Tucker

Purpose

TUCKER analysis for n-way arrays.

Synopsis

model = tucker(x,ncomp,initval,options) %tucker model

pred = tucker(x,model) %application

options = tucker('options')

Description

TUCKER decomposes an array of order K (where K ? 3) into the summation over the outer product of K vectors. As opposed to PARAFAC every combination of factors in each mode are included (subspaces). Missing values must be NaN or Inf.

INPUTS

• x = the multi-way array to be decomposed and

• ncomp = the number of components to estimate, or

• model = a TUCKER model structure.

OPTIONAL INPUTS

• initval = if initval is the loadings from a previous TUCKER model are then these are used as the initial starting values to estimate a final model,

• if initval is a TUCKER model structure then mode 1 loadings (scores) are estimated from x and the loadings in the other modes (see output pred),

• ''' options = discussed below.

OUTPUTS

• model = a structure array with the following fields:

• modeltype: 'TUCKER',

• datasource: structure array with information about input data,

• date: date of creation,

• time: time of creation,

• info: additional model information,

• loads: 1 by K+1 cell array with model loadings for each mode/dimension,

• pred: cell array with model predictions for each input data block,

• 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.

• pred = is a structure array, similar to model, that contains prediction results for new data fit to the TUCKER model.

Options

• options = a structure array with the following fields:

• display: [ {'on'} | 'off' ], governs level of display,

• plots: [ {'final'} | 'all' | 'none' ], governs level of plotting,

• weights: [], used for fitting a weighted loss function (discussed below),

• stopcrit: [1e-6 1e-6 10000 3600] defines the stopping criteria as [(relative tolerance) (absolute tolerance) (maximum number of iterations) (maximum time in seconds)],

• init: [ 0 ], defines how parameters are initialized (see PARAFAC),

• line: [ 0 | {1}] defines whether to use the line search {default uses it},

• algo: this option is not yet active,

• blockdetails: 'standard'

• missdat: this option is not yet active,

• samplemode: [1], defines which mode should be considered the sample or object mode and

• constraints: {4x1 cell}, defines constraints on parameters (see PARAFAC). The first three cells define constraints on loadings whereas the last cell defines constraints on the core.

The default options can be retreived using: options = tucker('options');.

See Also

datahat, gram, mpca, outerm, parafac, parafac2, tld, unfoldm