def test_simmetry_of_aligment(self):
"""Check registration using inverse composition"""
reg = ElasticRegistration(template=self.template)
reg.fit_transform(self.unimodal_samples)
warping = reg.warping_
inverse = invert_warping(warping)
register = self.template_rep.compose(inverse)
distances = np.diag(metric(self.unimodal_samples, register))
np.testing.assert_allclose(distances, 0, atol=12e-3)
def test_one_to_one_alignment(self):
"""Test alignment to 1 sample to a template"""
reg = ElasticRegistration(template=self.template)
register = reg.fit_transform(self.unimodal_samples[0])
distances = metric(self.template, register)
np.testing.assert_allclose(distances, 0, atol=12e-3)
def test_set_alignment(self):
"""Test alignment 3 curves to set with 3 templates"""
# Should give same result than test_template_alignment
reg = ElasticRegistration(template=self.template_rep)
register = reg.fit_transform(self.unimodal_samples)
distances = metric(self.template, register)
np.testing.assert_allclose(distances, 0, atol=12e-3)
def test_raises(self):
reg = ElasticRegistration()
# X not in fit, but template is not an FDataGrid
with np.testing.assert_raises(ValueError):
reg.fit()
# Inverse transform without previous transform
with np.testing.assert_raises(ValueError):
reg.inverse_transform(self.unimodal_samples)
# Inverse transform with different number of samples than transform
reg.fit_transform(self.unimodal_samples)
with np.testing.assert_raises(ValueError):
reg.inverse_transform(self.unimodal_samples[0])
# FDataGrid as template with n != 1 and n!= n_samples to transform
reg = ElasticRegistration(template=self.unimodal_samples).fit()
with np.testing.assert_raises(ValueError):
reg.transform(self.unimodal_samples[0])
def test_callable_alignment(self):
"""Test alignment by default"""
# Should give same result than test_template_alignment
reg = ElasticRegistration(template=elastic_mean)
register = reg.fit_transform(self.unimodal_samples)
values = register([-.25, -.1, 0, .1, .25])
expected = [[[0.599058], [0.997427], [0.772248],
[0.412342], [0.064725]],
[[0.626875], [0.997155], [0.791649],
[0.382181], [0.050098]],
[[0.620992], [0.997369], [0.785886],
[0.376556], [0.048804]]]
np.testing.assert_allclose(values, expected, atol=1e-4)
############################################################################## # In this example :math:`g` will be used as template and :math:`f` will be # aligned to it. In the following figure it is shown the result of the # registration process, wich can be computed using # :class:`~skfda.preprocessing.registration.ElasticRegistration`. # f, g = fd[0], fd[1] elastic_registration = ElasticRegistration(template=g) # Aligns f to g f_align = elastic_registration.fit_transform(f) fig = fd.plot() f_align.plot(fig=fig, color='C0', linestyle='--') # Legend fig.axes[0].legend(['$f$', '$g$', '$f \\circ \\gamma $']) ############################################################################## # The non-linear transformation :math:`\gamma` applied to :math:`f` in # the alignment is stored in the attribute `warping_`. # # Warping used in the last transformation
# It can be seen how the elastic mean better captures the geometry of the # curves compared to the standard mean, since it is not affected by the # deformations of the curves. fig = fd.mean().plot(label="L2 mean") elastic_mean(fd).plot(fig=fig, label="Elastic mean") fig.legend() ############################################################################## # In this case, the alignment completely reduces the amplitude variability # between the samples, aligning the maximum points correctly. elastic_registration = ElasticRegistration() fd_align = elastic_registration.fit_transform(fd) fd_align.plot() ############################################################################## # In general these type of alignments are not possible, in the following # figure it is shown how it works with a real dataset. # The :func:`berkeley growth dataset<skfda.datasets.fetch_growth>` # contains the growth curves of a set children, in this case will be used only # the males. The growth curves will be resampled using cubic interpolation and # derived to obtain the velocity curves. # # First we show the original curves: growth = fetch_growth()