/** * @file tests/nca_test.cpp * @author Ryan Curtin * * Unit tests for Neighborhood Components Analysis and related code (including * the softmax error function). * * mlpack is free software; you may redistribute it and/or modify it under the * terms of the 3-clause BSD license. You should have received a copy of the * 3-clause BSD license along with mlpack. If not, see * http://www.opensource.org/licenses/BSD-3-Clause for more information. */ #include #include #include #include #include "catch.hpp" using namespace mlpack; using namespace mlpack::metric; using namespace mlpack::nca; using namespace ens; // // Tests for the SoftmaxErrorFunction // /** * The Softmax error function should return the identity matrix as its initial * point. */ TEST_CASE("SoftmaxInitialPoint", "[NCATesT]") { // Cheap fake dataset. arma::mat data; data.randu(5, 5); arma::Row labels; labels.zeros(5); SoftmaxErrorFunction sef(data, labels); // Verify the initial point is the identity matrix. arma::mat initialPoint = sef.GetInitialPoint(); for (int row = 0; row < 5; row++) { for (int col = 0; col < 5; col++) { if (row == col) REQUIRE(initialPoint(row, col) == Approx(1.0).epsilon(1e-7)); else REQUIRE(initialPoint(row, col) == Approx(0.0).margin(1e-5)); } } } /*** * On a simple fake dataset, ensure that the initial function evaluation is * correct. */ TEST_CASE("SoftmaxInitialEvaluation", "[NCATesT]") { // Useful but simple dataset with six points and two classes. arma::mat data = "-0.1 -0.1 -0.1 0.1 0.1 0.1;" " 1.0 0.0 -1.0 1.0 0.0 -1.0 "; arma::Row labels = " 0 0 0 1 1 1 "; SoftmaxErrorFunction sef(data, labels); double objective = sef.Evaluate(arma::eye(2, 2)); // Result painstakingly calculated by hand by rcurtin (recorded forever in his // notebook). As a result of lack of precision of the by-hand result, the // tolerance is fairly high. REQUIRE(objective == Approx(-1.5115).epsilon(0.0001)); } /** * On a simple fake dataset, ensure that the initial gradient evaluation is * correct. */ TEST_CASE("SoftmaxInitialGradient", "[NCATesT]") { // Useful but simple dataset with six points and two classes. arma::mat data = "-0.1 -0.1 -0.1 0.1 0.1 0.1;" " 1.0 0.0 -1.0 1.0 0.0 -1.0 "; arma::Row labels = " 0 0 0 1 1 1 "; SoftmaxErrorFunction sef(data, labels); arma::mat gradient; arma::mat coordinates = arma::eye(2, 2); sef.Gradient(coordinates, gradient); // Results painstakingly calculated by hand by rcurtin (recorded forever in // his notebook). As a result of lack of precision of the by-hand result, the // tolerance is fairly high. REQUIRE(gradient(0, 0) == Approx(-0.089766).epsilon(0.0005)); REQUIRE(gradient(1, 0) == Approx(0.0).margin(1e-5)); REQUIRE(gradient(0, 1) == Approx(0.0).margin(1e-5)); REQUIRE(gradient(1, 1) == Approx(1.63823).epsilon(0.0001)); } /** * On optimally separated datasets, ensure that the objective function is * optimal (equal to the negative number of points). */ TEST_CASE("SoftmaxOptimalEvaluation", "[NCATesT]") { // Simple optimal dataset. arma::mat data = " 500 500 -500 -500;" " 1 0 1 0 "; arma::Row labels = " 0 0 1 1 "; SoftmaxErrorFunction sef(data, labels); double objective = sef.Evaluate(arma::eye(2, 2)); // Use a very close tolerance for optimality; we need to be sure this function // gives optimal results correctly. REQUIRE(objective == Approx(-4.0).epsilon(1e-12)); } /** * On