[mlpack] 196/324: Add test for the nystroem method.
Barak A. Pearlmutter
barak+git at cs.nuim.ie
Sun Aug 17 08:22:10 UTC 2014
This is an automated email from the git hooks/post-receive script.
bap pushed a commit to branch svn-trunk
in repository mlpack.
commit 81ad58f32313bf640012545574614b6f82c5855e
Author: marcus <marcus at 9d5b8971-822b-0410-80eb-d18c1038ef23>
Date: Fri Jul 18 22:02:38 2014 +0000
Add test for the nystroem method.
git-svn-id: http://svn.cc.gatech.edu/fastlab/mlpack/trunk@16838 9d5b8971-822b-0410-80eb-d18c1038ef23
---
src/mlpack/tests/data/german.csv | 1000 +++++++++++++++++++++++++++++
src/mlpack/tests/nystroem_method_test.cpp | 182 ++++++
2 files changed, 1182 insertions(+)
diff --git a/src/mlpack/tests/data/german.csv b/src/mlpack/tests/data/german.csv
new file mode 100644
index 0000000..4753ec7
--- /dev/null
+++ b/src/mlpack/tests/data/german.csv
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+2,21,3,24,1,3,1,4,2,47,3,2,1,1,1,1,0,1,0,0,1,0,0,1
+4,15,2,36,5,3,3,2,4,29,3,1,1,1,1,1,0,1,0,0,1,0,0,1
+4,24,2,24,3,5,3,2,3,35,1,2,1,2,1,0,0,1,0,0,1,0,0,1
+2,6,2,5,1,2,4,1,2,22,3,1,1,1,1,0,0,1,0,0,1,0,1,0
+2,30,2,17,5,3,2,1,3,26,3,1,1,1,1,0,0,1,0,0,1,0,0,1
+2,27,4,25,3,3,3,2,2,23,3,2,1,1,1,0,0,1,0,0,1,0,1,0
+4,15,2,36,1,5,2,2,3,54,1,1,1,2,1,0,0,1,0,1,0,0,0,0
+4,42,2,72,5,4,4,4,2,29,3,1,1,2,1,0,0,1,0,1,0,0,0,1
+1,11,4,39,1,3,3,2,1,40,3,2,2,1,1,1,0,1,0,0,1,0,1,0
+2,15,2,15,2,3,3,2,1,22,3,1,1,1,1,0,0,0,0,0,1,0,0,1
+4,24,2,74,1,3,3,4,2,43,3,1,2,1,1,1,0,1,0,0,1,0,1,0
+1,24,1,12,1,1,2,4,4,29,3,2,1,1,1,1,0,0,1,1,0,1,0,0
+1,60,2,73,1,5,3,4,4,36,3,1,1,1,1,0,0,0,1,1,0,0,0,1
+4,30,4,28,1,3,2,2,3,33,3,1,1,2,1,0,0,1,0,0,1,0,0,1
+3,24,2,13,3,3,2,3,3,57,3,1,1,1,1,0,0,1,0,0,1,0,1,0
+2,6,2,8,1,3,2,3,1,64,3,1,1,1,1,0,0,0,0,0,1,0,0,1
+2,18,3,24,5,5,3,2,2,42,3,2,1,1,1,0,0,1,0,0,1,0,0,1
+4,24,3,25,1,5,3,4,3,47,3,2,2,1,1,1,0,1,0,0,1,0,1,0
+2,15,1,13,2,3,4,2,2,25,3,1,1,1,1,1,0,1,0,1,0,0,0,1
+2,30,4,84,1,4,3,2,2,49,3,1,1,1,1,0,0,1,0,0,1,0,0,1
+4,48,2,48,1,1,3,2,3,33,1,1,1,2,1,0,0,1,0,1,0,0,0,0
+3,21,2,29,2,3,2,1,3,28,1,1,1,2,1,1,0,1,0,0,1,0,0,0
+1,36,2,82,1,3,3,2,2,26,3,1,2,1,1,0,1,1,0,0,1,0,0,1
+4,24,4,20,1,4,3,2,2,30,3,2,1,1,1,0,0,1,0,0,1,0,1,0
+1,15,4,14,1,3,2,3,2,25,3,2,1,1,1,0,0,1,0,1,0,0,0,1
+3,42,0,63,1,2,1,1,2,33,3,2,1,1,1,0,0,1,0,0,1,0,0,1
+4,13,2,14,2,1,2,4,1,64,3,1,1,1,1,0,0,1,0,0,1,0,0,1
+1,24,2,66,1,1,3,2,4,29,3,1,1,2,1,0,1,1,0,0,0,0,0,0
+2,24,4,17,1,5,3,2,2,48,3,2,1,1,1,0,0,1,0,0,1,0,1,0
+4,12,4,36,5,2,3,1,2,37,3,2,2,1,1,0,0,1,0,0,1,0,1,0
