Constrainfit

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Revision as of 11:26, 21 October 2008 by imported>Rasmus
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Purpose

Finds A minimizing ||X-A*B'|| subject to constraints, given the small matrices (X ' B) and (B ' B)

Synopsis

[A]=constrainfit(XB,BtB,Aold);  % Unconstrained
Setting global constraints on A
opt = constrainfit('options');
opt.type='nonnegativity';
[A]=constrainfit(XB,BtB,Aold,opt); % Nonnegative
Setting constraints on just one column of A
opt = constrainfit('options');
opt.type='columnwise';
opt.columnconstraints={0;2;0}; % If three columns
[A]=constrainfit(XB,BtB,Aold,opt); % Second column unimodal

Description

CONSTRAINTFIT solves the least squares problem behind bilinear, trilinear and other multilinear models. Assuming a model X = A*B ' and assuming that X and B are known, the least squares estimate of A is obtained. Rather than using X and B this algorithm uses the cross product matrices (X ' B) and (B ' B) which are generally smaller and less memory-demanding especially in multi-way models.

CONSTRAINFIT can do a number of general types of regression problems such as nonnegativity-constrained regression, regression with column-orthogonality of A etc. These constraints are simply set in the option field 'type', e.g. option.type='nonnegativity'. Thus, for most problems, only the 'type' field needs to be set. CONSTRAINFIT will provide a least squares solution to most of these problems.

CONSTRAINFIT can also find A subject to different constraints on different columns. In this case, the update of A will be an improvement of the initially provided estimate Aold. As CONSTRAINFIT is used inside iterative algorithms, an improvement is sufficient to guarantee overall convergence.


Inputs

  • XB = This is the matrix X ' B.
  • BtB = This is the matrix B ' B.
  • Aold = An initial estimate of A.

Optional Inputs

  • options = provides definitions for which type of constraint to impose.

Outputs

  • A = The improved estimate of A.

Options

options = a structure array with the following fields:

  • plots: [ {'none'} | 'final' ] governs plotting of results, and
  • order: positive integer for polynomial order {default = 1}.

Example

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See Also

baselinew, deresolv