Tucker

From Eigenvector Research Documentation Wiki
Revision as of 20:58, 2 September 2008 by imported>Jeremy (Importing text file)
Jump to navigation Jump to search

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