diff options
author | Vincent Rouvreau <10407034+VincentRouvreau@users.noreply.github.com> | 2020-01-14 06:36:54 +0100 |
---|---|---|
committer | GitHub <noreply@github.com> | 2020-01-14 06:36:54 +0100 |
commit | 5533e1f16c99512ff1966b31ba8f121d37462f52 (patch) | |
tree | b429491ba602ec48a1f54f7fa3404f892d568cf3 /src | |
parent | c5ab277ebe1a0ce032567d4ca47e487f356705f3 (diff) | |
parent | 9bbbc84ab7208ccd69934445202538e34439b304 (diff) |
Merge pull request #192 from tlacombe/wdist
Wdist
Diffstat (limited to 'src')
-rw-r--r-- | src/python/doc/wasserstein_distance_sum.inc | 6 | ||||
-rw-r--r-- | src/python/doc/wasserstein_distance_user.rst | 2 | ||||
-rw-r--r-- | src/python/gudhi/wasserstein.py | 47 | ||||
-rwxr-xr-x | src/python/test/test_wasserstein_distance.py | 34 |
4 files changed, 44 insertions, 45 deletions
diff --git a/src/python/doc/wasserstein_distance_sum.inc b/src/python/doc/wasserstein_distance_sum.inc index ffd4d312..a97f428d 100644 --- a/src/python/doc/wasserstein_distance_sum.inc +++ b/src/python/doc/wasserstein_distance_sum.inc @@ -2,12 +2,12 @@ :widths: 30 50 20 +-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------------------------------------------------+ - | .. figure:: | The p-Wasserstein distance measures the similarity between two | :Author: Theo Lacombe | + | .. figure:: | The q-Wasserstein distance measures the similarity between two | :Author: Theo Lacombe | | ../../doc/Bottleneck_distance/perturb_pd.png | persistence diagrams. It's the minimum value c that can be achieved | | | :figclass: align-center | by a perfect matching between the points of the two diagrams (+ all | :Introduced in: GUDHI 3.1.0 | | | diagonal points), where the value of a matching is defined as the | | - | Wasserstein distance is the p-th root of the sum of the | p-th root of the sum of all edge lengths to the power p. Edge lengths| :Copyright: MIT | - | edge lengths to the power p. | are measured in norm q, for :math:`1 \leq q \leq \infty`. | | + | Wasserstein distance is the q-th root of the sum of the | q-th root of the sum of all edge lengths to the power q. Edge lengths| :Copyright: MIT | + | edge lengths to the power q. | are measured in norm p, for :math:`1 \leq p \leq \infty`. | | | | | :Requires: Python Optimal Transport (POT) :math:`\geq` 0.5.1 | +-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------------------------------------------------+ | * :doc:`wasserstein_distance_user` | | diff --git a/src/python/doc/wasserstein_distance_user.rst b/src/python/doc/wasserstein_distance_user.rst index a049cfb5..32999a0c 100644 --- a/src/python/doc/wasserstein_distance_user.rst +++ b/src/python/doc/wasserstein_distance_user.rst @@ -30,7 +30,7 @@ Note that persistence diagrams must be submitted as (n x 2) numpy arrays and mus diag1 = np.array([[2.7, 3.7],[9.6, 14.],[34.2, 34.974]]) diag2 = np.array([[2.8, 4.45],[9.5, 14.1]]) - message = "Wasserstein distance value = " + '%.2f' % gudhi.wasserstein.wasserstein_distance(diag1, diag2, q=2., p=1.) + message = "Wasserstein distance value = " + '%.2f' % gudhi.wasserstein.wasserstein_distance(diag1, diag2, order=1., internal_p=2.) print(message) The output is: diff --git a/src/python/gudhi/wasserstein.py b/src/python/gudhi/wasserstein.py index 1906eeb1..db5ddff2 100644 --- a/src/python/gudhi/wasserstein.py +++ b/src/python/gudhi/wasserstein.py @@ -23,26 +23,26 @@ def _proj_on_diag(X): return np.array([Z , Z]).T -def _build_dist_matrix(X, Y, p=2., q=2.): +def _build_dist_matrix(X, Y, order=2., internal_p=2.): ''' :param X: (n x 2) numpy.array encoding the (points of the) first diagram. :param Y: (m x 2) numpy.array encoding the second diagram. - :param q: Ground metric (i.e. norm l_q). - :param p: exponent for the Wasserstein metric. + :param internal_p: Ground metric (i.e. norm l_p). + :param order: exponent for the Wasserstein metric. :returns: (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(q): - C = sc.cdist(X,Y, metric='chebyshev')**p - Cxd = np.linalg.norm(X - Xdiag, ord=q, axis=1)**p - Cdy = np.linalg.norm(Y - Ydiag, ord=q, axis=1)**p + if np.isinf(internal_p): + C = sc.cdist(X,Y, metric='chebyshev')**order + Cxd = np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**order + Cdy = np.linalg.norm(Y - Ydiag, ord=internal_p, axis=1)**order 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 + C = sc.cdist(X,Y, metric='minkowski', p=internal_p)**order + Cxd = np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**order + Cdy = np.linalg.norm(Y - Ydiag, ord=internal_p, axis=1)**order Cf = np.hstack((C, Cxd[:,None])) Cdy = np.append(Cdy, 0) @@ -51,24 +51,24 @@ def _build_dist_matrix(X, Y, p=2., q=2.): return Cf -def _perstot(X, p, q): +def _perstot(X, order, internal_p): ''' :param X: (n x 2) numpy.array (points of a given diagram). - :param q: Ground metric on the (upper-half) plane (i.e. norm l_q in R^2); Default value is 2 (Euclidean norm). - :param p: exponent for Wasserstein; Default value is 2. + :param internal_p: Ground metric on the (upper-half) plane (i.e. norm l_p in R^2); Default value is 2 (Euclidean norm). + :param order: exponent for Wasserstein. Default value is 2. :returns: float, the total persistence of the diagram (that is, its distance to the empty diagram). ''' Xdiag = _proj_on_diag(X) - return (np.sum(np.linalg.norm(X - Xdiag, ord=q, axis=1)**p))**(1./p) + return (np.sum(np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**order))**(1./order) -def wasserstein_distance(X, Y, p=2., q=2.): +def wasserstein_distance(X, Y, order=2., internal_p=2.): ''' :param X: (n x 2) numpy.array encoding the (finite points of the) first diagram. Must not contain essential points (i.e. with infinite coordinate). :param Y: (m x 2) numpy.array encoding the second diagram. - :param q: Ground metric on the (upper-half) plane (i.e. norm l_q in R^2); Default value is 2 (euclidean norm). - :param p: exponent for Wasserstein; Default value is 2. - :returns: the p-Wasserstein distance (1 <= p < infinity) with respect to the q-norm as ground metric. + :param internal_p: Ground metric on the (upper-half) plane (i.e. norm l_p in R^2); Default value is 2 (euclidean norm). + :param order: exponent for Wasserstein; Default value is 2. + :returns: the Wasserstein distance of order q (1 <= q < infinity) between persistence diagrams with respect to the internal_p-norm as ground metric. :rtype: float ''' n = len(X) @@ -79,20 +79,19 @@ def wasserstein_distance(X, Y, p=2., q=2.): if Y.size == 0: return 0. else: - return _perstot(Y, p, q) + return _perstot(Y, order, internal_p) elif Y.size == 0: - return _perstot(X, p, q) + return _perstot(X, order, internal_p) - M = _build_dist_matrix(X, Y, p=p, q=q) + M = _build_dist_matrix(X, Y, order=order, internal_p=internal_p) a = np.full(n+1, 1. / (n + m) ) # weight vector of the input diagram. Uniform here. a[-1] = a[-1] * m # normalized so that we have a probability measure, required by POT b = np.full(m+1, 1. / (n + m) ) # weight vector of the input diagram. Uniform