def test_knn_density(self):
"""
Test correctness of the knn density estimator in the DeBaCl utilities.
Tests the estimated value at a single arbitrary point.
"""
# Input parameters
r_k = np.array([1.])
n = 100
p = 2
k = 5.
# Correct density estimate
unit_ball_volume = np.pi**(p / 2.) / spspec.gamma(1 + p / 2.0)
normalizer = k / (n * unit_ball_volume)
answer = normalizer / (r_k**p)
# DeBaCl knn density utility
fhat = utl.knn_density(r_k, n, p, k)
self.assertEqual(fhat, answer)
## Check that undefined density estimates raise an error.
with self.assertRaises(ArithmeticError):
r_k = np.array([10., 10.])
fhat = utl.knn_density(r_k, n=1000, p=350, k=10)
def test_knn_density(self):
"""
Test correctness of the knn density estimator in the DeBaCl utilities.
Tests the estimated value at a single arbitrary point.
"""
# Input parameters
r_k = np.array([1.])
n = 100
p = 2
k = 5.
# Correct density estimate
unit_ball_volume = np.pi**(p / 2.) / spspec.gamma(1 + p / 2.0)
normalizer = k / (n * unit_ball_volume)
answer = normalizer / (r_k**p)
# DeBaCl knn density utility
fhat = utl.knn_density(r_k, n, p, k)
self.assertEqual(fhat, answer)
## Check that undefined density estimates raise an error.
with self.assertRaises(ArithmeticError):
r_k = np.array([10., 10.])
fhat = utl.knn_density(r_k, n=1000, p=350, k=10)
def construct_tree(X, k, prune_threshold=None, num_levels=None, verbose=False):
"""
Construct a level set tree from tabular data.
Parameters
----------
X : 2-dimensional numpy array
Numeric dataset, where each row represents one observation.
k : int
Number of observations to consider as neighbors to a given point.
prune_threshold : int, optional
Leaf nodes with fewer than this number of members are recursively
merged into larger nodes. If 'None' (the default), then no pruning
is performed.
num_levels : int, optional
Number of density levels in the constructed tree. If None (default),
`num_levels` is internally set to be the number of rows in `X`.
verbose : bool, optional
If True, a progress indicator is printed at every 100th level of tree
construction.
Returns
-------
T : LevelSetTree
A pruned level set tree.
See Also
--------
construct_tree_from_graph, LevelSetTree
Examples
--------
>>> X = numpy.random.rand(100, 2)
>>> tree = debacl.construct_tree(X, k=8, prune_threshold=5)
>>> print tree
+----+-------------+-----------+------------+----------+------+--------+----------+
| id | start_level | end_level | start_mass | end_mass | size | parent | children |
+----+-------------+-----------+------------+----------+------+--------+----------+
| 0 | 0.000 | 0.870 | 0.000 | 0.450 | 100 | None | [3, 4] |
| 3 | 0.870 | 3.364 | 0.450 | 0.990 | 17 | 0 | [] |
| 4 | 0.870 | 1.027 | 0.450 | 0.520 | 35 | 0 | [7, 8] |
| 7 | 1.027 | 1.755 | 0.520 | 0.870 | 8 | 4 | [] |
| 8 | 1.027 | 3.392 | 0.520 | 1.000 | 23 | 4 | [] |
+----+-------------+-----------+------------+----------+------+--------+----------+
"""
sim_graph, radii = _utl.knn_graph(X, k, method='brute_force')
n, p = X.shape
density = _utl.knn_density(radii, n, p, k)
tree = construct_tree_from_graph(adjacency_list=sim_graph, density=density,
prune_threshold=prune_threshold,
num_levels=num_levels, verbose=verbose)
return tree
def test_knn_density(self):
"""
Test correctness of the knn density estimator in the DeBaCl utilities.
Tests the estimated value at a single arbitrary point.
"""
# Input parameters
r_k = 1.
n = 100
p = 2
k = 5.
# Correct density estimate
unit_ball_volume = np.pi**(p / 2.) / spspec.gamma(1 + p / 2.0)
normalizer = k / (n * unit_ball_volume)
answer = normalizer / (r_k**p)
# DeBaCl knn density utility
fhat = utl.knn_density(r_k, n, p, k)
self.assertEqual(fhat, answer)
def test_knn_density(self):
"""
Test correctness of the knn density estimator in the DeBaCl utilities.
Tests the estimated value at a single arbitrary point.
"""
# Input parameters
r_k = 1.
n = 100
p = 2
k = 5.
# Correct density estimate
unit_ball_volume = np.pi**(p / 2.) / spspec.gamma(1 + p / 2.0)
normalizer = k / (n * unit_ball_volume)
answer = normalizer / (r_k**p)
# DeBaCl knn density utility
fhat = utl.knn_density(r_k, n, p, k)
self.assertEqual(fhat, answer)
