diff options
Diffstat (limited to 'ot/gromov')
| -rw-r--r-- | ot/gromov/_bregman.py | 6 | ||||
| -rw-r--r-- | ot/gromov/_dictionary.py | 10 | ||||
| -rw-r--r-- | ot/gromov/_gw.py | 17 | ||||
| -rw-r--r-- | ot/gromov/_semirelaxed.py | 15 | ||||
| -rw-r--r-- | ot/gromov/_utils.py | 8 |
5 files changed, 31 insertions, 25 deletions
diff --git a/ot/gromov/_bregman.py b/ot/gromov/_bregman.py index b0cccfb..aa25f1f 100644 --- a/ot/gromov/_bregman.py +++ b/ot/gromov/_bregman.py @@ -69,7 +69,7 @@ def entropic_gromov_wasserstein(C1, C2, p, q, loss_fun, epsilon, symmetric=None, symmetric : bool, optional Either C1 and C2 are to be assumed symmetric or not. If let to its default None value, a symmetry test will be conducted. - Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymetric). + Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymmetric). G0: array-like, shape (ns,nt), optional If None the initial transport plan of the solver is pq^T. Otherwise G0 must satisfy marginal constraints and will be used as initial transport of the solver. @@ -152,7 +152,7 @@ def entropic_gromov_wasserstein(C1, C2, p, q, loss_fun, epsilon, symmetric=None, def entropic_gromov_wasserstein2(C1, C2, p, q, loss_fun, epsilon, symmetric=None, G0=None, max_iter=1000, tol=1e-9, verbose=False, log=False): r""" - Returns the entropic gromov-wasserstein discrepancy between the two measured similarity matrices :math:`(\mathbf{C_1}, \mathbf{p})` and :math:`(\mathbf{C_2}, \mathbf{q})` + Returns the entropic Gromov-Wasserstein discrepancy between the two measured similarity matrices :math:`(\mathbf{C_1}, \mathbf{p})` and :math:`(\mathbf{C_2}, \mathbf{q})` The function solves the following optimization problem: @@ -194,7 +194,7 @@ def entropic_gromov_wasserstein2(C1, C2, p, q, loss_fun, epsilon, symmetric=None symmetric : bool, optional Either C1 and C2 are to be assumed symmetric or not. If let to its default None value, a symmetry test will be conducted. - Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymetric). + Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymmetric). G0: array-like, shape (ns,nt), optional If None the initial transport plan of the solver is pq^T. Otherwise G0 must satisfy marginal constraints and will be used as initial transport of the solver. diff --git a/ot/gromov/_dictionary.py b/ot/gromov/_dictionary.py index 5b32671..0d618d1 100644 --- a/ot/gromov/_dictionary.py +++ b/ot/gromov/_dictionary.py @@ -148,7 +148,7 @@ def gromov_wasserstein_dictionary_learning(Cs, D, nt, reg=0., ps=None, q=None, e Ts = [None] * batch_size for batch_idx, C_idx in enumerate(batch): - # BCD solver for Gromov-Wassersteisn linear unmixing used independently on each structure of the sampled batch + # BCD solver for Gromov-Wasserstein linear unmixing used independently on each structure of the sampled batch unmixings[batch_idx], Cs_embedded[batch_idx], Ts[batch_idx], current_loss = gromov_wasserstein_linear_unmixing( Cs[C_idx], Cdict, reg=reg, p=ps[C_idx], q=q, tol_outer=tol_outer, tol_inner=tol_inner, max_iter_outer=max_iter_outer, max_iter_inner=max_iter_inner, symmetric=symmetric, **kwargs @@ -252,7 +252,7 @@ def gromov_wasserstein_linear_unmixing(C, Cdict, reg=0., p=None, q=None, tol_out Returns ------- w: array-like, shape (D,) - gromov-wasserstein linear unmixing of :math:`(\mathbf{C},\mathbf{p})` onto the span of the dictionary. + Gromov-Wasserstein linear unmixing of :math:`(\mathbf{C},\mathbf{p})` onto the span of the dictionary. Cembedded: array-like, shape (nt,nt) embedded structure of :math:`(\mathbf{C},\mathbf{p})` onto the dictionary, :math:`\sum_d w_d\mathbf{C_{dict}[d]}`. T: array-like (ns, nt) @@ -559,7 +559,7 @@ def fused_gromov_wasserstein_dictionary_learning(Cs, Ys, D, nt, alpha, reg=0., p