void PCATestCase::decorrelation()
{
OpenANN::RandomNumberGenerator rng;
const int N = 100;
const int D = 2;
Eigen::MatrixXd X(N, D);
rng.fillNormalDistribution(X);
// Linear transformation (correlation)
Eigen::MatrixXd A(D, D);
A << 1.0, 0.5, 0.5, 2.0;
Eigen::MatrixXd Xt = X * A.transpose();
// Decorrelation (without dimensionality reduction)
OpenANN::PCA pca(D);
pca.fit(Xt);
Eigen::MatrixXd Y = pca.transform(Xt);
// Covariance matrix should be identity matrix
Eigen::MatrixXd cov = Y.transpose() * Y;
ASSERT_EQUALS_DELTA(cov(0, 0), (double) N, 1e-5);
ASSERT_EQUALS_DELTA(cov(1, 1), (double) N, 1e-5);
ASSERT_EQUALS_DELTA(cov(0, 1), 0.0, 1e-5);
ASSERT_EQUALS_DELTA(cov(1, 0), 0.0, 1e-5);
Eigen::VectorXd evr = pca.explainedVarianceRatio();
double evrSum = evr.sum();
ASSERT_EQUALS_DELTA(evrSum, 1.0, 1e-5);
}
void KMeansTestCase::clustering()
{
const int N = 1000;
const int D = 10;
Eigen::MatrixXd X(N, D);
OpenANN::RandomNumberGenerator rng;
rng.fillNormalDistribution(X);
OpenANN::KMeans kmeans(D, 5);
const int batchSize = 200;
double averageDistToCenter = std::numeric_limits<double>::max();
for(int i = 0; i < N/batchSize; i++)
{
// Data points will be closer to centers after each update
Eigen::MatrixXd Y = kmeans.fitPartial(X.block(i*batchSize, 0, batchSize, D)).transform(X);
const double newDistance = Y.array().rowwise().maxCoeff().sum();
ASSERT(newDistance < averageDistToCenter);
averageDistToCenter = newDistance;
}
}
void PCATestCase::dimensionalityReduction()
{
OpenANN::RandomNumberGenerator rng;
const int N = 100;
const int D = 5;
Eigen::MatrixXd X(N, D);
rng.fillNormalDistribution(X);
// Strong correlation
Eigen::MatrixXd A = Eigen::MatrixXd::Identity(D, D) * 0.5 +
Eigen::MatrixXd::Ones(D, D);
Eigen::MatrixXd Xt = X * A.transpose();
// Dimensionality reduction
OpenANN::PCA pca(1);
pca.fit(Xt);
Eigen::MatrixXd Y = pca.transform(Xt);
ASSERT_EQUALS(Y.rows(), N);
ASSERT_EQUALS(Y.cols(), 1);
ASSERT_EQUALS(pca.explainedVarianceRatio().rows(), 1);
ASSERT(pca.explainedVarianceRatio().sum() > 0.9);
}