factors).	vsmatrix	[]
	Dependent	no_factors	number of new factors.	integer scalar	0	nofactors
	Dependent	no_variables	number of original variables.	integer scalar	0	novariables

Empty instance (scalar)

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

syntax: lt = lintrans;

Empty instance (matrix)

a vector of empty lintrans instances.

syntax: lt = lintrans(size);

Copy constructor

one lintrans instance is copied into another.

syntax: lt_destination = lintrans(lt_origin);

Construction by field names

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

syntax: lt = lintrans(field_name, field_value, ...);

Display functions:

show

displays class content.

Operators:

mtimes

operating with the linear transformation

SET/GET functions:

eigvals

retrieves the eigenvalues of the linear transformation.

factornames

retrieves the names of the factors.

factors

retrieves the factors of the linear transformation.

get

get method

nofactors

retrieves the number of factors.

nosamples

retrieves the number of samples.

novariables

retrieves the number of original variables.

set

set method

variablenames

retrieves the names of the original variables.

Transformations:

deletefactors

excludes certain factors.

invertsign

inverts the signs of selected factors.

Visualization:

loadings

plots the loadings of the linear transformation.

scatter

plots factors versus factors for all data samples

scree

plots a scree diagram of the transformation eigenvalues.