Demo for PAA codes

copyright (c) Sohan Seth, sohan.seth@hiit.fi

Contents

Poisson observation

close all
rng default,
options = generate_options();
options.verbose = true;
options.display = true;
options.eps = 10^-10;
options.maxIter = 100000;
options.matFeatLat = [];
n = 100;

% Generating data
matFeatSam = [ceil(rand(1,n)*10); ceil(rand(1,n)*10)];

% Learning archetypes
[matSamLat, matLatSam_1, ~] = paa_Poisson(matFeatSam, 4, options);
archetypes = matFeatSam * matSamLat;
axis([0 11 0 11]), box on, set(gca, 'fontsize', 20)

% Computing projections given archetypes
options.matFeatLat = archetypes;
options.display = false;
[~, matLatSam_2, ~] = paa_Poisson(matFeatSam, [], options);

fprintf('difference between projections %0.6f\n', ...
    norm(archetypes * matLatSam_2 - archetypes * matLatSam_1, 1) / numel(matFeatSam))

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.....
convergence reached in 27547 iterations

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.........
convergence reached in 9991 iterations

difference between projections 0.000096

Bernoulli observation

close all
rng default,
options = generate_options();
options.verbose = true;
options.display = true;
options.eps = 10^-6;
options.maxIter = 1000;
options.matFeatLat = [];
n = 500;

% Generating data
matFeatSam = [rand(1,n) > 0.8; rand(1,n) > 0.2];

% Learning archetypes
[matSamLat, matLatSam_1, ~] = paa_Bernoulli(matFeatSam, 4, options);
archetypes = matFeatSam * matSamLat;
axis([-0.1 1.1 -0.1 1.1]), box on, set(gca, 'fontsize', 20)

% Computing projections given archetypes
options.matFeatLat = archetypes;
options.display = false;
[~, matLatSam_2, ~] = paa_Bernoulli(matFeatSam, [], options);

fprintf('difference between projections %0.6f\n', ...
    norm(archetypes * matLatSam_2 - archetypes * matLatSam_1, 1) / numel(matFeatSam))

.......... [100]

convergence reached in 105 iterations

.....
convergence reached in 54 iterations

difference between projections 0.000000

Multinomial observations

close all
rng default,
options = generate_options();
options.verbose = true;
options.display = true;
options.eps = 10^-6;
options.maxIter = 10000;
options.matFeatLat = [];
n = 500;

% Generating data
matFeatSam = rand(3, n); matFeatSam = bsxfun(@rdivide, matFeatSam, sum(matFeatSam));
nFeatSam = mnrnd(1000, matFeatSam')';
matFeatSam = bsxfun(@rdivide, nFeatSam, sum(nFeatSam)); % empirical probabilities

% Learning archetypes
[matSamLat, matLatSam_1, ~] = paa_stochastic(nFeatSam, 3, options);
archetypes = matFeatSam * matSamLat;
axis([0 1000 0 1000]), box on, set(gca, 'fontsize', 20)

% Computing projections given archetypes
options.matFeatLat = archetypes;
options.display = false;
[~, matLatSam_2, ~] = paa_stochastic(nFeatSam, [], options);

fprintf('difference between projections %0.6f\n', ...
    norm(archetypes * matLatSam_2 - archetypes * matLatSam_1, 1) / numel(matFeatSam))

More than two features. Only the first two will be displayed.
.......... [100]
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.....
convergence reached in 657 iterations

..
convergence reached in 23 iterations

difference between projections 0.000024

Normal observation

close all
rng default,
options = generate_options();
options.verbose = true;
options.display = true;
options.eps = 10^-6;
options.maxIter = 20;
options.matFeatLat = [];
n = 100;

% Generating data
matFeatSam = [rand(1,n); rand(1,n)];

% Learning archetypes
[matSamLat, matLatSam_1, ~] = paa_normal(matFeatSam, 4, options);
archetypes = matFeatSam * matSamLat;
axis([0 1 0 1]), box on, set(gca, 'fontsize', 20)

% Computing projections given archetypes
options.matFeatLat = archetypes;
options.display = false;
[~, matLatSam_2, ~] = paa_normal(matFeatSam, [], options);

fprintf('difference between projections %0.6f\n', ...
    norm(archetypes * matLatSam_2 - archetypes * matLatSam_1, 1) / numel(matFeatSam))

alpha 1.00 beta 1.00
[Iteration 1]
[Iteration 2]
[Iteration 3]
[Iteration 4]
[Iteration 5]
[Iteration 6]
[Iteration 7]
[Iteration 8]
[Iteration 9]
[Iteration 10]
[Iteration 11]
[Iteration 12]
[Iteration 13]
[Iteration 14]
[Iteration 15]
[Iteration 16]
[Iteration 17]
[Iteration 18]
[Iteration 19]
[Iteration 20]

alpha 1.00 beta 1.00

difference between projections 0.001373

Normal observation with R interface

close all
rng default,
% Generating data
matFeatSam = [rand(1,n); rand(1,n)];

% Learning archetypes
[matSamLat, matLatSam_1, ~] = classic_aa(matFeatSam, 4);
archetypes = matFeatSam * matSamLat;

% Computing projections given archetypes
matLatSam_2 = classic_aa_test(matFeatSam);

fprintf('difference between projections %0.6f\n', ...
    norm(archetypes * matLatSam_2 - archetypes * matLatSam_1, 1) / numel(matFeatSam))

Loading required package: methods
Loading required package: modeltools
Loading required package: stats4
Loading required package: nnls
R.matlab v3.1.1 (2014-10-10) successfully loaded. See ?R.matlab for help.

Attaching package: 'R.matlab'

The following objects are masked from 'package:base':

    getOption, isOpen


*** k=4, rep=1:

*** k=4, rep=2:

*** k=4, rep=3:

*** k=4, rep=4:

*** k=4, rep=5:

*** k=4, rep=6:

*** k=4, rep=7:

*** k=4, rep=8:

*** k=4, rep=9:

*** k=4, rep=10:
Warning messages:
1: In method(..., k = k[i]) :
  k=4: Error in qr.solve(alphas %*% t(alphas)): singular matrix 'a' in solve

2: In method(..., k = k[i]) :
  k=4: Error in qr.solve(alphas %*% t(alphas)): singular matrix 'a' in solve

Loading required package: methods
Loading required package: modeltools
Loading required package: stats4
Loading required package: nnls
R.matlab v3.1.1 (2014-10-10) successfully loaded. See ?R.matlab for help.

Attaching package: 'R.matlab'

The following objects are masked from 'package:base':

    getOption, isOpen

difference between projections 0.000000

Published with MATLAB® R2014b