diff options
| -rw-r--r-- | src/python/CMakeLists.txt | 5 | ||||
| -rw-r--r-- | src/python/gudhi/representations/vector_methods.py | 159 | ||||
| -rwxr-xr-x | src/python/test/test_betti_curve_representations.py | 59 | ||||
| -rwxr-xr-x | src/python/test/test_representations.py | 3 |
4 files changed, 193 insertions, 33 deletions
diff --git a/src/python/CMakeLists.txt b/src/python/CMakeLists.txt index 1314b444..a507d34c 100644 --- a/src/python/CMakeLists.txt +++ b/src/python/CMakeLists.txt @@ -547,6 +547,11 @@ if(PYTHONINTERP_FOUND) add_gudhi_py_test(test_representations) endif() + # Betti curves + if(SKLEARN_FOUND AND SCIPY_FOUND) + add_gudhi_py_test(test_betti_curve_representations) + endif() + # Time Delay add_gudhi_py_test(test_time_delay) diff --git a/src/python/gudhi/representations/vector_methods.py b/src/python/gudhi/representations/vector_methods.py index e883b5dd..f8078d03 100644 --- a/src/python/gudhi/representations/vector_methods.py +++ b/src/python/gudhi/representations/vector_methods.py @@ -1,15 +1,17 @@ # This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. # See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. -# Author(s): Mathieu Carrière, Martin Royer +# Author(s): Mathieu Carrière, Martin Royer, Gard Spreemann # # Copyright (C) 2018-2020 Inria # # Modification(s): # - 2020/06 Martin: ATOL integration +# - 2020/12 Gard: A more flexible Betti curve class capable of computing exact curves. # - 2021/11 Vincent Rouvreau: factorize _automatic_sample_range import numpy as np from sklearn.base import BaseEstimator, TransformerMixin +from sklearn.exceptions import NotFittedError from sklearn.preprocessing import MinMaxScaler, MaxAbsScaler from sklearn.neighbors import DistanceMetric from sklearn.metrics import pairwise @@ -306,67 +308,162 @@ class Silhouette(BaseEstimator, TransformerMixin): """ return self.fit_transform([diag])[0,:] + class BettiCurve(BaseEstimator, TransformerMixin): """ - This is a class for computing Betti curves from a list of persistence diagrams. A Betti curve is a 1D piecewise-constant function obtained from the rank function. It is sampled evenly on a given range and the vector of samples is returned. See https://www.researchgate.net/publication/316604237_Time_Series_Classification_via_Topological_Data_Analysis for more details. + Compute Betti curves from persistence diagrams. There are several modes of operation: with a given resolution (with or without a sample_range), with a predefined grid, and with none of the previous. With a predefined grid, the class computes the Betti numbers at those grid points. Without a predefined grid, if the resolution is set to None, it can be fit to a list of persistence diagrams and produce a grid that consists of (at least) the filtration values at which at least one of those persistence diagrams changes Betti numbers, and then compute the Betti numbers at those grid points. In the latter mode, the exact Betti curve is computed for the entire real line. Otherwise, if the resolution is given, the Betti curve is obtained by sampling evenly using either the given sample_range or based on the persistence diagrams. """ - def __init__(self, resolution=100, sample_range=[np.nan, np.nan]): + + def __init__(self, resolution=100, sample_range=[np.nan, np.nan], predefined_grid=None): """ Constructor for the BettiCurve class. Parameters: resolution (int): number of sample for the piecewise-constant function (default 100). sample_range ([double, double]): minimum and maximum of the piecewise-constant function domain, of the form [x_min, x_max] (default [numpy.nan, numpy.nan]). It is the interval on which samples will be drawn evenly. If one of the values is numpy.nan, it can be computed from the persistence diagrams with the fit() method. + predefined_grid (1d array or None, default=None): Predefined filtration grid points at which to compute the Betti curves. Must be strictly ordered. Infinities are ok. If None (default), and resolution is given, the grid will be uniform from x_min to x_max in 'resolution' steps, otherwise a grid will be computed that captures all changes in Betti numbers in the provided data. + + Attributes: + grid_ (1d array): The grid on which the Betti numbers are computed. If predefined_grid was specified, `grid_` will always be that grid, independently of data. If not, the grid is fitted to capture all filtration values at which