Feature matrices composing the dictionary. The dictionary leading to the best loss over an epoch is saved and returned. log: dict - If use_log is True, contains loss evolutions by batches and epoches. + If use_log is True, contains loss evolutions by batches and epochs. References ------- .. [38] C. Vincent-Cuaz, T. Vayer, R. Flamary, M. Corneli, N. Courty, Online @@ -634,7 +634,7 @@ def fused_gromov_wasserstein_dictionary_learning(Cs, Ys, D, nt, alpha, reg=0., p Ts = [None] * batch_size for batch_idx, C_idx in enumerate(batch): - # BCD solver for Gromov-Wassersteisn linear unmixing used independently on each structure of the sampled batch + # BCD solver for Gromov-Wasserstein linear unmixing used independently on each structure of the sampled batch unmixings[batch_idx], Cs_embedded[batch_idx], Ys_embedded[batch_idx], Ts[batch_idx], current_loss = fused_gromov_wasserstein_linear_unmixing( Cs[C_idx], Ys[C_idx], Cdict, Ydict, alpha, reg=reg, p=ps[C_idx], q=q, tol_outer=tol_outer, tol_inner=tol_inner, max_iter_outer=max_iter_outer, max_iter_inner=max_iter_inner, symmetric=symmetric, **kwargs @@ -736,7 +736,7 @@ def fused_gromov_wasserstein_linear_unmixing(C, Y, Cdict, Ydict, alpha, reg=0., Returns ------- w: array-like, shape (D,) - fused gromov-wasserstein linear unmixing of (C,Y,p) onto the span of the dictionary. + fused Gromov-Wasserstein linear unmixing of (C,Y,p) onto the span of the dictionary. Cembedded: array-like, shape (nt,nt) embedded structure of :math:`(\mathbf{C},\mathbf{Y}, \mathbf{p})` onto the dictionary, :math:`\sum_d w_d\mathbf{C_{dict}[d]}`. Yembedded: array-like, shape (nt,d) diff --git a/ot/gromov/_gw.py b/ot/gromov/_gw.py index bc4719d..cdfa9a3 100644 --- a/ot/gromov/_gw.py +++ b/ot/gromov/_gw.py @@ -26,7 +26,7 @@ from ._utils import update_square_loss, update_kl_loss def gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', symmetric=None, log=False, armijo=False, G0=None, max_iter=1e4, tol_rel=1e-9, tol_abs=1e-9, **kwargs): r""" - Returns the gromov-wasserstein transport between :math:`(\mathbf{C_1}, \mathbf{p})` and :math:`(\mathbf{C_2}, \mathbf{q})` + Returns the Gromov-Wasserstein transport between :math:`(\mathbf{C_1}, \mathbf{p})` and :math:`(\mathbf{C_2}, \mathbf{q})` The function solves the following optimization problem: @@ -39,6 +39,7 @@ def gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', symmetric=None, log \mathbf{\gamma}^T \mathbf{1} &= \mathbf{q} \mathbf{\gamma} &\geq 0 + Where : - :math:`\mathbf{C_1}`: Metric cost matrix in the source space @@ -68,7 +69,7 @@ def gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', symmetric=None, log symmetric : bool, optional Either C1 and C2 are to be assumed symmetric or not. If let to its default None value, a symmetry test will be conducted. - Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymetric). + Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymmetric). verbose : bool, optional Print information along iterations log : bool, optional @@ -170,7 +171,7 @@ def gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', symmetric=None, log def gromov_wasserstein2(C1, C2, p, q, loss_fun='square_loss', symmetric=None, log=False, armijo=False, G0=None, max_iter=1e4, tol_rel=1e-9, tol_abs=1e-9, **kwargs): r""" - Returns the gromov-wasserstein discrepancy between :math:`(\mathbf{C_1}, \mathbf{p})` and :math:`(\mathbf{C_2}, \mathbf{q})` + Returns the Gromov-Wasserstein discrepancy between :math:`(\mathbf{C_1}, \mathbf{p})` and :math:`(\mathbf{C_2}, \mathbf{q})` The function solves the following optimization problem: @@ -183,6 +184,7 @@ def gromov_wasserstein2(C1, C2, p, q, loss_fun='square_loss', symmetric=None, lo \mathbf{\gamma}^T \mathbf{1} &= \mathbf{q} \mathbf{\gamma} &\geq 0 + Where : - :math:`\mathbf{C_1}`: Metric cost matrix in the source space @@ -216,7 +218,7 @@ def gromov_wasserstein2(C1, C2, p, q, loss_fun='square_loss', symmetric=None, lo symmetric : bool, optional Either C1 and C2 are to be assumed symmetric or not. If let to its default None value, a symmetry test will be conducted. - Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymetric). + Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymmetric). verbose : bool, optional Print information along iterations log : bool, optional @@ -241,7 +243,7 @@ def gromov_wasserstein2(C1, C2, p, q, loss_fun='square_loss', symmetric=None, lo gw_dist : float Gromov-Wasserstein distance log : dict - convergence information and Coupling marix + convergence information and Coupling matrix References ---------- @@ -310,6 +312,7 @@ def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', symmetric= which can lead to copy overhead on GPU arrays. .. note:: All computations in the conjugate gradient solver are done with numpy to limit memory overhead. + The algorithm used for solving the problem is conditional gradient as discussed in :ref:`[24] <references-fused-gromov-wasserstein>` Parameters @@ -329,7 +332,7 @@ def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', symmetric= symmetric : bool, optional Either C1 and C2 are to be assumed symmetric or not. If let to its default None value, a symmetry test will be conducted. - Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymetric). + Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymmetric). alpha : float, optional Trade-off parameter (0 < alpha < 1) armijo : bool, optional @@ -503,7 +506,7 @@ def fused_gromov_wasserstein2(M, C1, C2, p, q, loss_fun='square_loss', symmetric Returns ------- fgw-distance : float - Fused gromov wasserstein distance for the given parameters. + Fused Gromov-Wasserstein distance for the given parameters. log : dict Log dictionary return only if log==True in parameters. diff --git a/ot/gromov/_semirelaxed.py b/ot/gromov/_semirelaxed.py index 638bb1c..cb2bf28 100644 --- a/ot/gromov/_semirelaxed.py +++ b/ot/gromov/_semirelaxed.py @@ -21,7 +21,7 @@ from ._utils import init_matrix_semirelaxed, gwloss, gwggrad def semirelaxed_gromov_wasserstein(C1, C2, p, loss_fun='square_loss', symmetric=None, log=False, G0=None, max_iter=1e4, tol_rel=1e-9, tol_abs=1e-9, **kwargs): r""" - Returns the semi-relaxed gromov-wasserstein divergence transport from :math:`(\mathbf{C_1}, \mathbf{p})` to :math:`\mathbf{C_2}` + Returns the semi-relaxed Gromov-Wasserstein divergence transport from :math:`(\mathbf{C_1}, \mathbf{p})` to :math:`\mathbf{C_2}` The function solves the following optimization problem: @@ -32,6 +32,7 @@ def semirelaxed_gromov_wasserstein(C1, C2, p, loss_fun='square_loss', symmetric= s.t. \ \mathbf{\gamma} \mathbf{1} &= \mathbf{p} \mathbf{\gamma} &\geq 0 + Where : - :math:`\mathbf{C_1}`: Metric cost matrix in the source space @@ -58,7 +59,7 @@ def semirelaxed_gromov_wasserstein(C1, C2, p, loss_fun='square_loss', symmetric= symmetric : bool, optional Either C1 and C2 are to be assumed symmetric or not. If let to its default None value, a symmetry test will be conducted. - Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymetric). + Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymmetric). verbose : bool, optional Print information along iterations log : bool, optional @@ -156,6 +157,7 @@ def semirelaxed_gromov_wasserstein2(C1, C2, p, loss_fun='square_loss', symmetric s.t. \ \mathbf{\gamma} \mathbf{1} &= \mathbf{p} \mathbf{\gamma} &\geq 0 + Where : - :math:`\mathbf{C_1}`: Metric cost matrix in the source space @@ -166,6 +168,7 @@ def semirelaxed_gromov_wasserstein2(C1, C2, p, loss_fun='square_loss', symmetric Note that