Load data and create a classifier.

Create a linear discriminant analysis classifier for theovariancancerdata. Set theSaveMemoryandFillCoeffsname-value pair arguments to keep the resulting model reasonably small. For computational ease, this example uses a random subset of about one third of the predictors to train the classifier.

loadovariancancerrng(1);% For reproducibilitynumPred = size(obs,2); obs = obs(:,randsample(numPred,ceil(numPred/3))); Mdl = fitcdiscr(obs,grp,'SaveMemory','on','FillCoeffs','off');

Cross validate the classifier.

Use 25 levels ofGammaand 25 levels ofDeltato search for good parameters. This search is time consuming. SetVerboseto1to view the progress.

[err,gamma,delta,numpred] = cvshrink(Mdl,...'NumGamma',24,'NumDelta',24,'Verbose',1);

Done building cross-validated model. Processing Gamma step 1 out of 25. Processing Gamma step 2 out of 25. Processing Gamma step 3 out of 25. Processing Gamma step 4 out of 25. Processing Gamma step 5 out of 25. Processing Gamma step 6 out of 25. Processing Gamma step 7 out of 25. Processing Gamma step 8 out of 25. Processing Gamma step 9 out of 25. Processing Gamma step 10 out of 25. Processing Gamma step 11 out of 25. Processing Gamma step 12 out of 25. Processing Gamma step 13 out of 25. Processing Gamma step 14 out of 25. Processing Gamma step 15 out of 25. Processing Gamma step 16 out of 25. Processing Gamma step 17 out of 25. Processing Gamma step 18 out of 25. Processing Gamma step 19 out of 25. Processing Gamma step 20 out of 25. Processing Gamma step 21 out of 25. Processing Gamma step 22 out of 25. Processing Gamma step 23 out of 25. Processing Gamma step 24 out of 25. Processing Gamma step 25 out of 25.

Examine the quality of the regularized classifiers.

Plot the number of predictors against the error.

plot(err,numpred,'k.') xlabel('Error rate') ylabel(根据这些得分确定那种的数量rs')

Examine the lower-left part of the plot more closely.

axis([0 .1 0 1000])

There is a clear tradeoff between lower number of predictors and lower error.

Choose an optimal tradeoff between model size and accuracy.

Multiple pairs ofGammaandDeltavalues produce about the same minimal error. Display the indices of these pairs and their values.

First, find the minimal error value.

minerr = min(min(err))

minerr = 0.0139

Find the subscripts oferrproducing minimal error.

[p,q] = find(err < minerr + 1e-4);

Convert from subscripts to linear indices.

idx = sub2ind(size(delta),p,q);

Display theGammaandDeltavalues.

[gamma(p) delta(idx)]

ans =4×20.7202 0.1145 0.7602 0.1131 0.8001 0.1128 0.8001 0.1410

These points have as few as 29% of the total predictors with nonzero coefficients in the model.

numpred(idx)/ceil(numPred/3)*100

ans =4×139.8051 38.9805 36.8066 28.7856

To further lower the number of predictors, you must accept larger error rates. For example, to choose theGammaandDeltathat give the lowest error rate with 200 or fewer predictors.

low200 = min(min(err(numpred <= 200))); lownum = min(min(numpred(err == low200))); [low200 lownum]

ans =1×20.0185 173.0000

You need 173 predictors to achieve an error rate of 0.0185, and this is the lowest error rate among those that have 200 predictors or fewer.

Display theGammaandDeltathat achieve this error/number of predictors.

[r,s] = find((err == low200) & (numpred == lownum)); [gamma(r); delta(r,s)]

ans =2×10.6403 0.2399

Set the regularization parameters.

To set the classifier with these values ofGammaandDelta, use dot notation.

Mdl.Gamma = gamma(r); Mdl.Delta = delta(r,s);

Heatmap plot

To compare thecvshrinkcalculation to that in Guo, Hastie, and Tibshirani[1], plot heatmaps of error and number of predictors againstGamma和的索引Deltaparameter. (TheDeltaparameter range depends on the value of theGammaparameter. So to get a rectangular plot, use theDeltaindex, not the parameter itself.)

% Create the Delta index matrixindx = repmat(1:size(delta,2),size(delta,1),1); figure subplot(1,2,1) imagesc(err) colorbar colormap('jet') title('Classification error') xlabel('Delta index') ylabel('Gamma index') subplot(1,2,2) imagesc(numpred) colorbar title(根据这些得分确定那种的数量rs in the model') xlabel('Delta index') ylabel('Gamma index')

You see the best classification error whenDeltais small, but fewest predictors whenDeltais large.