the Betti numbers change. + + Examples + -------- + If pd is a persistence diagram and xs is a nonempty grid of finite values such that xs[0] >= pd.min(), then the results of: + + >>> bc = BettiCurve(predefined_grid=xs) # doctest: +SKIP + >>> result = bc(pd) # doctest: +SKIP + + and + + >>> from scipy.interpolate import interp1d # doctest: +SKIP + >>> bc = BettiCurve(resolution=None, predefined_grid=None) # doctest: +SKIP + >>> bettis = bc.fit_transform([pd]) # doctest: +SKIP + >>> interp = interp1d(bc.grid_, bettis[0, :], kind="previous", fill_value="extrapolate") # doctest: +SKIP + >>> result = np.array(interp(xs), dtype=int) # doctest: +SKIP + + are the same. """ - self.resolution, self.sample_range = resolution, sample_range - def fit(self, X, y=None): + if (predefined_grid is not None) and (not isinstance(predefined_grid, np.ndarray)): + raise ValueError("Expected predefined_grid as array or None.") + + self.predefined_grid = predefined_grid + self.resolution = resolution + self.sample_range = sample_range + + def is_fitted(self): + return hasattr(self, "grid_") + + def fit(self, X, y = None): """ - Fit the BettiCurve class on a list of persistence diagrams: if any of the values in **sample_range** is numpy.nan, replace it with the corresponding value computed on the given list of persistence diagrams. + Fit the BettiCurve class on a list of persistence diagrams: if any of the values in **sample_range** is numpy.nan, replace it with the corresponding value computed on the given list of persistence diagrams. When no predefined grid is provided and resolution set to None, compute a filtration grid that captures all changes in Betti numbers for all the given persistence diagrams. Parameters: - X (list of n x 2 numpy arrays): input persistence diagrams. - y (n x 1 array): persistence diagram labels (unused). + X (list of 2d arrays): Persistence diagrams. + y (None): Ignored. """ - self.sample_range = _automatic_sample_range(np.array(self.sample_range), X, y) + + if self.predefined_grid is None: + if self.resolution is None: # Flexible/exact version + events = np.unique(np.concatenate([pd.flatten() for pd in X] + [[-np.inf]], axis=0)) + self.grid_ = np.array(events) + else: + self.sample_range = _automatic_sample_range(np.array(self.sample_range), X, y) + self.grid_ = np.linspace(self.sample_range[0], self.sample_range[1], self.resolution) + else: + self.grid_ = self.predefined_grid # Get the predefined grid from user + return self def transform(self, X): """ - Compute the Betti curve for each persistence diagram individually and concatenate the results. + Compute Betti curves. Parameters: - X (list of n x 2 numpy arrays): input persistence diagrams. - + X (list of 2d arrays): Persistence diagrams. + Returns: - numpy array with shape (number of diagrams) x (**resolution**): output Betti curves. + `len(X).len(self.grid_)` array of ints: Betti numbers of the given persistence diagrams at the grid points given in `self.grid_` """ - Xfit = [] - x_values = np.linspace(self.sample_range[0], self.sample_range[1], self.resolution) - step_x = x_values[1] - x_values[0] - for diagram in X: - diagram_int = np.clip(np.ceil((diagram[:,:2] - self.sample_range[0]) / step_x), 0, self.resolution).astype(int) - bc = np.zeros(self.resolution) - for interval in diagram_int: - bc[interval[0]:interval[1]] += 1 - Xfit.append(np.reshape(bc,[1,-1])) + if not self.is_fitted(): + raise NotFittedError("Not fitted.") - Xfit = np.concatenate(Xfit, 0) + if not X: + X = [np.zeros((0, 2))] + + N = len(X) - return Xfit + events = np.concatenate([pd.flatten(order="F") for pd in X], axis=0) + sorting = np.argsort(events) + offsets = np.zeros(1 + N, dtype=int) + for i in range(0, N): + offsets[i+1] = offsets[i] + 2*X[i].shape[0] + starts = offsets[0:N] + ends = offsets[1:N + 1] - 1 - def __call__(self, diag): + bettis = [[0] for i in range(0, N)] + + i = 0 + for x in self.grid_: + while i < len(sorting) and events[sorting[i]] <= x: + j = np.searchsorted(ends, sorting[i]) + delta = 1 if sorting[i] - starts[j] < len(X[j]) else -1 + bettis[j][-1] += delta + i += 1 + for k in range(0, N): + bettis[k].append(bettis[k][-1]) + + return np.array(bettis, dtype=int)[:, 0:-1] + + def fit_transform(self, X): + """ + The result is the same as fit(X) followed by transform(X), but potentially faster. """ - Apply BettiCurve on a single persistence diagram and outputs the