imported>Rasmus |
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| ===Purpose=== | | __TOC___ |
| | ==Importing / Exporting== |
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| Finds A minimizing ||X-A*B'|| subject to constraints, given the small matrices ('''X''' ' '''B''') and ('''B''' ' '''B''')
| | [[faq_concatenate_multiple_files|How do I concatenate multiple files into a single DataSet?]] |
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| ===Synopsis===
| | [[faq_create_multivariate_image_from_separate_images|How do I create a multivariate image from separate images?]] |
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| : [A]=constrainfit(XB,BtB,Aold); % Unconstrained
| | [[faq_export_PCA_scores_and_loadings_to_text_file|How do I export PCA scores and loadings to a text file (to read into MS Excel, for example)?]] |
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| : '''Setting global constraints on A'''
| | [[faq_import_three-way_data|How do I import three-way data into Solo or PLS_Toolbox?]] |
| : opt = constrainfit('options');
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| : opt.type='nonnegativity';
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| : [A]=constrainfit(XB,BtB,Aold,opt); % Nonnegative
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| : '''Setting constraints on just one column of A'''
| | [[faq_import_horiba_NGC_64bit |Why can't I import a Horiba NGC file on my 64-bit computer?]] |
| : opt = constrainfit('options');
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| : opt.type='columnwise';
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| : opt.columnconstraints={0;2;0}; % If three columns
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| : [A]=constrainfit(XB,BtB,Aold,opt); % Second column unimodal
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| ===Description===
| | [[faq_SPCREADR_cant_read_multiple_files |Why can't SPCREADR read multiple files I've selected?]] |
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| 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.
| | [[faq_some_EXCEL_files_fail_to_import |Why do some Excel files fail to import?]] |
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| 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.
| | ==General== |
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| 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.
| | [[faq_PARALIND_in_PLS_Toolbox |Can I do PARALIND in PLS_Toolbox?]] |
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| | [[faq_install_on_more_than_one_PC | Can I install PLS_Toolbox (or Solo) on more than one PC, such as on my desktop and laptop computer?]] |
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| ====Inputs====
| | [[faq_multiple_class_sets_together_in_SIMCA_PLSDA_LDA | Can I use multiple class sets (categorical variables) together in a SIMCA, PLSDA, or LDA model?]] |
| * '''XB''' = This is the matrix '''X''' ' '''B'''.
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| * '''BtB''' = This is the matrix '''B''' ' '''B'''.
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| * '''Aold''' = An initial estimate of '''A'''.
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| ====Optional Inputs====
| | [[faq_more_info_on_R_Squared_statistic | Can you give me more information on the R-Squared statistic?]] |
| * '''options''' = provides definitions for which type of constraint to impose.
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| ====Outputs====
| | [[faq_how_RMSEC_and_RMSECV_related to R2Y_and_Q2Y_seen_other_software | How are RMSEC and RMSECV related to R2Y and Q2Y I see in other software?]] |
| * '''A''' = The improved estimate of '''A'''.
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| ===Options===
| | [[ faq_convergence_of_PARAFAC| Convergence of PARAFAC. How much variation between models is expected a particular PARAFAC is fit multiple times with the same settings?]] |
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| options = a structure array with the following fields:
| | [[ faq_does_software_stop_working_if_maintenance_expires | Does the software stop working if my maintenance expires?]] |
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| * '''type''': [ {'unconstrained'} | 'nonnegativity' | 'unimodality' | 'orthogonality' | 'columnorthogonal' | 'equality' | 'exponential' | 'rightprod' | 'columnwise']
| | ==Command Line== |
| | ==Manual== |
| | ==GUI== |
| | ==Installation== |
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| * '''columnconstraints''': cell where element f defines constraints on column f (only applicable if options.type = 'columnwise'). For applicable column constraints see below.
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| * '''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.
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| * '''nonnegativity''': defines which algorithm to use for imposing nonnegativity when options.type = 'nonnegativity'. If set to 0, the default NNLS algorithm is used. If set to 1, a faster columnwise update is used which only improves the current least squares fit, if set to 2, an ad hoc approach is used where '''A''' is estimated in a least squares sense and then negative numbers are set to zero. This will not provide a well-defined solution in terms of the least squares loss function. If set to 3, the NMF algorithm is used. This requires that all elements of the data array are nonnegative in order to work properly.
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| * '''smoothness''': defines how much smoothness is imposed when smoothness is imposed as a columnconstraint. smoothness.alpha is a number between 0 (no smoothness) and 1 (full smoothness)
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| * '''fixed''':
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| * '''advanced''':
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| * '''equality''':
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| * '''unimodality''':
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| * '''functional''':
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| * '''definitions''': @optiondefs
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| ===Example===
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| <pre>
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| >>This is an example on the use of CONSTRAINFIT in PARAFAC
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| % Make a noisy dataset such that PARAFAC gives noisy loadings
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| load aminoacids
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| x = X.data;
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| x = x+randn(size(x))*100;
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| % define parafac options
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| op=parafac('options');
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| % set constraints in second mode to be defined columnwise
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| op.constraints{2}.type='columnwise';
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| % Define that first column is smooth, second and third unconstrained
| | [[Category:FAQ]] |
| op.constraints{2}.columnconstraints={4 0 0};
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| % Fit model
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| model = parafac(x,3,op);
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| Note how the first loading in the second mode is more smooth than the rest
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| if needed smoothness can be turned up (to one) and down (to zero) using
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| op.constraints{2}.smoothness.alpha=0.6
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| </pre>
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| ===See Also===
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| [[baselinew]], [[deresolv]] | |