/
_metrics.py
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/
_metrics.py
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# License: Apache 2.0
import numpy as np
from scipy.spatial.distance import cdist, pdist, squareform
from giotto_bottleneck import bottleneck_distance
from giotto_wasserstein import wasserstein_distance
from scipy.ndimage import gaussian_filter
from joblib import Parallel, delayed, effective_n_jobs
from sklearn.utils.validation import _num_samples
from sklearn.utils import gen_even_slices
from ._utils import _subdiagrams
def betti_curves(diagrams, sampling):
born = sampling >= diagrams[:, :, 0]
not_dead = sampling < diagrams[:, :, 1]
alive = np.logical_and(born, not_dead)
betti = np.sum(alive, axis=2).T
return betti
def landscapes(diagrams, sampling, n_layers):
n_points = diagrams.shape[1]
midpoints = (diagrams[:, :, 1] + diagrams[:, :, 0]) / 2.
heights = (diagrams[:, :, 1] - diagrams[:, :, 0]) / 2.
fibers = np.maximum(-np.abs(sampling - midpoints) + heights, 0)
top_pos = range(n_points - n_layers, n_points)
fibers.partition(top_pos, axis=2)
fibers = np.flip(fibers[:, :, -n_layers:], axis=2)
fibers = np.transpose(fibers, (1, 2, 0))
pad_with = ((0, 0), (0, max(0, n_layers - n_points)), (0, 0))
fibers = np.pad(fibers, pad_with, 'constant', constant_values=0)
return fibers
def _heat(heat, sampled_diag, sigma):
unique, counts = np.unique(sampled_diag, axis=0, return_counts=True)
unique = tuple(tuple(row) for row in unique.T)
heat[unique] = counts
heat[:, :] = gaussian_filter(heat, sigma, mode='reflect')
def heats(diagrams, sampling, step_size, sigma):
heats_ = np.zeros((diagrams.shape[0], sampling.shape[0],
sampling.shape[0]))
sampled_diags = np.copy(diagrams)
sampling_ = sampling.reshape((-1,))
sampled_diags[diagrams < sampling_[0]] = sampling_[0]
sampled_diags[diagrams > sampling_[-1]] = sampling_[-1]
sampled_diags = np.array((sampled_diags - sampling_[0]) / step_size,
dtype=int)
[_heat(heats_[i], sampled_diag, sigma)
for i, sampled_diag in enumerate(sampled_diags)]
heats_ = heats_ - np.transpose(heats_, (0, 2, 1))
heats_ = np.rot90(heats_, k=1, axes=(1, 2))
return heats_
def betti_distances(diagrams_1, diagrams_2, sampling, step_size,
p=2., **kwargs):
betti_curves_1 = betti_curves(diagrams_1, sampling)
if np.array_equal(diagrams_1, diagrams_2):
unnorm_dist = squareform(pdist(betti_curves_1, 'minkowski', p=p))
return (step_size ** (1 / p)) * unnorm_dist
betti_curves_2 = betti_curves(diagrams_2, sampling)
unnorm_dist = cdist(betti_curves_1, betti_curves_2, 'minkowski', p=p)
return (step_size ** (1 / p)) * unnorm_dist
def landscape_distances(diagrams_1, diagrams_2, sampling, step_size,
p=2., n_layers=1, **kwargs):
n_samples_1, n_points_1 = diagrams_1.shape[:2]
n_layers_1 = min(n_layers, n_points_1)
if np.array_equal(diagrams_1, diagrams_2):
ls_1 = landscapes(diagrams_1, sampling, n_layers_1).reshape(
n_samples_1, -1)
unnorm_dist = squareform(pdist(ls_1, 'minkowski', p=p))
return (step_size ** (1 / p)) * unnorm_dist
n_samples_2, n_points_2 = diagrams_2.shape[:2]
n_layers_2 = min(n_layers, n_points_2)
n_layers = max(n_layers_1, n_layers_2)
ls_1 = landscapes(diagrams_1, sampling, n_layers).reshape(
n_samples_1, -1)
ls_2 = landscapes(diagrams_2, sampling, n_layers).reshape(
n_samples_2, -1)
unnorm_dist = cdist(ls_1, ls_2, 'minkowski', p=p)
return (step_size ** (1 / p)) * unnorm_dist
def bottleneck_distances(diagrams_1, diagrams_2, delta=0.01, **kwargs):
return np.array([[
bottleneck_distance(
diagram_1[diagram_1[:, 0] != diagram_1[:, 1]],
diagram_2[diagram_2[:, 0] != diagram_2[:, 1]], delta)
for diagram_2 in diagrams_2] for diagram_1 in diagrams_1])
def wasserstein_distances(diagrams_1, diagrams_2, p=2, delta=0.01,
**kwargs):
return np.array([[
wasserstein_distance(
diagram_1[diagram_1[:, 0] != diagram_1[:, 1]],
diagram_2[diagram_2[:, 0] != diagram_2[:, 1]], p, delta)
for diagram_2 in diagrams_2] for diagram_1 in diagrams_1])
