mpca
Purpose
Multi-way (unfold) principal components analysis.
Synopsis
model = mpca(mwa,ncomp,options)
model = mpca(mwa,ncomp,preprostring)
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.
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');.
It is also possible to input just the preprocessing option as
an ordinary string in place of options and have the remainder of options
filled in with the defaults from above. The following strings are valid:
'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
