Gaselctr

Purpose

Genetic algorithm for variable selection with PLS.

Synopsis

model = gaselctr(x,y,options)

[fit,pop,cavfit,cbfit] = 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).

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.

For the second output syntax shown above,

• fit is the same as model.rmsecv
• pop is the same as model.icol
• cavfit is the same as model.detail.avefit
• cbfit is the same as model.detail.bestfit

Options

options is 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<it<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).

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