optimally separated datasets, ensure that the gradient is zero. */ TEST_CASE("SoftmaxOptimalGradient", "[NCATesT]") { // Simple optimal dataset. arma::mat data = " 500 500 -500 -500;" " 1 0 1 0 "; arma::Row labels = " 0 0 1 1 "; SoftmaxErrorFunction sef(data, labels); arma::mat gradient; sef.Gradient(arma::eye(2, 2), gradient); REQUIRE(gradient(0, 0) == Approx(0.0).margin(1e-5)); REQUIRE(gradient(0, 1) == Approx(0.0).margin(1e-5)); REQUIRE(gradient(1, 0) == Approx(0.0).margin(1e-5)); REQUIRE(gradient(1, 1) == Approx(0.0).margin(1e-5)); } /** * Ensure the separable objective function is right. */ TEST_CASE("SoftmaxSeparableObjective", "[NCATesT]") { // Useful but simple dataset with six points and two classes. arma::mat data = "-0.1 -0.1 -0.1 0.1 0.1 0.1;" " 1.0 0.0 -1.0 1.0 0.0 -1.0 "; arma::Row labels = " 0 0 0 1 1 1 "; SoftmaxErrorFunction sef(data, labels); // Results painstakingly calculated by hand by rcurtin (recorded forever in // his notebook). As a result of lack of precision of the by-hand result, the // tolerance is fairly high. arma::mat coordinates = arma::eye(2, 2); REQUIRE(sef.Evaluate(coordinates, 0, 1) == Approx(-0.22480).epsilon(0.0001)); REQUIRE(sef.Evaluate(coordinates, 1, 1) == Approx(-0.30613).epsilon(0.0001)); REQUIRE(sef.Evaluate(coordinates, 2, 1) == Approx(-0.22480).epsilon(0.0001)); REQUIRE(sef.Evaluate(coordinates, 3, 1) == Approx(-0.22480).epsilon(0.0001)); REQUIRE(sef.Evaluate(coordinates, 4, 1) == Approx(-0.30613).epsilon(0.0001)); REQUIRE(sef.Evaluate(coordinates, 5, 1) == Approx(-0.22480).epsilon(0.0001)); } /** * Ensure the optimal separable objective function is right. */ TEST_CASE("OptimalSoftmaxSeparableObjective", "[NCATesT]") { // Simple optimal dataset. arma::mat data = " 500 500 -500 -500;" " 1 0 1 0 "; arma::Row labels = " 0 0 1 1 "; SoftmaxErrorFunction sef(data, labels); arma::mat coordinates = arma::eye(2, 2); // Use a very close tolerance for optimality; we need to be sure this function // gives optimal results correctly. REQUIRE(sef.Evaluate(coordinates, 0, 1) == Approx(-1.0).epsilon(1e-12)); REQUIRE(sef.Evaluate(coordinates, 1, 1) == Approx(-1.0).epsilon(1e-12)); REQUIRE(sef.Evaluate(coordinates, 2, 1) == Approx(-1.0).epsilon(1e-12)); REQUIRE(sef.Evaluate(coordinates, 3, 1) == Approx(-1.0).epsilon(1e-12)); } /** * Ensure the separable gradient is right. */ TEST_CASE("SoftmaxSeparableGradient", "[NCATesT]") { // Useful but simple dataset with six points and two classes. arma::mat data = "-0.1 -0.1 -0.1 0.1 0.1 0.1;" " 1.0 0.0 -1.0 1.0 0.0 -1.0 "; arma::Row labels = " 0 0 0 1 1 1 "; SoftmaxErrorFunction sef(data, labels); arma::mat coordinates = arma::eye(2, 2); arma::mat gradient(2, 2); sef.Gradient(coordinates, 0, gradient, 1); REQUIRE(gradient(0, 0) == Approx(-2.0 * 0.0069708).epsilon(0.0001)); REQUIRE(gradient(0, 1) == Approx(-2.0 * -0.0101707).epsilon(0.0001)); REQUIRE(gradient(1, 0) == Approx(-2.0 * -0.0101707).epsilon(0.0001)); REQUIRE(gradient(1, 1) == Approx(-2.0 * -0.14359).epsilon(0.0001)); sef.Gradient(coordinates, 1, gradient, 1); REQUIRE(gradient(0, 0) == Approx(-2.0 * 0.008496).epsilon(0.0001)); REQUIRE(gradient(0, 1) == Approx(0.0).margin(1e-5)); REQUIRE(gradient(1, 0) == Approx(0.0).margin(1e-5)); REQUIRE(gradient(1, 1) == Approx(-2.0 * -0.12238).epsilon(0.0001)); sef.Gradient(coordinates, 2, gradient, 