Tucker
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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