def test_pca_variance_after_trim():
samples = [PointCloud(np.random.randn(10)) for _ in range(10)]
model = PCAModel(samples)
# set number of active components
model.trim_components(5)
# kept variance must be smaller than total variance
assert(model.variance() < model.original_variance())
# kept variance ratio must be smaller than 1.0
assert(model.variance_ratio() < 1.0)
# noise variance must be bigger than 0.0
assert(model.noise_variance() > 0.0)
# noise variance ratio must also be bigger than 0.0
assert(model.noise_variance_ratio() > 0.0)
# inverse noise variance is computable
assert(model.inverse_noise_variance() == 1 / model.noise_variance())
def test_pca_init_from_covariance():
n_samples = 30
n_features = 10
n_dims = 2
centre_values = [True, False]
for centre in centre_values:
# generate samples list and convert it to nd.array
samples = [
PointCloud(np.random.randn(n_features, n_dims))
for _ in range(n_samples)
]
data, template = as_matrix(samples, return_template=True)
# compute covariance matrix and mean
if centre:
mean_vector = np.mean(data, axis=0)
mean = template.from_vector(mean_vector)
X = data - mean_vector
C = np.dot(X.T, X) / (n_samples - 1)
else:
mean = samples[0]
C = np.dot(data.T, data) / (n_samples - 1)
# create the 2 pca models
pca1 = PCAModel.init_from_covariance_matrix(C,
mean,
centred=centre,
n_samples=n_samples)
pca2 = PCAModel(samples, centre=centre)
# compare them
assert_array_almost_equal(pca1.component_vector(0, with_mean=False),
pca2.component_vector(0, with_mean=False))
assert_array_almost_equal(
pca1.component(7).as_vector(),
pca2.component(7).as_vector())
assert_array_almost_equal(pca1.components, pca2.components)
assert_array_almost_equal(pca1.eigenvalues, pca2.eigenvalues)
assert_array_almost_equal(pca1.eigenvalues_cumulative_ratio(),
pca2.eigenvalues_cumulative_ratio())
assert_array_almost_equal(pca1.eigenvalues_ratio(),
pca2.eigenvalues_ratio())
weights = np.random.randn(pca1.n_active_components)
assert_array_almost_equal(
pca1.instance(weights).as_vector(),
pca2.instance(weights).as_vector())
weights2 = np.random.randn(pca1.n_active_components - 4)
assert_array_almost_equal(pca1.instance_vector(weights2),
pca2.instance_vector(weights2))
assert_array_almost_equal(pca1.mean().as_vector(),
pca2.mean().as_vector())
assert_array_almost_equal(pca1.mean_vector, pca2.mean_vector)
assert (pca1.n_active_components == pca2.n_active_components)
assert (pca1.n_components == pca2.n_components)
assert (pca1.n_features == pca2.n_features)
assert (pca1.n_samples == pca2.n_samples)
assert (pca1.noise_variance() == pca2.noise_variance())
assert (pca1.noise_variance_ratio() == pca2.noise_variance_ratio())
assert_almost_equal(pca1.variance(), pca2.variance())
assert_almost_equal(pca1.variance_ratio(), pca2.variance_ratio())
assert_array_almost_equal(pca1.whitened_components(),
pca2.whitened_components())
def test_pca_init_from_covariance():
n_samples = 30
n_features = 10
n_dims = 2
centre_values = [True, False]
for centre in centre_values:
# generate samples list and convert it to nd.array
samples = [PointCloud(np.random.randn(n_features, n_dims))
for _ in range(n_samples)]
data, template = as_matrix(samples, return_template=True)
# compute covariance matrix and mean
if centre:
mean_vector = np.mean(data, axis=0)
mean = template.from_vector(mean_vector)
X = data - mean_vector
C = np.dot(X.T, X) / (n_samples - 1)
else:
mean = samples[0]
C = np.dot(data.T, data) / (n_samples - 1)
# create the 2 pca models
pca1 = PCAModel.init_from_covariance_matrix(C, mean,
centred=centre,
n_samples=n_samples)
pca2 = PCAModel(samples, centre=centre)
# compare them
assert_array_almost_equal(pca1.component_vector(0, with_mean=False),
pca2.component_vector(0, with_mean=False))
assert_array_almost_equal(pca1.component(7).as_vector(),
pca2.component(7).as_vector())
assert_array_almost_equal(pca1.components, pca2.components)
assert_array_almost_equal(pca1.eigenvalues, pca2.eigenvalues)
assert_array_almost_equal(pca1.eigenvalues_cumulative_ratio(),
pca2.eigenvalues_cumulative_ratio())
assert_array_almost_equal(pca1.eigenvalues_ratio(),
pca2.eigenvalues_ratio())
weights = np.random.randn(pca1.n_active_components)
assert_array_almost_equal(pca1.instance(weights).as_vector(),
pca2.instance(weights).as_vector())
weights2 = np.random.randn(pca1.n_active_components - 4)
assert_array_almost_equal(pca1.instance_vector(weights2),
pca2.instance_vector(weights2))
assert_array_almost_equal(pca1.mean().as_vector(),
pca2.mean().as_vector())
assert_array_almost_equal(pca1.mean_vector,
pca2.mean_vector)
assert(pca1.n_active_components == pca2.n_active_components)
assert(pca1.n_components == pca2.n_components)
assert(pca1.n_features == pca2.n_features)
assert(pca1.n_samples == pca2.n_samples)
assert(pca1.noise_variance() == pca2.noise_variance())
assert(pca1.noise_variance_ratio() == pca2.noise_variance_ratio())
assert_almost_equal(pca1.variance(), pca2.variance())
assert_almost_equal(pca1.variance_ratio(), pca2.variance_ratio())
assert_array_almost_equal(pca1.whitened_components(),
pca2.whitened_components())
def test_pca_variance():
samples = [PointCloud(np.random.randn(10)) for _ in range(10)]
model = PCAModel(samples)
# kept variance must be equal to total variance
assert_equal(model.variance(), model.original_variance())
# kept variance ratio must be 1.0
assert_equal(model.variance_ratio(), 1.0)
# noise variance must be 0.0
assert_equal(model.noise_variance(), 0.0)
# noise variance ratio must be also 0.0
assert_equal(model.noise_variance_ratio(), 0.0)
def test_pca_variance():
samples = [PointCloud(np.random.randn(10)) for _ in range(10)]
model = PCAModel(samples)
# kept variance must be equal to total variance
assert_equal(model.variance(), model.original_variance())
# kept variance ratio must be 1.0
assert_equal(model.variance_ratio(), 1.0)
# noise variance must be 0.0
assert_equal(model.noise_variance(), 0.0)
# noise variance ratio must be also 0.0
assert_equal(model.noise_variance_ratio(), 0.0)