here. b[-1] = b[-1] * 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. + # Note: it is the Wasserstein distance to the power q. # The default numItermax=100000 is not sufficient for some examples with 5000 points, what is a good value? ot_cost = (n+m) * ot.emd2(a, b, M, numItermax=2000000) - return ot_cost ** (1./p) - + return ot_cost ** (1./order) diff --git a/src/python/test/test_wasserstein_distance.py b/src/python/test/test_wasserstein_distance.py index bb59b3c2..43dda77e 100755 --- a/src/python/test/test_wasserstein_distance.py +++ b/src/python/test/test_wasserstein_distance.py @@ -23,26 +23,26 @@ def test_basic_wasserstein(): diag4 = np.array([[0, 3], [4, 8]]) emptydiag = np.array([[]]) - assert wasserstein_distance(emptydiag, emptydiag, q=2., p=1.) == 0. - assert wasserstein_distance(emptydiag, emptydiag, q=np.inf, p=1.) == 0. - assert wasserstein_distance(emptydiag, emptydiag, q=np.inf, p=2.) == 0. - assert wasserstein_distance(emptydiag, emptydiag, q=2., p=2.) == 0. + assert wasserstein_distance(emptydiag, emptydiag, internal_p=2., order=1.) == 0. + assert wasserstein_distance(emptydiag, emptydiag, internal_p=np.inf, order=1.) == 0. + assert wasserstein_distance(emptydiag, emptydiag, internal_p=np.inf, order=2.) == 0. + assert wasserstein_distance(emptydiag, emptydiag, internal_p=2., order=2.) == 0. - assert wasserstein_distance(diag3, emptydiag, q=np.inf, p=1.) == 2. - assert wasserstein_distance(diag3, emptydiag, q=1., p=1.) == 4. + assert wasserstein_distance(diag3, emptydiag, internal_p=np.inf, order=1.) == 2. + assert wasserstein_distance(diag3, emptydiag, internal_p=1., order=1.) == 4. - assert wasserstein_distance(diag4, emptydiag, q=1., p=2.) == 5. # thank you Pythagorician triplets - assert wasserstein_distance(diag4, emptydiag, q=np.inf, p=2.) == 2.5 - assert wasserstein_distance(diag4, emptydiag, q=2., p=2.) == 3.5355339059327378 + assert wasserstein_distance(diag4, emptydiag, internal_p=1., order=2.) == 5. # thank you Pythagorician triplets + assert wasserstein_distance(diag4, emptydiag, internal_p=np.inf, order=2.) == 2.5 + assert wasserstein_distance(diag4, emptydiag, internal_p=2., order=2.) == 3.5355339059327378 - assert wasserstein_distance(diag1, diag2, q=2., p=1.) == 1.4453593023967701 - assert wasserstein_distance(diag1, diag2, q=2.35, p=1.74) == 0.9772734057168739 + assert wasserstein_distance(diag1, diag2, internal_p=2., order=1.) == 1.4453593023967701 + assert wasserstein_distance(diag1, diag2, internal_p=2.35, order=1.74) == 0.9772734057168739 - assert wasserstein_distance(diag1, emptydiag, q=2.35, p=1.7863) == 3.141592214572228 + assert wasserstein_distance(diag1, emptydiag, internal_p=2.35, order=1.7863) == 3.141592214572228 - assert wasserstein_distance(diag3, diag4, q=1., p=1.) == 3. - assert wasserstein_distance(diag3, diag4, q=np.inf, p=1.) == 3. # no diag matching here - assert wasserstein_distance(diag3, diag4, q=np.inf, p=2.) == np.sqrt(5) - assert wasserstein_distance(diag3, diag4, q=1., p=2.) == np.sqrt(5) - assert wasserstein_distance(diag3, diag4, q=4.5, p=2.) == np.sqrt(5) + assert wasserstein_distance(diag3, diag4, internal_p=1., order=1.) == 3. + assert wasserstein_distance(diag3, diag4, internal_p=np.inf, order=1.) == 3. # no diag matching here + assert wasserstein_distance(diag3, diag4, internal_p=np.inf, order=2.) == np.sqrt(5) + assert wasserstein_distance(diag3, diag4, internal_p=1., order=2.) == np.sqrt(5) + assert wasserstein_distance(diag3, diag4, internal_p=4.5, order=2.) == np.sqrt(5) |