def plot_samples_distance(dataset, sortbyattr=None):
"""Plot the euclidean distances between all samples of a dataset.
Parameters
----------
dataset : Dataset
Providing the samples.
sortbyattr : None or str
If None, the samples distances will be in the same order as their
appearance in the dataset. Alternatively, the name of a samples
attribute can be given, which wil then be used to sort/group the
samples, e.g. to investigate the similarity samples by label or by
chunks.
"""
if sortbyattr is not None:
slicer = []
for attr in dataset.sa[sortbyattr].unique:
slicer += \
get_samples_by_attr(dataset, sortbyattr, attr).tolist()
samples = dataset.samples[slicer]
else:
samples = dataset.samples
ed = np.sqrt(squared_euclidean_distance(samples))
pl.imshow(ed, interpolation='nearest')
pl.colorbar()
def test_euclid_dist(self):
"""Euclidean distance kernel testing"""
# select some block of data from already generated
data = datasets['uni4large'].samples[:5, :8]
ed = squared_euclidean_distance(data)
# XXX not sure if that is right: 'weight' seems to be given by
# feature (i.e. column), but distance is between samples (i.e. rows)
# current behavior is:
true_size = (5, 5)
self.assertTrue(ed.shape == true_size)
# slow version to compute distance matrix
ed_manual = np.zeros(true_size, 'd')
for i in range(true_size[0]):
for j in range(true_size[1]):
#ed_manual[i,j] = np.sqrt(((data[i,:] - data[j,:] )** 2).sum())
ed_manual[i,j] = ((data[i,:] - data[j,:] )** 2).sum()
ed_manual[ed_manual < 0] = 0
self.assertTrue(np.diag(ed_manual).sum() < 0.0000000001)
self.assertTrue(np.diag(ed).sum() < 0.0000000001)
# let see whether Kernel does the same
self.assertTrue((ed - ed_manual).sum() < 0.0000001)
def test_euclid_dist(self):
"""Euclidean distance kernel testing"""
# select some block of data from already generated
data = datasets['uni4large'].samples[:5, :8]
ed = squared_euclidean_distance(data)
# XXX not sure if that is right: 'weight' seems to be given by
# feature (i.e. column), but distance is between samples (i.e. rows)
# current behavior is:
true_size = (5, 5)
self.assertTrue(ed.shape == true_size)
# slow version to compute distance matrix
ed_manual = np.zeros(true_size, 'd')
for i in range(true_size[0]):
for j in range(true_size[1]):
#ed_manual[i,j] = np.sqrt(((data[i,:] - data[j,:] )** 2).sum())
ed_manual[i, j] = ((data[i, :] - data[j, :])**2).sum()
ed_manual[ed_manual < 0] = 0
self.assertTrue(np.diag(ed_manual).sum() < 0.0000000001)
self.assertTrue(np.diag(ed).sum() < 0.0000000001)
# let see whether Kernel does the same
self.assertTrue((ed - ed_manual).sum() < 0.0000001)
def _compute(self, data1, data2):
"""Compute kernel matrix.
Parameters
----------
data1 : numpy.ndarray
lhs data
data2 : numpy.ndarray
rhs data
"""
tmp = squared_euclidean_distance(
data1, data2, weight=1.0 / (self.length_scale ** 2))
self._k = \
self.sigma_f**2 * (1.0 + tmp / (2.0 * self.alpha)) ** -self.alpha
def _compute(self, data1, data2):
"""Compute kernel matrix.
Parameters
----------
data1 : numpy.ndarray
data
data2 : numpy.ndarray
data
(Defaults to None)
"""
# weighted squared euclidean distance matrix:
self.wdm2 = squared_euclidean_distance(data1, data2, weight=(self.length_scale**-2))
self._k = self.sigma_f**2 * np.exp(-0.5*self.wdm2)
def _compute(self, data1, data2):
"""Compute kernel matrix.
Parameters
----------
data1 : numpy.ndarray
lhs data
data2 : numpy.ndarray
rhs data
"""
tmp = squared_euclidean_distance(data1,
data2,
weight=1.0 / (self.length_scale**2))
self._k = \
self.sigma_f**2 * (1.0 + tmp / (2.0 * self.alpha)) ** -self.alpha
def _compute(self, data1, data2):
"""Compute kernel matrix.
Parameters
----------
data1 : numpy.ndarray
data
data2 : numpy.ndarray
data
(Defaults to None)
"""
# weighted squared euclidean distance matrix:
self.wdm2 = squared_euclidean_distance(data1,
data2,
weight=(self.length_scale**-2))
self._k = self.sigma_f**2 * np.exp(-0.5 * self.wdm2)
def _compute(self, data1, data2):
"""Compute kernel matrix.
Parameters
----------
data1 : numpy.ndarray
lhs data
data2 : numpy.ndarray
rhs data
"""
params = self.params
# XXX the following computation can be (maybe) made more
# efficient since length_scale is squared and then
# square-rooted uselessly.
# Weighted euclidean distance matrix:
self.wdm = np.sqrt(squared_euclidean_distance(
data1, data2, weight=(params.length_scale**-2)))
self._k = \
params.sigma_f**2 * np.exp(-self.wdm)
def _compute(self, data1, data2):
"""Compute kernel matrix.
Parameters
----------
data1 : numpy.ndarray
lhs data
data2 : numpy.ndarray
rhs data
"""
params = self.params
# XXX the following computation can be (maybe) made more
# efficient since length_scale is squared and then
# square-rooted uselessly.
# Weighted euclidean distance matrix:
self.wdm = np.sqrt(
squared_euclidean_distance(data1,
data2,
weight=(params.length_scale**-2)))
self._k = \
params.sigma_f**2 * np.exp(-self.wdm)
def _compute(self, data1, data2):
"""Compute kernel matrix.
Parameters
----------
data1 : numpy.ndarray
lhs data
data2 : numpy.ndarray
rhs data
"""
tmp = squared_euclidean_distance(
data1, data2, weight=0.5 / (self.length_scale ** 2))
if self.numerator == 3.0:
tmp = np.sqrt(tmp)
self._k = \
self.sigma_f**2 * (1.0 + np.sqrt(3.0) * tmp) \
* np.exp(-np.sqrt(3.0) * tmp)
elif self.numerator == 5.0:
tmp2 = np.sqrt(tmp)
self._k = \
self.sigma_f**2 * (1.0 + np.sqrt(5.0) * tmp2 + 5.0 / 3.0 * tmp) \
* np.exp(-np.sqrt(5.0) * tmp2)
def _compute(self, data1, data2):
"""Compute kernel matrix.
Parameters
----------
data1 : numpy.ndarray
lhs data
data2 : numpy.ndarray
rhs data
"""
tmp = squared_euclidean_distance(data1,
data2,
weight=0.5 / (self.length_scale**2))
if self.numerator == 3.0:
tmp = np.sqrt(tmp)
self._k = \
self.sigma_f**2 * (1.0 + np.sqrt(3.0) * tmp) \
* np.exp(-np.sqrt(3.0) * tmp)
elif self.numerator == 5.0:
tmp2 = np.sqrt(tmp)
self._k = \
self.sigma_f**2 * (1.0 + np.sqrt(5.0) * tmp2 + 5.0 / 3.0 * tmp) \
* np.exp(-np.sqrt(5.0) * tmp2)
def _compute(self, d1, d2):
# Do the Rbf
self._k = np.exp(-squared_euclidean_distance(d1,d2) / self.params.sigma)
def _compute(self, d1, d2):
# Do the Rbf
self._k = np.exp(-squared_euclidean_distance(d1, d2) /
self.params.sigma)
