This MATLAB script is used to generate data for testing the various vMAT functions used for clustering observations.

Contents

Input Test Data

First off, we need some data to play with. Since we don’t have anything more interesting at hand for the moment, let’s start with a repeatable random sample from a normal distribution.

X = gallery('normaldata', [10 3], 13, 'double');
cmap = gray; cmap(:, 1:3) = .95;
makeHtmlTable(X, [], seqlabels('obs', 10), seqlabels('x', 3), cmap, 4);

	x1	x2	x3
obs1	1.203	0.06809	-0.5938
obs2	0.6676	-0.3744	0.2813
obs3	1.737	1.532	-1.225
obs4	-0.474	-0.1009	0.02343
obs5	1.677	-0.7548	0.8096
obs6	-1.28	-0.6805	-0.009285
obs7	-0.9427	1.165	-0.7701
obs8	0.2707	1.155	0.4899
obs9	-1.429	0.7309	-2.161
obs10	-0.5094	1.479	0.406

pdist and linkage

Now we can compute the pairwise-distances between observations (pdist) and then the hierarchical cluster tree (linkage). The dendrogram plot provides a nice visual summary of the hierarchical cluster tree. (It’s only here for informational purposes, as vMAT doesn’t have any plotting functions.)

NOTE: Don’t forget, vMAT_pdist wants X’, and vMAT_linkage has zero-based indexes in the first two columns. The data in the MAT file includes the variable Zv for validating the test results.

Y = pdist(X);
Z = linkage(Y);
Zv = [Z(:,1:2)-1 Z(:,3)];
makeHtmlTable(Zv,[], ...
    seqlabels('link', length(Zv)), {'idx1', 'idx2', 'distance'}, cmap, 4);
dendrogram(Z);

	idx1	idx2	distance
link1	7	9	0.8487
link2	3	5	0.9934
link3	0	1	1.117
link4	4	12	1.201
link5	11	13	1.202
link6	6	10	1.292
link7	14	15	1.533
link8	8	16	1.536
link9	2	17	1.681

inconsistent

Two methods of clustering are supported in vMAT (for now): ‘cutoff:’ uses an inconsistency coefficient to produce an arbitrary number of clusters, and ‘maxclust:’ returns at most a specified number of clusters. [The MATLAB cluster function of course has a number of additional options, but these are two commonly useful ones.]

When you’re actually using vMAT_cluster it’s not necessary to call the vMAT_inconsistent function explicitly; it’s called from vMAT_cluster as necessary. But for the purpose of testing, we’re going to call it so we can validate that vMAT’s function matches the output of MATLAB’s. (If the two implementations are inconsistent [sic], the clustering is likely to come out differently as well.) The inconsistency coefficient is explained in the documentation for the inconsistent function.

Wv = inconsistent(Z);
ZW = [Zv Wv];
makeHtmlTable(ZW, [], ...
    seqlabels('link', length(Z)), ...
    {'idx1', 'idx2', 'distance', 'mean', 'std', 'n', 'coefficient'}, cmap, 4);

	idx1	idx2	distance	mean	std	n	coefficient
link1	7	9	0.8487	0.8487	0	1	0
link2	3	5	0.9934	0.9934	0	1	0
link3	0	1	1.117	1.117	0	1	0
link4	4	12	1.201	1.159	0.05934	2	0.7071
link5	11	13	1.202	1.132	0.1202	3	0.58
link6	6	10	1.292	1.07	0.3135	2	0.7071
link7	14	15	1.533	1.342	0.1711	3	1.114
link8	8	16	1.536	1.534	0.002258	2	0.7071
link9	2	17	1.681	1.609	0.1026	2	0.7071

cluster

Now, finally we’re ready to see how the data clusters.

VCv = cluster(Z, 'cutoff', [.5 .75]) - 1;
VMv = cluster(Z, 'maxclust', [3 4]) - 1;
Summary = [VCv VMv];
makeHtmlTable(Summary, [], ...
    seqlabels('obs', length(Z) + 1), {'cutoff: 0.5', 'cutoff: 0.75', 'maxclust: 3', 'maxclust: 4'}, cmap, 4);

	cutoff: 0.5	cutoff: 0.75	maxclust: 3	maxclust: 4
obs1	5	0	1	0
obs2	5	0	1	0
obs3	4	2	2	3
obs4	1	0	1	0
obs5	0	0	1	0
obs6	1	0	1	0
obs7	2	3	1	1
obs8	6	3	1	1
obs9	3	1	0	2
obs10	6	3	1	1

cluster-normaldata-10x3-13.mat

Save the data in a MAT file, so it can be loaded by the unit test cases.

save('cluster-normaldata-10x3-13', '-v6', ...
    'X', 'Zv', 'Wv', 'VCv', 'VMv');
attach('cluster-normaldata-10x3-13.mat');

cluster-normaldata-10x3-13.mat

Published with MATLAB® R2013a