1); REQUIRE(gradient(0, 0) == Approx(-2.0 * 0.0069708).epsilon(0.0001)); REQUIRE(gradient(0, 1) == Approx(-2.0 * 0.0101707).epsilon(0.0001)); REQUIRE(gradient(1, 0) == Approx(-2.0 * 0.0101707).epsilon(0.0001)); REQUIRE(gradient(1, 1) == Approx(-2.0 * -0.1435886).epsilon(0.0001)); sef.Gradient(coordinates, 3, gradient, 1); REQUIRE(gradient(0, 0) == Approx(-2.0 * 0.0069708).epsilon(0.0001)); REQUIRE(gradient(0, 1) == Approx(-2.0 * 0.0101707).epsilon(0.0001)); REQUIRE(gradient(1, 0) == Approx(-2.0 * 0.0101707).epsilon(0.0001)); REQUIRE(gradient(1, 1) == Approx(-2.0 * -0.1435886).epsilon(0.0001)); sef.Gradient(coordinates, 4, gradient, 1); REQUIRE(gradient(0, 0) == Approx(-2.0 * 0.008496).epsilon(0.0001)); REQUIRE(gradient(0, 1) == Approx(0.0).margin(1e-5)); REQUIRE(gradient(1, 0) == Approx(0.0).margin(1e-5)); REQUIRE(gradient(1, 1) == Approx(-2.0 * -0.12238).epsilon(0.0001)); sef.Gradient(coordinates, 5, gradient, 1); REQUIRE(gradient(0, 0) == Approx(-2.0 * 0.0069708).epsilon(0.0001)); REQUIRE(gradient(0, 1) == Approx(-2.0 * -0.0101707).epsilon(0.0001)); REQUIRE(gradient(1, 0) == Approx(-2.0 * -0.0101707).epsilon(0.0001)); REQUIRE(gradient(1, 1) == Approx(-2.0 * -0.1435886).epsilon(0.0001)); } // // Tests for the NCA algorithm. // /** * On our simple dataset, ensure that the NCA algorithm fully separates the * points. */ TEST_CASE("NCASGDSimpleDataset", "[NCATesT]") { // Useful but simple dataset with six points and two classes. arma::mat data = "-0.1 -0.1 -0.1 0.1 0.1 0.1;" " 1.0 0.0 -1.0 1.0 0.0 -1.0 "; arma::Row labels = " 0 0 0 1 1 1 "; // Huge learning rate because this is so simple. NCA nca(data, labels); nca.Optimizer().StepSize() = 1.2; nca.Optimizer().MaxIterations() = 300000; nca.Optimizer().Tolerance() = 0; nca.Optimizer().Shuffle() = true; arma::mat outputMatrix; nca.LearnDistance(outputMatrix); // Ensure that the objective function is better now. SoftmaxErrorFunction sef(data, labels); double initObj = sef.Evaluate(arma::eye(2, 2)); double finalObj = sef.Evaluate(outputMatrix); arma::mat finalGradient; sef.Gradient(outputMatrix, finalGradient); // finalObj must be less than initObj. REQUIRE(finalObj < initObj); // Verify that final objective is optimal. REQUIRE(finalObj == Approx(-6.0).epsilon(0.00005)); // The solution is not unique, so the best we can do is ensure the gradient // norm is close to 0. REQUIRE(arma::norm(finalGradient, 2) < 1e-4); } TEST_CASE("NCALBFGSSimpleDataset", "[NCATesT]") { // Useful but simple dataset with six points and two classes. arma::mat data = "-0.1 -0.1 -0.1 0.1 0.1 0.1;" " 1.0 0.0 -1.0 1.0 0.0 -1.0 "; arma::Row labels = " 0 0 0 1 1 1 "; // Huge learning rate because this is so simple. NCA nca(data, labels); nca.Optimizer().NumBasis() = 5; arma::mat outputMatrix; nca.LearnDistance(outputMatrix); // Ensure that the objective function is better now. SoftmaxErrorFunction sef(data, labels); double initObj = sef.Evaluate(arma::eye(2, 2)); double finalObj = sef.Evaluate(outputMatrix); arma::mat finalGradient; sef.Gradient(outputMatrix, finalGradient); // finalObj must be less than initObj. REQUIRE(finalObj < initObj); // Verify that final objective is optimal. REQUIRE(finalObj == Approx(-6.0).epsilon(1e-7)); // The solution is not unique, so the best we can do is ensure the gradient // norm is close to 0. REQUIRE(arma::norm(finalGradient, 2) < 1e-6); }