when using backends, this loss function is differentiable wrt the matrices (C1, C2) but not yet for the weights p. + .. note:: This function is backend-compatible and will work on arrays from all compatible backends. However all the steps in the conditional gradient are not differentiable. @@ -184,7 +187,7 @@ def semirelaxed_gromov_wasserstein2(C1, C2, p, loss_fun='square_loss', symmetric symmetric : bool, optional Either C1 and C2 are to be assumed symmetric or not. If let to its default None value, a symmetry test will be conducted. - Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymetric). + Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymmetric). verbose : bool, optional Print information along iterations log : bool, optional @@ -278,7 +281,7 @@ def semirelaxed_fused_gromov_wasserstein(M, C1, C2, p, loss_fun='square_loss', s symmetric : bool, optional Either C1 and C2 are to be assumed symmetric or not. If let to its default None value, a symmetry test will be conducted. - Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymetric). + Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymmetric). alpha : float, optional Trade-off parameter (0 < alpha < 1) G0: array-like, shape (ns,nt), optional @@ -415,7 +418,7 @@ def semirelaxed_fused_gromov_wasserstein2(M, C1, C2, p, loss_fun='square_loss', symmetric : bool, optional Either C1 and C2 are to be assumed symmetric or not. If let to its default None value, a symmetry test will be conducted. - Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymetric). + Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymmetric). alpha : float, optional Trade-off parameter (0 < alpha < 1) G0: array-like, shape (ns,nt), optional @@ -435,7 +438,7 @@ def semirelaxed_fused_gromov_wasserstein2(M, C1, C2, p, loss_fun='square_loss', Returns ------- srfgw-divergence : float - Semi-relaxed Fused gromov wasserstein divergence for the given parameters. + Semi-relaxed Fused Gromov-Wasserstein divergence for the given parameters. log : dict Log dictionary return only if log==True in parameters. diff --git a/ot/gromov/_utils.py b/ot/gromov/_utils.py index e842250..ef8cd88 100644 --- a/ot/gromov/_utils.py +++ b/ot/gromov/_utils.py @@ -20,7 +20,7 @@ def init_matrix(C1, C2, p, q, loss_fun='square_loss', nx=None): r"""Return loss matrices and tensors for Gromov-Wasserstein fast computation Returns the value of :math:`\mathcal{L}(\mathbf{C_1}, \mathbf{C_2}) \otimes \mathbf{T}` with the - selected loss function as the loss function of Gromow-Wasserstein discrepancy. + selected loss function as the loss function of Gromov-Wasserstein discrepancy. The matrices are computed as described in Proposition 1 in :ref:`[12] <references-init-matrix>` @@ -195,7 +195,7 @@ def gwloss(constC, hC1, hC2, T, nx=None): Returns ------- loss : float - Gromov Wasserstein loss + Gromov-Wasserstein loss .. _references-gwloss: @@ -235,7 +235,7 @@ def gwggrad(constC, hC1, hC2, T, nx=None): Returns ------- grad : array-like, shape (`ns`, `nt`) - Gromov Wasserstein gradient + Gromov-Wasserstein gradient .. _references-gwggrad: @@ -328,7 +328,7 @@ def init_matrix_semirelaxed(C1, C2, p, loss_fun='square_loss', nx=None): r"""Return loss matrices and tensors for semi-relaxed Gromov-Wasserstein fast computation Returns the value of :math:`\mathcal{L}(\mathbf{C_1}, \mathbf{C_2}) \otimes \mathbf{T}` with the - selected loss function as the loss function of semi-relaxed Gromow-Wasserstein discrepancy. + selected loss function as the loss function of semi-relaxed Gromov-Wasserstein discrepancy. The matrices are computed as described in Proposition 1 in :ref:`[12] <references-init-matrix>` and adapted to the semi-relaxed problem where the second marginal is not a constant anymore. |