result. - Parameters: - diag (n x 2 numpy array): input persistence diagram. + if self.predefined_grid is None and self.resolution is None: + if not X: + X = [np.zeros((0, 2))] - Returns: - numpy array with shape (**resolution**): output Betti curve. + N = len(X) + + events = np.concatenate([pd.flatten(order="F") for pd in X], axis=0) + sorting = np.argsort(events) + offsets = np.zeros(1 + N, dtype=int) + for i in range(0, N): + offsets[i+1] = offsets[i] + 2*X[i].shape[0] + starts = offsets[0:N] + ends = offsets[1:N + 1] - 1 + + xs = [-np.inf] + bettis = [[0] for i in range(0, N)] + + for i in sorting: + j = np.searchsorted(ends, i) + delta = 1 if i - starts[j] < len(X[j]) else -1 + if events[i] == xs[-1]: + bettis[j][-1] += delta + else: + xs.append(events[i]) + for k in range(0, j): + bettis[k].append(bettis[k][-1]) + bettis[j].append(bettis[j][-1] + delta) + for k in range(j+1, N): + bettis[k].append(bettis[k][-1]) + + self.grid_ = np.array(xs) + return np.array(bettis, dtype=int) + + else: + return self.fit(X).transform(X) + + def __call__(self, diag): """ - return self.fit_transform([diag])[0,:] + Shorthand for transform on a single persistence diagram. + """ + return self.fit_transform([diag])[0, :] + + class Entropy(BaseEstimator, TransformerMixin): """ diff --git a/src/python/test/test_betti_curve_representations.py b/src/python/test/test_betti_curve_representations.py new file mode 100755 index 00000000..6a45da4d --- /dev/null +++ b/src/python/test/test_betti_curve_representations.py @@ -0,0 +1,59 @@ +import numpy as np +import scipy.interpolate +import pytest + +from gudhi.representations.vector_methods import BettiCurve + +def test_betti_curve_is_irregular_betti_curve_followed_by_interpolation(): + m = 10 + n = 1000 + pinf = 0.05 + pzero = 0.05 + res = 100 + + pds = [] + for i in range(0, m): + pd = np.zeros((n, 2)) + pd[:, 0] = np.random.uniform(0, 10, n) + pd[:, 1] = np.random.uniform(pd[:, 0], 10, n) + pd[np.random.uniform(0, 1, n) < pzero, 0] = 0 + pd[np.random.uniform(0, 1, n) < pinf, 1] = np.inf + pds.append(pd) + + bc = BettiCurve(resolution=None, predefined_grid=None) + bc.fit(pds) + bettis = bc.transform(pds) + + bc2 = BettiCurve(resolution=None, predefined_grid=None) + bettis2 = bc2.fit_transform(pds) + assert((bc2.grid_ == bc.grid_).all()) + assert((bettis2 == bettis).all()) + + for i in range(0, m): + grid = np.linspace(pds[i][np.isfinite(pds[i])].min(), pds[i][np.isfinite(pds[i])].max() + 1, res) + bc_gridded = BettiCurve(predefined_grid=grid) + bc_gridded.fit([]) + bettis_gridded = bc_gridded(pds[i]) + + interp = scipy.interpolate.interp1d(bc.grid_, bettis[i, :], kind="previous", fill_value="extrapolate") + bettis_interp = np.array(interp(grid), dtype=int) + assert((bettis_interp == bettis_gridded).all()) + + +def test_empty_with_predefined_grid(): + random_grid = np.sort(np.random.uniform(0, 1, 100)) + bc = BettiCurve(predefined_grid=random_grid) + bettis = bc.fit_transform([]) + assert((bc.grid_ == random_grid).all()) + assert((bettis == 0).all()) + + +def test_empty(): + bc = BettiCurve(resolution=None, predefined_grid=None) + bettis = bc.fit_transform([]) + assert(bc.grid_ == [-np.inf]) + assert((bettis == 0).all()) + +def test_wrong_value_of_predefined_grid(): + with pytest.raises(ValueError): + BettiCurve(predefined_grid=[1, 2, 3]) diff --git a/src/python/test/test_representations.py b/src/python/test/test_representations.py index 93461f1e..d219ce7a 100755 --- a/src/python/test/test_representations.py +++ b/src/python/test/test_representations.py @@ -105,7 +105,6 @@ def test_dummy_atol(): from gudhi.representations.vector_methods import BettiCurve - def test_infinity(): a = np.array([[1.0, 8.0], [2.0, np.inf], [3.0, 4.0]]) c = BettiCurve(20, [0.0, 10.0])(a) @@ -113,7 +112,6 @@ def test_infinity(): assert c[7] == 3 assert c[9] == 2 - def test_preprocessing_empty_diagrams(): empty_diag = np.empty(shape = [0, 2]) assert not np.any(BirthPersistenceTransform()(empty_diag)) @@ -169,3 +167,4 @@ def test_kernel_empty_diagrams(): # PersistenceScaleSpaceKernel(kernel_approx=RBFSampler(gamma=1./2, n_components=100000).fit(np.ones([1,2])))(empty_diag, empty_diag) # PersistenceFisherKernel(bandwidth_fisher=1., bandwidth=1.)(empty_diag, empty_diag) # PersistenceFisherKernel(bandwidth_fisher=1., bandwidth=1., kernel_approx=RBFSampler(gamma=1./2, n_components=100000).fit(np.ones([1,2])))(empty_diag, empty_diag) + |