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author | tlacombe <lacombe1993@gmail.com> | 2019-09-23 11:14:24 +0200 |
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committer | tlacombe <lacombe1993@gmail.com> | 2019-09-23 11:14:24 +0200 |
commit | 1b007fc59f08bd01e1521eb1c0773b598bdf158b (patch) | |
tree | 6a5169be2dd87c28a27cd0054a8d0cd3b251c178 /src/python/gudhi/wasserstein.py | |
parent | 36d82a6ffe7c099da9241f7268637feaeef6bf55 (diff) |
wasserstein distance added on fork
Diffstat (limited to 'src/python/gudhi/wasserstein.py')
-rw-r--r-- | src/python/gudhi/wasserstein.py | 75 |
1 files changed, 75 insertions, 0 deletions
diff --git a/src/python/gudhi/wasserstein.py b/src/python/gudhi/wasserstein.py new file mode 100644 index 00000000..cc527ed8 --- /dev/null +++ b/src/python/gudhi/wasserstein.py @@ -0,0 +1,75 @@ +import numpy as np +import scipy.spatial.distance as sc +try: + import ot +except ImportError: + print("POT (Python Optimal Transport) package is not installed. Try to run $ pip install POT") + +""" 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): Theo Lacombe + + Copyright (C) 2016 Inria + + Modification(s): + - YYYY/MM Author: Description of the modification +""" + +def proj_on_diag(X): + ''' + param X: (n x 2) array encoding the points of a persistent diagram. + return: (n x 2) arary encoding the (respective orthogonal) projections of the points onto the diagonal + ''' + Z = (X[:,0] + X[:,1]) / 2. + return np.array([Z , Z]).T + + +def build_dist_matrix(X, Y, p=2., q=2.): + ''' + param X: (n x 2) np.array encoding the (points of the) first diagram. + param Y: (m x 2) np.array encoding the second diagram. + param q: Ground metric (i.e. norm l_q). + param p: exponent for the Wasserstein metric. + return: (n+1) x (m+1) np.array encoding the cost matrix C. + For 1 <= i <= n, 1 <= j <= m, C[i,j] encodes the distance between X[i] and Y[j], while C[i, m+1] (resp. C[n+1, j]) encodes the distance (to the p) between X[i] (resp Y[j]) and its orthogonal proj onto the diagonal. + note also that C[n+1, m+1] = 0 (it costs nothing to move from the diagonal to the diagonal). + ''' + Xdiag = proj_on_diag(X) + Ydiag = proj_on_diag(Y) + if np.isinf(p): + C = sc.cdist(X,Y, metric='chebyshev', p=q)**p + Cxd = np.linalg.norm(X - Xdiag, ord=q, axis=1)**p + Cdy = np.linalg.norm(Y - Ydiag, ord=q, axis=1)**p + else: + C = sc.cdist(X,Y, metric='minkowski', p=q)**p + Cxd = np.linalg.norm(X - Xdiag, ord=q, axis=1)**p + Cdy = np.linalg.norm(Y - Ydiag, ord=q, axis=1)**p + Cf = np.hstack((C, Cxd[:,None])) + Cdy = np.append(Cdy, 0) + + Cf = np.vstack((Cf, Cdy[None,:])) + + return Cf + + +def wasserstein_distance(X, Y, p=2., q=2.): + ''' + param X, Y: (n x 2) and (m x 2) numpy array (points of persistence diagrams) + param q: Ground metric (i.e. norm l_q); Default value is 2 (euclidean norm). + param p: exponent for Wasserstein; Default value is 2. + return: float, the p-Wasserstein distance (1 <= p < infty) with respect to the q-norm as ground metric. + ''' + M = build_dist_matrix(X, Y, p=p, q=q) + n = len(X) + m = len(Y) + a = 1.0 / (n + m) * np.ones(n) # weight vector of the input diagram. Uniform here. + hat_a = np.append(a, m/(n+m)) # so that we have a probability measure, required by POT + b = 1.0 / (n + m) * np.ones(m) # weight vector of the input diagram. Uniform here. + hat_b = np.append(b, n/(m+n)) # so that we have a probability measure, required by POT + + # Comptuation of the otcost using the ot.emd2 library. + # Note: it is the squared Wasserstein distance. + ot_cost = (n+m) * ot.emd2(hat_a, hat_b, M) + + return np.power(ot_cost, 1./p) + |