Lintrans object (Multivariate Analysis Toolbox for MatlabŪ)

written by: Liran Carmel

Last modified: 16:21, Sun 12-Sep-2010

General Description
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 UTX 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.

Navigate to:     General Description     Class Structure     Class Construction     Class Functions

Class Structure
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  

Class Construction
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, ...);

List of Functions

Display functions:

displays class content.


operating with the linear transformation

SET/GET functions:

retrieves the eigenvalues of the linear transformation.
retrieves the names of the factors.
retrieves the factors of the linear transformation.
get method
retrieves the number of factors.
retrieves the number of samples.
retrieves the number of original variables.
set method
retrieves the names of the original variables.


excludes certain factors.
inverts the signs of selected factors.


plots the loadings of the linear transformation.
plots factors versus factors for all data samples
plots a scree diagram of the transformation eigenvalues.