+4,15,1,16,2,5,3,4,3,34,1,1,2,1,1,0,0,1,0,0,1,0,1,0
+1,18,2,19,5,4,4,4,3,23,3,2,1,1,1,0,0,1,0,1,0,0,1,0
+1,36,2,40,1,1,3,3,2,30,3,1,1,2,1,0,0,1,0,0,1,0,0,0
+4,12,2,24,5,5,3,3,3,50,3,1,1,2,1,1,0,1,0,0,1,0,0,1
+4,12,2,17,1,4,2,4,1,31,3,1,1,1,1,0,0,1,0,0,1,0,1,0
+1,30,2,39,1,3,1,4,2,40,3,1,1,2,1,0,1,1,0,0,1,0,0,0
+4,12,2,8,1,5,3,4,3,38,3,1,1,1,1,0,0,1,0,0,1,0,0,1
+1,45,2,18,1,3,3,4,4,23,3,1,1,2,1,0,0,1,0,0,0,0,0,1
+2,45,4,46,2,1,3,4,3,27,3,1,1,1,1,0,1,1,0,0,1,0,0,1
diff --git a/src/mlpack/tests/nystroem_method_test.cpp b/src/mlpack/tests/nystroem_method_test.cpp
new file mode 100644
index 0000000..55d90f8
--- /dev/null
+++ b/src/mlpack/tests/nystroem_method_test.cpp
@@ -0,0 +1,182 @@
+/**
+ * @file nystroem_method_test.cpp
+ * @author Ryan Curtin
+ *
+ * Test the NystroemMethod class and ensure that the reconstructed kernel matrix
+ * errors are comparable with those in the literature.
+ */
+#include <mlpack/core.hpp>
+
+#include <boost/test/unit_test.hpp>
+#include "old_boost_test_definitions.hpp"
+
+#include <mlpack/methods/nystroem_method/ordered_selection.hpp>
+#include <mlpack/methods/nystroem_method/random_selection.hpp>
+#include <mlpack/methods/nystroem_method/kmeans_selection.hpp>
+#include <mlpack/methods/nystroem_method/nystroem_method.hpp>
+
+using namespace mlpack;
+using namespace mlpack::kernel;
+
+BOOST_AUTO_TEST_SUITE(NystroemMethodTest);
+
+/**
+ * Make sure that if the rank is the same and we do a full-rank approximation,
+ * the result is virtually identical (a little bit of tolerance for floating
+ * point error).
+ */
+BOOST_AUTO_TEST_CASE(FullRankTest)
+{
+ // Run several trials.
+ for (size_t trial = 0; trial < 5; ++trial)
+ {
+ arma::mat data;
+ data.randu(5, trial * 200);
+
+ GaussianKernel gk;
+ NystroemMethod<GaussianKernel, OrderedSelection> nm(data, gk, trial * 200);
+
+ arma::mat g;
+ nm.Apply(g);
+
+ // Construct exact kernel matrix.
+ arma::mat kernel(trial * 200, trial * 200);
+ for (size_t i = 0; i < trial * 200; ++i)
+ for (size_t j = 0; j < trial * 200; ++j)
+ kernel(i, j) = gk.Evaluate(data.col(i), data.col(j));
+
+ // Reconstruct approximation.
+ arma::mat approximation = g * g.t();
+
+ // Check closeness.
+ for (size_t i = 0; i < trial * 200; ++i)
+ {
+ for (size_t j = 0; j < trial * 200; ++j)
+ {
+ if (kernel(i, j) < 1e-5)
+ BOOST_REQUIRE_SMALL(approximation(i, j), 1e-4);
+ else
+ BOOST_REQUIRE_CLOSE(kernel(i, j), approximation(i, j), 1e-5);
+ }
+ }
+ }
+}
+
+/**
+ * Can we accurately represent a rank-10 matrix?
