diff options
Diffstat (limited to 'src/python/gudhi/wasserstein.py')
| -rw-r--r-- | src/python/gudhi/wasserstein.py | 57 |
1 files changed, 42 insertions, 15 deletions
diff --git a/src/python/gudhi/wasserstein.py b/src/python/gudhi/wasserstein.py index 13102094..3dd993f9 100644 --- a/src/python/gudhi/wasserstein.py +++ b/src/python/gudhi/wasserstein.py @@ -30,8 +30,10 @@ def _build_dist_matrix(X, Y, order=2., internal_p=2.): :param order: exponent for the Wasserstein metric. :param internal_p: Ground metric (i.e. norm L^p). :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). + For 0 <= i < n, 0 <= j < m, C[i,j] encodes the distance between X[i] and Y[j], + while C[i, m] (resp. C[n, j]) encodes the distance (to the p) between X[i] (resp Y[j]) + and its orthogonal projection onto the diagonal. + note also that C[n, m] = 0 (it costs nothing to move from the diagonal to the diagonal). ''' Xdiag = _proj_on_diag(X) Ydiag = _proj_on_diag(Y) @@ -62,14 +64,20 @@ def _perstot(X, order, internal_p): return (np.sum(np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**order))**(1./order) -def wasserstein_distance(X, Y, order=2., internal_p=2.): +def wasserstein_distance(X, Y, matching=False, 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 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 matching: if True, computes and returns the optimal matching between X and Y, encoded as + a (n x 2) np.array [...[i,j]...], meaning the i-th point in X is matched to + the j-th point in Y, with the convention (-1) represents the diagonal. :param order: 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). - :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 + :param internal_p: Ground metric on the (upper-half) plane (i.e. norm L^p in R^2); + Default value is 2 (Euclidean norm). + :returns: the Wasserstein distance of order q (1 <= q < infinity) between persistence diagrams with + respect to the internal_p-norm as ground metric. + If matching is set to True, also returns the optimal matching between X and Y. ''' n = len(X) m = len(Y) @@ -77,21 +85,40 @@ def wasserstein_distance(X, Y, order=2., internal_p=2.): # handle empty diagrams if X.size == 0: if Y.size == 0: - return 0. + if not matching: + return 0. + else: + return 0., np.array([]) else: - return _perstot(Y, order, internal_p) + if not matching: + return _perstot(Y, order, internal_p) + else: + return _perstot(Y, order, internal_p), np.array([[-1, j] for j in range(m)]) elif Y.size == 0: - return _perstot(X, order, internal_p) + if not matching: + return _perstot(X, order, internal_p) + else: + return _perstot(X, order, internal_p), np.array([[i, -1] for i in range(n)]) 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 + a = np.ones(n+1) # weight vector of the input diagram. Uniform here. + a[-1] = m + b = np.ones(m+1) # weight vector of the input diagram. Uniform here. + b[-1] = n + + if matching: + P = ot.emd(a=a,b=b,M=M, numItermax=2000000) + ot_cost = np.sum(np.multiply(P,M)) + P[-1, -1] = 0 # Remove matching corresponding to the diagonal + match = np.argwhere(P) + # Now we turn to -1 points encoding the diagonal + match[:,0][match[:,0] >= n] = -1 + match[:,1][match[:,1] >= m] = -1 + return ot_cost ** (1./order) , match # Comptuation of the otcost using the ot.emd2 library. # 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) + ot_cost = ot.emd2(a, b, M, numItermax=2000000) return ot_cost ** (1./order) |