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 weightedprincipal
component analysis (
wpcatrans).
Let
X be the original
pby
n matrix, with
p the number of variables, and
n the number of samples. Linear dimensionality
reduction is achieved by a
pby
d matrix
U, with
d <= p, such that
U^{T}X is a
dby
n matrix,
usually called the
scores matrix,
describing the new data in a reduceddimensional space. Each column
in
U is called a
factor.
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General Description
Class Structure
Class Construction
Class Functions
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 