+ */
+BOOST_AUTO_TEST_CASE(Rank10Test)
+{
+ arma::mat data;
+ data.randu(500, 500); // Just so it's square.
+
+ // Use SVD and only keep the first ten singular vectors.
+ arma::mat U;
+ arma::vec s;
+ arma::mat V;
+ arma::svd(U, s, V, data);
+
+ // Don't set completely to 0; the hope is that K is still positive definite.
+ s.subvec(10, s.n_elem - 1).fill(1e-10);
+ arma::mat dataMod = U * arma::diagmat(s) * V.t();
+
+ // Add some noise.
+ dataMod += 1e-5 * arma::randu<arma::mat>(dataMod.n_rows, dataMod.n_cols);
+
+ // Calculate the true kernel matrix.
+ LinearKernel lk;
+ arma::mat kernel = dataMod.t() * dataMod;
+
+ // Now use the linear kernel to get a Nystroem approximation; try this several
+ // times.
+ double normalizedFroAverage = 0.0;
+ for (size_t trial = 0; trial < 20; ++trial)
+ {
+ LinearKernel lk;
+ NystroemMethod<LinearKernel, RandomSelection> nm(dataMod, lk, 10);
+
+ arma::mat g;
+ nm.Apply(g);
+
+ arma::mat approximation = g * g.t();
+
+ // Check the normalized Frobenius norm.
+ const double normalizedFro = arma::norm(kernel - approximation, "fro") /
+ arma::norm(kernel, "fro");
+
+ normalizedFroAverage += normalizedFro;
+ }
+
+ normalizedFroAverage /= 20;
+ BOOST_REQUIRE_SMALL(normalizedFroAverage, 1e-3);
+}
+
+/**
+ * Can we reproduce the results in Zhang, Tsang, and Kwok (2008)?
+ * They provide the following test points (approximately) in their experiments
+ * in Section 4.1, for the german dataset:
+ *
+ * rank = 0.02n; approximation error: ~27
+ * rank = 0.04n; approximation error: ~15
+ * rank = 0.06n; approximation error: ~10
+ * rank = 0.08n; approximation error: ~7
+ * rank = 0.10n; approximation error: ~3
+ */
+BOOST_AUTO_TEST_CASE(GermanTest)
+{
+ // Load the dataset.
+ arma::mat dataset;
+ data::Load("german.csv", dataset, true);
+
+ // These are our tolerance bounds.
+ double results[5] = { 32.0, 20.0, 15.0, 12.0, 9.0 };
+
+ // The bandwidth of the kernel is selected to be the half the average
+ // distance between each point and the mean of the dataset. This isn't
+ // _exactly_ what the paper says, but I've modified what it said because our
+ // formulation of what the Gaussian kernel is is different.
+ GaussianKernel gk(16.461);
+
+ // Calculate the true kernel matrix.
+ arma::mat kernel(dataset.n_cols, dataset.n_cols);
+ for (size_t i = 0; i < dataset.n_cols; ++i)
+ for (size_t j = 0; j < dataset.n_cols; ++j)
+ kernel(i, j) = gk.Evaluate(dataset.col(i), dataset.col(j));
+
+ for (size_t trial = 0; trial < 5; ++trial)
+ {
+ // We will repeat each trial 20 times.
+ double avgError = 0.0;
+ for (size_t z = 0; z < 20; ++z)
+ {
+ NystroemMethod<GaussianKernel, KMeansSelection<> > nm(dataset, gk,
+ size_t((double((trial + 1) * 2) / 100.0) * dataset.n_cols));
+ arma::mat g;
+ nm.Apply(g);
+
+ // Reconstruct kernel matrix.
+ arma::mat approximation = g * g.t();
+
+ const double error = arma::norm(kernel - approximation, "fro");
+ if (error != error)
+ {
+ // Sometimes K' is singular. Unlucky.
+ --z;
+ continue;
+ }
+ else
+ {
+ Log::Debug << "Trial " << trial << ": error " << error << ".\n";
+ avgError += arma::norm(kernel - approximation, "fro");
+ }
+ }
+
+ avgError /= 20;
+
+ // Ensure that this is within tolerance, which is at least as good as the
+ // paper's results (plus a little bit for noise).
+ BOOST_REQUIRE_SMALL(avgError, results[trial]);
+ }
+}
+
+BOOST_AUTO_TEST_SUITE_END();
--
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