"""Persistent homology on grids."""
# License: GNU AGPLv3
from numbers import Real
import numpy as np
from joblib import Parallel, delayed
from sklearn.base import BaseEstimator, TransformerMixin
from sklearn.utils.validation import check_is_fitted
from ._utils import _postprocess_diagrams
from ..base import PlotterMixin
from ..externals.python import CubicalComplex, PeriodicCubicalComplex
from ..plotting import plot_diagram
from ..utils.intervals import Interval
from ..utils.validation import validate_params, check_collection
[docs]class CubicalPersistence(BaseEstimator, TransformerMixin, PlotterMixin):
""":ref:`Persistence diagrams <persistence_diagram>` resulting from
:ref:`filtered cubical complexes <cubical_complex>`.
Given a :ref:`greyscale image <cubical_chains_and_cubical_homology>`,
information about the appearance and disappearance of topological features
(technically, :ref:`homology classes <homology_and_cohomology>`) of various
dimensions and at different scales is summarised in the corresponding
persistence diagram.
**Important note**:
- Persistence diagrams produced by this class must be interpreted with
care due to the presence of padding triples which carry no
information. See :meth:`transform` for additional information.
Parameters
----------
homology_dimensions : list or tuple, optional, default: ``(0, 1)``
Dimensions (non-negative integers) of the topological features to be
detected.
coeff : int prime, optional, default: ``2``
Compute homology with coefficients in the prime field
:math:`\\mathbb{F}_p = \\{ 0, \\ldots, p - 1 \\}` where :math:`p`
equals `coeff`.
periodic_dimensions : boolean ndarray of shape (n_dimensions,) or None, \
optional, default: ``None``
Periodicity of the boundaries along each of the axes, where
``n_dimensions`` is the dimension of the images of the collection. The
boolean in the `d`th position expresses whether the boundaries along
the `d`th axis are periodic. The default ``None`` is equivalent to
passing ``numpy.zeros((n_dimensions,), dtype=bool)``, i.e. none of the
boundaries are periodic.
infinity_values : float or None, default: ``None``
Which death value to assign to features which are still alive at
filtration value ``numpy.inf``. ``None`` assigns the maximum pixel
values within all images passed to :meth:`fit`.
reduced_homology : bool, optional, default: ``True``
If ``True``, the earliest-born triple in homology dimension 0 which has
infinite death is discarded from each diagram computed in
:meth:`transform`.
n_jobs : int or None, optional, default: ``None``
The number of jobs to use for the computation. ``None`` means 1 unless
in a :obj:`joblib.parallel_backend` context. ``-1`` means using all
processors.
Attributes
----------
periodic_dimensions_ : boolean ndarray of shape (n_dimensions,)
Effective periodicity of the boundaries along each of the axes. Set in
:meth:`fit`.
infinity_values_ : float
Effective death value to assign to features which have infinite
persistence. Set in :meth:`fit`.
See also
--------
images.HeightFiltration, images.RadialFiltration, \
images.DilationFiltration, images.ErosionFiltration, \
images.SignedDistanceFiltration
Notes
-----
`GUDHI <https://github.com/GUDHI/gudhi-devel>`_ is used as a C++ backend
for computing cubical persistent homology [1]_. Python bindings were
modified for performance.
References
----------
.. [1] P. Dlotko, "Cubical complex", 2015; `GUDHI User and Reference
Manual <http://gudhi.gforge.inria.fr/doc/latest/group__cubical__\
complex.html>`_.
"""
_hyperparameters = {
'homology_dimensions': {
'type': (list, tuple),
'of': {'type': int, 'in': Interval(0, np.inf, closed='left')}
},
'coeff': {'type': int, 'in': Interval(2, np.inf, closed='left')},
'periodic_dimensions': {'type': (np.ndarray, type(None)),
'of': {'type': np.bool_}},
'infinity_values': {'type': (Real, type(None))},
'reduced_homology': {'type': bool}
}
[docs] def __init__(self, homology_dimensions=(0, 1), coeff=2,
periodic_dimensions=None, infinity_values=None,
reduced_homology=True, n_jobs=None):
self.homology_dimensions = homology_dimensions
self.coeff = coeff
self.periodic_dimensions = periodic_dimensions
self.infinity_values = infinity_values
self.reduced_homology = reduced_homology
self.n_jobs = n_jobs
def _gudhi_diagram(self, X):
cubical_complex = self._filtration(
dimensions=X.shape,
top_dimensional_cells=X.flatten(order="F"),
**self._filtration_kwargs
)
Xdgm = cubical_complex.persistence(homology_coeff_field=self.coeff,
min_persistence=0)
return Xdgm
[docs] def fit(self, X, y=None):
"""Do nothing and return the estimator unchanged.
This method is here to implement the usual scikit-learn API and hence
work in pipelines.
Parameters
----------
X : ndarray of shape (n_samples, n_pixels_1, ..., n_pixels_d)
Input data. Array of d-dimensional images.
y : None
There is no need of a target in a transformer, yet the pipeline API
requires this parameter.
Returns
-------
self : object
"""
X = check_collection(X, force_all_finite=False)
validate_params(
self.get_params(), self._hyperparameters, exclude=['n_jobs'])
self._filtration_kwargs = {}
if self.periodic_dimensions is None or \
np.sum(self.periodic_dimensions) == 0:
self._filtration = CubicalComplex
self.periodic_dimensions_ = np.zeros(len(X) - 1, dtype=bool)
else:
self._filtration = PeriodicCubicalComplex
self.periodic_dimensions_ = np.array(self.periodic_dimensions,
dtype=bool)
self._filtration_kwargs['periodic_dimensions'] = \
self.periodic_dimensions_
if self.infinity_values is None:
if hasattr(X, 'shape'):
self.infinity_values_ = np.max(X)
else:
self.infinity_values_ = max(map(np.max, X))
else:
self.infinity_values_ = self.infinity_values
self._homology_dimensions = sorted(self.homology_dimensions)
self._max_homology_dimension = self._homology_dimensions[-1]
return self
[docs] @staticmethod
def plot(Xt, sample=0, homology_dimensions=None, plotly_params=None):
"""Plot a sample from a collection of persistence diagrams, with
homology in multiple dimensions.
Parameters
----------
Xt : ndarray of shape (n_samples, n_features, 3)
Collection of persistence diagrams, such as returned by
:meth:`transform`.
sample : int, optional, default: ``0``
Index of the sample in `Xt` to be plotted.
homology_dimensions : list, tuple or None, optional, default: ``None``
Which homology dimensions to include in the plot. ``None`` means
plotting all dimensions present in ``Xt[sample]``.
plotly_params : dict or None, optional, default: ``None``
Custom parameters to configure the plotly figure. Allowed keys are
``"traces"`` and ``"layout"``, and the corresponding values should
be dictionaries containing keyword arguments as would be fed to the
:meth:`update_traces` and :meth:`update_layout` methods of
:class:`plotly.graph_objects.Figure`.
Returns
-------
fig : :class:`plotly.graph_objects.Figure` object
Plotly figure.
"""
return plot_diagram(
Xt[sample], homology_dimensions=homology_dimensions,
plotly_params=plotly_params
)