edsd

This file is a complete demo of the capability of the |edsd|function from the CODES toolbox.

Documentation
Set rng
Simple example
Obtain classification error statistics
Plot functions
Obtain extra outputs from the function
References

Documentation

The documentation for the edsd function can be found here.

Set rng

Set random number generator seed:

rng(0)

Simple example

Define a simple sinusoidal problem:

f=@(x)x(:,2)-sin(10*x(:,1))/4-0.5;
x=CODES.sampling.cvt(10,2);
y=f(x);

Train an SVM and perform edsd while watching the convergence plot:

svm=CODES.fit.svm(x,y,'UseParallel',true);
svm_col=CODES.sampling.edsd(f,svm,[0 0],[1 1],'iter_max',20,'plot_conv',true,'display_edsd',false);

Plot first and last contour:

[X,Y]=meshgrid(linspace(0,1,100));
Z=reshape(f([X(:) Y(:)]),100,100);

figure('Position',[200 200 500 500])
contour(X,Y,Z,[0 0],'r')
hold on
svm_col{1}.isoplot('lb',[0 0],'ub',[1 1],'prev_leg',{'True LS'})
axis square

figure('Position',[200 200 500 500])
contour(X,Y,Z,[0 0],'r')
hold on
svm_col{end}.isoplot('lb',[0 0],'ub',[1 1],'prev_leg',{'True LS'})
axis square

A video of this sequential update can be found here.

Obtain classification error statistics

Compare the relative change of class, used as a convergence metric in Basudhar and Missoum (2008), to the generalization error:

error_gen=zeros(size(svm_col,1),1);
class_change=zeros(size(svm_col,1)-1,1);

for i=1:size(svm_col,1)
    error_gen(i,:)=svm_col{i}.me([X(:) Y(:)],Z(:));
    if i>1
        class_change(i-1,:)=svm_col{i}.class_change(svm_col{i-1},[X(:) Y(:)]);
    end
end

figure('Position',[200 200 500 500])
plot(1:size(svm_col,1),error_gen(:,1),'b-')
hold on
plot(2:size(svm_col,1),class_change(:,1),'r-')
plot(2:size(svm_col,1),abs(diff(error_gen(:,1))),'g-')
legend('Generalization error','Class change','Absolute change in generalization error')

Plot functions

Perform a simple EDSD and plot AUC on a test set:

f=@(x)x(:,2)-sin(10*x(:,1))/4-0.5;
x=CODES.sampling.cvt(10,2);
y=f(x);

x_t=rand(1e4,2);
y_t=f(x_t);

plot_auc=@(svm,iter)plot(iter,svm.auc(x_t,y_t),'bs');

svm=CODES.fit.svm(x,y,'UseParallel',true);
[~]=CODES.sampling.edsd(f,svm,[0 0],[1 1],'iter_max',5,'plot_conv',true,'plotfcn',plot_auc);

EDSD: iteration 1 out of 5 is done
EDSD: iteration 2 out of 5 is done
EDSD: iteration 3 out of 5 is done
EDSD: iteration 4 out of 5 is done
EDSD: iteration 5 out of 5 is done
EDSD: Stopped because maximum number of iteration was reached

Obtain extra outputs from the function

Consider a function that returns other information than just the performance. For example, consider a dummy function returning 3 random numbers for each sample calculated.

f=@(x)deal(x(:,2)-sin(10*x(:,1))/4-0.5,num2cell(rand(size(x,1),3)));
x=CODES.sampling.cvt(10,2);
[y,extra_outputs]=f(x);

svm=CODES.fit.svm(x,y,'UseParallel',true);
[svm_col,extras]=CODES.sampling.edsd(f,svm,[0 0],[1 1],'iter_max',5,'extra_output',true);

disp([svm_col{end}.X [cell2mat(extra_outputs);cell2mat(extras)]])

EDSD: iteration 1 out of 5 is done
EDSD: iteration 2 out of 5 is done
EDSD: iteration 3 out of 5 is done
EDSD: iteration 4 out of 5 is done
EDSD: iteration 5 out of 5 is done
EDSD: Stopped because maximum number of iteration was reached
    0.1176    0.1648    0.8440    0.3873    0.1000
    0.5469    0.4778    0.5728    0.4732    0.1202
    0.4615    0.8109    0.5479    0.9344    0.3501
    0.8679    0.1976    0.1869    0.3405    0.5470
    0.1765    0.5094    0.2816    0.1760    0.1172
    0.8050    0.8568    0.5348    0.3591    0.4756
    0.3577    0.1945    0.9662    0.8280    0.1733
    0.8519    0.5529    0.1612    0.1190    0.2818
    0.1510    0.8399    0.4978    0.1914    0.5873
    0.6110    0.1414    0.2211    0.3812    0.3221
    0.3560    0.4057    0.3206    0.6285    0.2456
    0.7032    0.3374    0.7859    0.4738    0.7413
   -0.0000    0.9296    0.7991    0.9546    0.2973
    0.1404    0.6734    0.9947    0.3241    0.0340
    0.9032    1.0000    0.8030    0.9237    0.7396

References

Basudhar and Missoum (2008): Basudhar A., Missoum S., (2008) Adaptive explicit decision functions for probabilistic design and optimization using support vector machines. Computers & Structures 86(19):1904-1917 - DOI

Computational Optimal Design of
Engineering Systems