def heat_distances(diagrams_1, diagrams_2, sampling, step_size,
sigma=1., p=2., **kwargs):
heat_1 = heats(diagrams_1, sampling, step_size, sigma).\
reshape(diagrams_1.shape[0], -1)
if np.array_equal(diagrams_1, diagrams_2):
unnorm_dist = squareform(pdist(heat_1, 'minkowski', p=p))
return (step_size ** (1 / p)) * unnorm_dist
heat_2 = heats(diagrams_2, sampling, step_size, sigma).\
reshape(diagrams_2.shape[0], -1)
unnorm_dist = cdist(heat_1, heat_2, 'minkowski', p=p)
return (step_size ** (1 / p)) * unnorm_dist
implemented_metric_recipes = {'bottleneck': bottleneck_distances,
'wasserstein': wasserstein_distances,
'landscape': landscape_distances,
'betti': betti_distances,
'heat': heat_distances}
def _matrix_wrapper(distance_func, distance_matrices, slice_, dim,
*args, **kwargs):
distance_matrices[:, slice_, int(dim)] = distance_func(*args, **kwargs)
def _parallel_pairwise(X1, X2, metric, metric_params,
homology_dimensions, n_jobs):
metric_func = implemented_metric_recipes[metric]
effective_metric_params = metric_params.copy()
none_dict = {dim: None for dim in homology_dimensions}
samplings = effective_metric_params.pop('samplings', none_dict)
step_sizes = effective_metric_params.pop('step_sizes', none_dict)
if X2 is None:
X2 = X1
distance_matrices = Parallel(n_jobs=n_jobs)(delayed(metric_func)(
_subdiagrams(X1, [dim], remove_dim=True),
_subdiagrams(X2[s], [dim], remove_dim=True),
sampling=samplings[dim], step_size=step_sizes[dim],
**effective_metric_params) for dim in homology_dimensions
for s in gen_even_slices(X2.shape[0], effective_n_jobs(n_jobs)))
distance_matrices = np.concatenate(distance_matrices, axis=1)
distance_matrices = np.stack(
[distance_matrices[:, i*X2.shape[0]: (i+1)*X2.shape[0]]
for i in range(len(homology_dimensions))], axis=2)
return distance_matrices
def betti_amplitudes(diagrams, sampling, step_size, p=2., **kwargs):
bcs = betti_curves(diagrams, sampling)
return (step_size ** (1 / p)) * np.linalg.norm(bcs, axis=1, ord=p)
def landscape_amplitudes(diagrams, sampling, step_size, p=2., n_layers=1,
**kwargs):
ls = landscapes(diagrams, sampling, n_layers).reshape(len(diagrams), -1)
return (step_size ** (1 / p)) * np.linalg.norm(ls, axis=1, ord=p)
def bottleneck_amplitudes(diagrams, **kwargs):
dists_to_diago = np.sqrt(2) / 2. * (diagrams[:, :, 1] - diagrams[:, :, 0])
return np.linalg.norm(dists_to_diago, axis=1, ord=np.inf)
def wasserstein_amplitudes(diagrams, p=2., **kwargs):
dists_to_diago = np.sqrt(2) / 2. * (diagrams[:, :, 1] - diagrams[:, :, 0])
return np.linalg.norm(dists_to_diago, axis=1, ord=p)
def heat_amplitudes(diagrams, sampling, step_size, sigma=1., p=2.,
**kwargs):
heat = heats(diagrams, sampling, step_size, sigma)
return np.linalg.norm(heat, axis=(1, 2), ord=p)
implemented_amplitude_recipes = {'bottleneck': bottleneck_amplitudes,
'wasserstein': wasserstein_amplitudes,
'landscape': landscape_amplitudes,
'betti': betti_amplitudes,
'heat': heat_amplitudes}
def _arrays_wrapper(amplitude_func, amplitude_arrays, slice_, dim,
*args, **kwargs):
amplitude_arrays[slice_, int(dim)] = amplitude_func(*args, **kwargs)
def _parallel_amplitude(X, metric, metric_params, homology_dimensions, n_jobs):
amplitude_func = implemented_amplitude_recipes[metric]
effective_metric_params = metric_params.copy()
none_dict = {dim: None for dim in homology_dimensions}
samplings = effective_metric_params.pop('samplings', none_dict)
step_sizes = effective_metric_params.pop('step_sizes', none_dict)
amplitude_arrays = Parallel(n_jobs=n_jobs)(delayed(amplitude_func)(
_subdiagrams(X, [dim], remove_dim=True)[s], sampling=samplings[dim],
step_size=step_sizes[dim], **effective_metric_params)
for dim in homology_dimensions
for s in gen_even_slices(_num_samples(X), effective_n_jobs(n_jobs)))
amplitude_arrays = np.concatenate(amplitude_arrays).reshape(
len(homology_dimensions), X.shape[0]).T
return amplitude_arrays