DisTools introductory 2D example

Get rid of old figures, generate a trainset and a testset and give them proper names

delfigs
AT = setname(gendatb,'TrainSet')
AS = setname(gendatb,'TestSet')

The following statements just show how in PRTools a 2D space can be mapped onto a 6D polynomial space in which every direction corresponds to an original feature raised to some power, here for degrees 1, 2 and 3.

XP = AT*cmapm(2,[1 0; 0 1; 2 0; 0 2; 3 0; 0 3;]);
+XP(1:5,:) % show result for first 5 objects


The next statements show how a a mapping VM to a Minkowsky-2 (i.e. Euclidean) set dissimilarities is defined using all training objects AT for representation. After that the training set is mapped into that space, constructing thereby square dissimilarity matrix XM.

VM = AT*proxm([],'m',2); % the dissimilarity mapping
XM = AT*VM               % map the training set
+XM(1:5,1:5)             % show the first 5 dissimilarities of 5 objects


Define a set of untrained classifiers all based on Fisher’s Linear Discriminant: in the original 2D feature space, in the 6D polynomial space, in the 100D dissimilarity space and in a 10D PCA projection of the last one. Give them proper names and train them by AT.

U1 = fisherc;                         % Fisher in 2D feature space
U2 = cmapm(2,[1 0; 0 1; 2 0; 0 2; 3 0; 0 3;])*fisherc;
U2 = setname(U2,'PolyFisher');        % Fisher in polynomial space
U3 = proxm([],'m',2)*fisherc;
U3 = setname(U3,'DisSpaceFisher');    % Fisher in disspace
U4 = proxm([],'m',2)*pca([],10)*fisherc;
U4 = setname(U4,'DisSpacePCAFisher'); % Fisher in PCA disspace
W = AT*{U1,U2,U3,U4};                 % Train them all


Show results in a scatter plot

scatterd(AT)
plotc(W)

Classify trainset and testset and show results.

testc({AT,AS},W)