Stepwise regrcls

Purpose

STEPWISE_REGRCLS Step-wise regression for CLS models.

Synopsis

[c,ikeep,res] = stepwise_regrcls(x,targspec,options);

options = stepwise_regrcls('options');

Description

For a given set of measured spectra (x), STEPWISE_REGRCLS finds the subset of target spectra (targspec) that best fit each measured spectrum in (x). This can be used for classification i.e. an analyte identification algorithm. The model is:

    x(i,:) = c(i,:)*targspec(ikeep{i},:)

where c(i,:) can be determined using non-negative least-squares [see optional input (options)].

Inputs

• x = MxN matrix of measured spectra (each row corresponds to a measured spectrum).
• targspec = KxN matrix of target (candidate) spectra.

Outputs

• c = MxK matrix of concentrations / contributions, c is non-zero only if a corresponding target spectrum is retained. If (options.p) is not empty, then (c) is Mx(Kp+K) where the first Kp rows correspond to the spectra in (options.p).
• ikeep = Mx1 cell array of indices, each cell corresponds to a row of input (x) and includes the indices of retained target spectra.
• res = Mx1 vector of mean sum-squared-residuals.

Options

options = an optional options structure containing one or more of the following fields:

• display: [ 'off' | {'on'} ], governs level of display to command window,
• automate: [ {'yes'} | 'no' ], automate the algorithm?

automate = 'yes', makes no plots, and the step-wise regression stops when the fit improvement is not sigificant in an F Test at the probability level given in options.fstat.

automate = 'no', requires interactive user input for each of the M spectra in (x).

        fstat: 0.95, probability level the F test that determines the
               significance of fit improvement.
         ccon: [ 'none' | {'nnls'} ], uses non-negativity on concentrations,
               in the concentration estimates.
         ccov: [], sqrt inverse noise/clutter covariance matrix,
               e.g. if Xc is a matrix of measured clutter spectra then
               ccov = inv(sqrt(cov(Xc))) [see COV_CV].
            p: KpxN matrix of spectra that are always included in the
               model.
         scls: [1:N],   % 1xN spectra scale axis {default = 1:N}.