Constrainfit
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:
- type: [ {'unconstrained'} | 'nonnegativity' | 'unimodality' | 'orthogonality' | 'columnorthogonal' | 'equality' | 'exponential' | 'rightprod' | 'columnwise']
- columnconstraints: cell where element f defines constraints on column f (only applicable if options.type = 'columnwise')
- inequality : Defines a cutoff. If inequality is defined in columnwise, all elements of that column will be > options.inequality.scalar. Thus, when set to zero, nonnegativity is imposed.
nonnegativity: [1x1 struct]
orth: [1x1 struct]
smoothness: [1x1 struct]
fixed: [1x1 struct]
advanced: [1x1 struct]
equality: [1x1 struct]
unimodality: [1x1 struct]
functional: {[1x1 struct]}
definitions: @optiondefs
functionname: 'constrainfit'
Example
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