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Multilinear-PLS (N-PLS) for true multi-way regression.


model = npls(x,y,ncomp,options)
pred = npls(x,ncomp,model,options)


NPLS fits a multilinear PLS1 or PLS2 regression model to x and y [R. Bro, J. Chemom., 1996, 10(1), 47-62]. The NPLS function also can be used for calibration and prediction.


  • x = X-block,
  • y = Y-block, and
  • ncomp = the number of factors to compute, or
  • model = in prediction mode, this is a structure containing a NPLS model.

Optional Inputs

  • options = discussed below.


  • modeltype: 'NPLS',
  • datasource: structure array with information about input data,
  • date: date of creation,
  • time: time of creation,
  • info: additional model information,
  • reg: cell array with regression coefficients,
  • loads: cell array with model loadings for each mode/dimension,
  • core: cell array with the NPLS core,
  • 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.


  • options = options structure containing the fields:
  • display: [ 'off' | {'on'} ], governs level of display to command window,
  • plots: [ 'none' | {'final'} ], governs level of plotting,
  • preprocessing: {[] []}, two element cell array containing preprocessing structures (see PREPROCESS) defining preprocessing to use on the x- and y-blocks (first and second elements respectively)
  • outputregrescoef: if this is set to 0 no regressions coefficients associated with the X-block directly are calculated (relevant for large arrays), and
  • blockdetails: [ 'compact' | {'standard'} | 'all' ] level of detail (predictions, raw residuals, and calibration data) included in the model.
  • ‘Standard’ = the predictions and raw residuals for the X-block as well as the X-block itself are not stored in the model to reduce its size in memory. Specifically, these fields in the model object are left empty: 'model.pred{1}', 'model.detail.res{1}', '{1}'.
  • ‘Compact’ = for this function, 'compact' is identical to 'standard'.
  • 'All' = keep predictions, raw residuals for both X- & Y-blocks as well as the X- & Y-blocks themselves.

See Also

conload, datahat, explode, gram, modlrder, mpca, crossval, outerm, parafac, pls, tld, unfoldm