Gaselctr

Purpose

Genetic algorithm for variable selection with PLS.

Synopsis

model = gaselctr(x,y,options)

[fit,pop,avefit,bstfit] = gaselctr(x,y,options)

Description

GASELCTR uses a genetic algorithm optimization to minimize cross validation error for variable selection.

Inputs

• x = the predictor block (x-block), and

• y = the predicted block (y-block) (note that all scaling should be done prior to running GASELCTR).

Options

• options = a structure array with the following fields:

• plots: ['none' | {'intermediate'} | 'replicates' | 'final' ] Governs plots.

• 'final' gives only a final summary plot.

• 'replicates' gives plots at the end of each replicate.

• 'intermediate' gives plots during analysis.

• 'none' gives no plots.

• popsize: {64} the population size (16?popsize?256 and popsize must be divisible by 4),

• maxgenerations: {100} the maximum number of generations (25?mg?500),

• mutationrate: {0.005} the mutation rate (typically 0.001?mt?0.01),

• windowwidth: {1} the number of variables in a window (integer window width),

• convergence: {50} percent of population the same at convergence (typically cn=80),

• initialterms: {30} percent terms included at initiation (10?bf?50),

• crossover: {2} breeding cross-over rule (cr = 1: single cross-over; cr = 2: double cross-over),

• algorithm: [ 'mlr' | {'pls'} ] regression algorithm,

• ncomp: {10} maximum number of latent variables for PLS models,

• cv: [ 'rnd' | {'con'} ] cross-validation option ('rnd': random subset cross-validation; 'con': contiguous block subset cross-validation),

• split: {5} number of subsets to divide data into for cross-validation,

• iter: {1} number of iterations for cross-validation at each generation,

• preprocessing: {[] []} a cell containing standard preprocessing structures for the X- and Y-blocks respectively (see PREPROCESS),

• preapply: [ {0} | 1 } If 1, preprocessing is applied to data prior to GA. This speeds up the performance of the selection, but my reduce the accuracy of the cross-validation results. Output "fit" values should only be compared to each other. A full cross-validation should be run after analysis to get more accurate RMSECV values.

• reps: {1} the number of replicate runs to perform,

• target: a two element vector [target_min target_max] describing the target range for number of variables/terms included in a model n. Outside of this range, the penaltyslope option is applied by multiplying the fitness for each member of the population by:

• penaltyslope\*(target_min-n) when n<target_min, or

• penaltyslope\*(n-target_max) when n>target_max.

• Field target is used to bias models towards a given range of included variables (see penaltyslope below),

• targetpct: {1} flag indicating if values in field target are given in percent of variables (1) or in absolute number of variables (0), and

• penaltyslope: {0} the slope of the penalty function (see target above).

The default options can be retreived using: options = gaslctr('options');.

Outputs

• model = a standard GENALG model structure with the following fields:

• modeltype: 'GENALG' This field will always have this value,

• datasource: {[1x1 struct] [1x1 struct]}, structures defining where the X- and Y-blocks came from

• date: date stamp for when GASELCTR was run,

• time: time stamp for when GASELCTR was run,

• info: 'Fit results in "rmsecv", population included variables in "icol"', information field describing where the fitness results for each member of the population are contained,

• rmsecv: fitness results for each member of the population, for X MxN and Mp unique populations at convergence then rmsecv will be 1xMp,

• icol: each row of icol corresponds to the variables used for that member of the population (a 1 [one] means that variable was used and a 0 [zero] means that it was not), for X MxN and Mp unique populations at convergence then icol will be MpxN, and

• detail: [1x1 struct], a structure array containing model details including the following fields:

• avefit: the average fitness at each generation,

• bestfit: the best fitness at each generation, and

• options: a structure corresponding to the options discussed above.

Examples

To use mean centering outside the genetic algorithm (no additional centering will be performed within the algorithm) do the following:

x2 = mncn(x);

y2 = mncn(y);

[fit,pop] = gaselctr(x2,y2);

To use mean centering inside the genetic algorithm (centering will be performed for each cross-validation subset) do the following:

options = gaselctr('options');

options.preprocessing{1} = preprocess('default', 'mean center');

options.preprocessing{2} = preprocess('default', 'mean center');

[fit,pop] = gaselctr(x2,y2,options);

See Also

calibsel, fullsearch, genalg, genalgplot