def witness(
features: np.ndarray, sample_size: int = 64, gamma: Optional[float] = None) \
-> Tuple[np.ndarray, np.ndarray]:
"""Compute the persistence intervals for the dataset of features using the witness complex.
Args:
features: Array with shape (N_samples, data_dim) representing the dataset.
sample_size: Number of landmarks to use on each iteration.
gamma: Parameter determining maximum persistence value. Default is `1.0 / 128 * N_imgs / 5000`
Returns
A list of persistence intervals and the maximal persistence value.
"""
N = features.shape[0]
if gamma is None:
gamma = 1.0 / 128 * N / 5000
# Randomly sample `sample_size` points from X
np.random.seed()
idx = np.random.choice(N, sample_size)
landmarks = features[idx]
distances, max_dist = lmrk_table(witnesses=features, landmarks=landmarks)
wc = gudhi.WitnessComplex(distances)
alpha_max = max_dist * gamma
st = wc.create_simplex_tree(max_alpha_square=alpha_max, limit_dimension=2)
# This seems to modify the st object
st.persistence(homology_coeff_field=2)
intervals = st.persistence_intervals_in_dimension(1)
return intervals, alpha_max
def pseudo_alpha_beta_witness_complex(n_lm, alpha_beta, n_landmarks):
indices_remaining = list(range(0, n_landmarks))
pairings = []
keep_searching_pairs = True
i = 0
while keep_searching_pairs:
alpha, beta = alpha_beta[i][0], alpha_beta[i][1]
n_lm_current = filter_alpha(n_lm, alpha)
witness_complex = gudhi.WitnessComplex(
nearest_landmark_table=n_lm_current)
simplex_tree = witness_complex.create_simplex_tree(
max_alpha_square=beta, limit_dimension=1)
skeleton = simplex_tree.get_skeleton(1)
indices_remaining, pairings = get_pairings(skeleton, indices_remaining,
pairings)
i += 1
if len(indices_remaining) == 0:
keep_searching_pairs = False
elif len(alpha_beta) == i:
keep_searching_pairs = False
print('Stopped early')
else:
pass
return pairings
def witness(
features: np.ndarray, sample_size: int = 64, gamma: Optional[float] = None) \
-> Tuple[np.ndarray, np.ndarray]:
"""Compute the persistence intervals for the dataset of features using the witness complex.
Args:
features: Array of shape (N_samples, data_dim) representing the dataset.
sample_size: Number of landmarks to use on each iteration.
gamma: Parameter determining maximum persistence value. Default is `1.0 / 128 * N_imgs / 5000`
Returns
A list of persistence intervals and the maximal persistence value.
"""
# Install gudhi only if needed
try:
import gudhi
except ImportError as e:
import six
error = e.__class__(
"You are likely missing your GUDHI installation, "
"you should visit http://gudhi.gforge.inria.fr/python/latest/installation.html "
"for further instructions.\nIf you use conda, you can use\nconda install -c conda-forge gudhi"
)
six.raise_from(error, e)
N = features.shape[0]
if gamma is None:
gamma = 1.0 / 128 * N / 5000
# Randomly sample `sample_size` points from X
np.random.seed()
idx = np.random.choice(N, sample_size)
landmarks = features[idx]
distances, max_dist = lmrk_table(witnesses=features, landmarks=landmarks)
wc = gudhi.WitnessComplex(distances)
alpha_max = max_dist * gamma
st = wc.create_simplex_tree(max_alpha_square=alpha_max, limit_dimension=2)
# This seems to modify the st object
st.persistence(homology_coeff_field=2)
intervals = st.persistence_intervals_in_dimension(1)
return intervals, alpha_max
def witness(features: np.ndarray, sample_size: int = 64, gamma: Optional[float] = None) \
-> Tuple[np.ndarray, np.ndarray]:
"""Compute the persistence intervals for the dataset of features using the witness complex.
Args:
features: Array with shape (N_samples, data_dim) representing the dataset.
sample_size: Number of landmarks to use on each iteration.
gamma: Parameter determining maximum persistence value. Default is `1.0 / 128 * N_imgs / 5000`
Returns
A list of persistence intervals and the maximal persistence value.
"""
try:
import gudhi
except ImportError:
raise ImportError("GUDHI is required for computation of the Geometry Score but not installed. "
"Please install scipy using the following command: pip install --user gudhi")
recommended_gudhi_version = "3.2"
if _version_tuple(gudhi.__version__) < _version_tuple(recommended_gudhi_version):
warn(f'GUDHI of version {gudhi.__version__} is used while version >= {recommended_gudhi_version} is '
f'recommended. Consider updating GUDHI to avoid potential problems.')
N = features.shape[0]
if gamma is None:
gamma = 1.0 / 128 * N / 5000
# Randomly sample `sample_size` points from X
np.random.seed()
idx = np.random.choice(N, sample_size)
landmarks = features[idx]
distances, max_dist = lmrk_table(witnesses=features, landmarks=landmarks)
wc = gudhi.WitnessComplex(distances)
alpha_max = max_dist * gamma
st = wc.create_simplex_tree(max_alpha_square=alpha_max, limit_dimension=2)
# This seems to modify the st object
st.persistence(homology_coeff_field=2)
intervals = st.persistence_intervals_in_dimension(1)
return intervals, alpha_max
def witness(X, gamma=1.0 / 128, L_0=64):
"""
This function computes the persistence intervals for the dataset
X using the witness complex.
Args:
X: 2d array representing the dataset.
gamma: parameter determining the maximal persistence value.
L_0: int, number of landmarks to use.
Returns
A list of persistence intervals and the maximal persistence value.
"""
L = random_landmarks(X, L_0)
W = X
lmrk_tab, max_dist = lmrk_table(W, L)
wc = gudhi.WitnessComplex(lmrk_tab)
alpha_max = max_dist * gamma
st = wc.create_simplex_tree(max_alpha_square=alpha_max, limit_dimension=2)
big_diag = st.persistence(homology_coeff_field=2)
diag = st.persistence_intervals_in_dimension(1)
return diag, alpha_max
print(pers_pairs)
result_str = 'Witness complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \
repr(simplex_tree.num_simplices()) + ' simplices - ' + \
repr(simplex_tree.num_vertices()) + ' vertices.'
print(result_str)
nlt = [
[[0,1],[3,9],[1,29],[2,34]],
[[1,1],[0,16],[2,26],[3,39]],
[[2,4],[1,9],[3,29],[0,34]],
[[3,4],[2,9],[0,29],[1,34]]
]
wcomp = gudhi.WitnessComplex(nlt)
simplex_tree = wcomp.create_simplex_tree(max_alpha_square=50)
skeleton = simplex_tree.get_skeleton(1)
pairs = []
for element in skeleton:
if len(element[0]) == 2:
if element[1] == 0:
pairs.append(element[0])
print('Skeleton W-LIST: {}'.format(skeleton))
print('Pairs W-LIST: {}'.format(pairs))
dataset_sampler = SwissRoll()