mpca
Purpose
Multi-way (unfold) principal components analysis.
Synopsis
model = mpca(mwa,ncomp,options)
pred = mpca(mwa,model,options)
options = mpca('options')
Description
Principal Components Analysis of multi-way data using
unfolding to a 2-way matrix followed by conventional PCA.
Inputs to MPCA
are the multi-way array mwa
(class "double" or "dataset") and the number of components to use in the model nocomp. To make predictions
with new data the inputs are the multi-way array mwa and the MPCA model model. Optional input options is discussed below.
The output model
is a structure array with the following fields:
modeltype: 'MPCA',
datasource: structure
array with information about the x-block,
date: date
of creation,
time: time
of creation,
info: additional
model information,
loads: 1
by 2 cell array with model loadings for each mode/dimension,
pred: cell
array with model predictions for each input data block (this is empty if options.blockdetail = 'normal'),
tsqs: cell
array with T2 values for each mode,
ssqresiduals: cell
array with sum of squares residuals for each mode,
description: cell
array with text description of model, and
detail: sub-structure
with additional model details and results.
Options
options = a structure array with the following fields.
name: 'options', name indicating that this is an options structure,
display: [
'off' | {'on'} ] governs level of display to command window,
plots: [ 'none' | {'final'} ] governs level of plotting,
outputversion: [ 2 | {3} ] governs output
format,
preprocessing: { [] } preprocessing
structure, {default is mean centering i.e. options.preprocessing = preprocess('default', 'mean center')} (see PREPROCESS),
blockdetails: [ 'compact' | {'standard'} | 'all'
] extent of detail in predictions and residuals included in model
structure ('standard'
results in sum of squared residuals, and 'all' gives all x-block residuals), and
samplemode: [ {3} ] mode (dimension) to use
as the sample mode e.g. if it is 3 then it is assumed that mode 3 is the
sample/object dimension i.e. if mwa
is 7x9x10 then the scores model.loads{1}
will have 10 rows (it will be 10xncomp).
The default options can be retreived using: options = mpca('options');.
To use the defaults options and change the preprocessing,
(options) can be input as a string with the following values:
'none': no scaling,
'auto': unfolds array then applies autoscaling,
'mncn': unfolds array then applies mean centering,
or
'grps': {default} unfolds array then group/block
scales each variable, i.e. the same variance scaling is used for each variable
along its time trajectory (see GSCALE).
MPCA
will work with arrays of order 3 and higher. For higher order arrays, the last
order is assumed to be the sample order, i.e. for an array of order n
with the dimension of order n being m, the unfolded matrix will
have m samples. For arrays of higher order the group scaling option will
group together all data with the same order 2 index, for multiway array mwa, each mwa(:,j,:, ... ,:) will be
scaled as a group.
See Also
analysis, evolvfa, ewfa, explode, parafac, pca, preprocess
