DisTools examples: Characterization of Dissimilarity Matrices

Dissimilarity matrices may be non-Euclidean, non-metric, have some complexity defined in various ways. Some examples will be treated. It is assumed that readers are familiar with PRTools and will consult the following pages where needed:

• PRTools User Guide, See at the bottom of the page for a TOC
• Introduction to DisTools
• Dissimilarity Representation Course
• The following packages should be in the Matlab path: PRTools, DisTools, PRDisData

display, pca, classical scaling, asymmetry, nef, intrdim, disstat, signature, ner, trineq, subeucl, nnerror

Some figures to inspect the data of a given dissimilarity matrix:

delfigs
D = chickenpieces(29,45)*makesym;
figure; imagesc(+D);
title('Dissimilarity matrix')
W = D*pe_em;
figure; scatterd(D*W(:,[1 2]));
title('Embedding, first 2 features')
[p,q] = getsig(W);
figure; scatterd(D*W(:,[1 p+1]))
title('PE space');
xlabel('First positive feature')
ylabel('First negative feature')
figure; plotspectrum(W);
showfigs

Some properties:

D = chickenpieces(29,45);
fprintf('Number of objects:        %6.0fn',size(D,1));
fprintf('Number of classes:        %6.0fn',getsize(D,3));
fprintf('Asymmetry:                %6.4fn',D*asymmetry);
D = D*makesym;
[f,r] = nef(D*pe_em);
fprintf('Negative eigen-fraction:  %6.4fn',f);
fprintf('Negative eigen-ratio:     %6.4fn',r);
fprintf('Intrinsic dimensionality: %6.0fn',intrdim(D));
[p,c] = D*disnorm(D)*nmf;
fprintf('Non-metric fraction:      %6.4fn',p);
fprintf('Non-metricity:            %6.4fn',c);
fprintf('LOO NN error:             %6.4fn',nne(D))

Study the meanings of these properties from the help files.

Exercise

Study the behavior of the negative eigenfraction nef as a function of the number of objects used for the construction of the dissimilarity matrix. Use a larger dataset like zongker (2000 x 2000) and take subsets of various sizes by genddat.

elements: datasets datafiles cells and doubles mappings classifiers mapping types.
operations: datasets datafiles cells and doubles mappings classifiers stacked parallel sequential dyadic.
user commands: datasets representation classifiers evaluation clustering examples support routines.
introductory examples: Introduction Scatterplots Datasets Datafiles Mappings Classifiers Evaluation Learning curves Feature curves Dimension reduction Combining classifiers Dissimilarities.
advanced examples.