def test_varmat1(self):
X = pd.DataFrame({'x': np.arange(1, 10), 'y': np.arange(2, 11)})
res = variation_matrix(X)
exp = DistanceMatrix(
[[0, 0.032013010420979787 / 2], [0.032013010420979787 / 2, 0]],
ids=['x', 'y'])
self.assertEqual(str(res), str(exp))
def test_varmat1(self):
X = pd.DataFrame({'x': np.arange(1, 10),
'y': np.arange(2, 11)})
res = variation_matrix(X)
exp = DistanceMatrix([[0, 0.032013010420979787 / 2],
[0.032013010420979787 / 2, 0]], ids=['x', 'y'])
self.assertEqual(str(res), str(exp))
def test_varmat_larg(self):
np.random.seed(123)
D = 50
N = 100
mean = np.ones(D) * 10
cov = np.eye(D)
n__ = np.random.multivariate_normal(mean, cov, size=N)
X = pd.DataFrame(np.abs(n__), columns=np.arange(D).astype(np.str))
res = variation_matrix(X)
exp = DistanceMatrix.read(get_data_path('exp_varmat.txt'))
self.assertEqual(str(res), str(exp))
def test_varmat_larg(self):
np.random.seed(123)
D = 50
N = 100
mean = np.ones(D)*10
cov = np.eye(D)
X = pd.DataFrame(np.abs(np.random.multivariate_normal(mean, cov,
size=N)),
columns=np.arange(D).astype(np.str))
res = variation_matrix(X)
exp = DistanceMatrix.read(get_data_path('exp_varmat.txt'))
self.assertEqual(str(res), str(exp))
def proportional_linkage(X, method='ward'):
r"""
Principal Balance Analysis using Hierarchical Clustering
based on proportionality.
The hierarchy is built based on the proportionality between
any two pairs of features. Specifically the proportionality between
two features :math:`x` and :math:`y` is measured by
.. math::
p(x, y) = var (\ln \frac{x}{y})
If :math:`p(x, y)` is very small, then :math:`x` and :math:`y`
are said to be highly proportional. A hierarchical clustering is
then performed using this proportionality as a distance metric.
Parameters
----------
X : pd.DataFrame
Contingency table where the samples are rows and the features
are columns.
method : str
Clustering method. (default='ward')
Returns
-------
skbio.TreeNode
Tree generated from principal balance analysis.
References
----------
.. [1] Pawlowsky-Glahn V, Egozcue JJ, and Tolosana-Delgado R.
Principal Balances (2011).
Examples
--------
>>> import pandas as pd
>>> from gneiss.cluster import proportional_linkage
>>> table = pd.DataFrame([[1, 1, 0, 0, 0],
... [0, 1, 1, 0, 0],
... [0, 0, 1, 1, 0],
... [0, 0, 0, 1, 1]],
... columns=['s1', 's2', 's3', 's4', 's5'],
... index=['o1', 'o2', 'o3', 'o4']).T
>>> tree = proportional_linkage(table+0.1)
"""
dm = variation_matrix(X)
lm = linkage(dm.condensed_form(), method=method)
return TreeNode.from_linkage_matrix(lm, X.columns)
def correlation_linkage(X, method='ward'):
r"""
Hierarchical Clustering based on proportionality.
The hierarchy is built based on the correlationity between
any two pairs of features. Specifically the correlation between
two features :math:`x` and :math:`y` is measured by
.. math::
p(x, y) = var (\ln \frac{x}{y})
If :math:`p(x, y)` is very small, then :math:`x` and :math:`y`
are said to be highly correlation. A hierarchical clustering is
then performed using this correlation as a distance metric.
This can be useful for constructing principal balances [1]_.
Parameters
----------
X : pd.DataFrame
Contingency table where the samples are rows and the features
are columns.
method : str
Clustering method. (default='ward')
Returns
-------
skbio.TreeNode
Tree for constructing principal balances.
References
----------
.. [1] Pawlowsky-Glahn V, Egozcue JJ, and Tolosana-Delgado R.
Principal Balances (2011).
Examples
--------
>>> import pandas as pd
>>> from gneiss.cluster import correlation_linkage
>>> table = pd.DataFrame([[1, 1, 0, 0, 0],
... [0, 1, 1, 0, 0],
... [0, 0, 1, 1, 0],
... [0, 0, 0, 1, 1]],
... columns=['s1', 's2', 's3', 's4', 's5'],
... index=['o1', 'o2', 'o3', 'o4']).T
>>> tree = correlation_linkage(table+0.1)
>>> print(tree.ascii_art())
/-o1
/y1------|
| \-o2
-y0------|
| /-o3
\y2------|
\-o4
"""
dm = variation_matrix(X)
lm = linkage(dm.condensed_form(), method=method)
t = TreeNode.from_linkage_matrix(lm, X.columns)
t = rename_internal_nodes(t)
return t