From 9c6ac880d426b7577918b0c77bd74b3b01930ef6 Mon Sep 17 00:00:00 2001 From: ncassereau-idris <84033440+ncassereau-idris@users.noreply.github.com> Date: Wed, 3 Nov 2021 17:29:16 +0100 Subject: [MRG] Docs updates (#298) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * bregman docs * sliced docs * docs partial * unbalanced docs * stochastic docs * plot docs * datasets docs * utils docs * dr docs * dr docs corrected * smooth docs * docs da * pep8 * docs gromov * more space after min and argmin * docs lp * bregman docs * bregman docs mistake corrected * pep8 Co-authored-by: Rémi Flamary --- ot/gromov.py | 35 ++++++++++++++++++++--------------- 1 file changed, 20 insertions(+), 15 deletions(-) (limited to 'ot/gromov.py') diff --git a/ot/gromov.py b/ot/gromov.py index a0fbf48..465693d 100644 --- a/ot/gromov.py +++ b/ot/gromov.py @@ -327,7 +327,8 @@ def gromov_wasserstein(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwargs The function solves the following optimization problem: .. math:: - \mathbf{GW} = \mathop{\arg \min}_\mathbf{T} \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} + \mathbf{GW} = \mathop{\arg \min}_\mathbf{T} \quad \sum_{i,j,k,l} + L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} Where : @@ -410,7 +411,8 @@ def gromov_wasserstein2(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwarg The function solves the following optimization problem: .. math:: - GW = \min_\mathbf{T} \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} + GW = \min_\mathbf{T} \quad \sum_{i,j,k,l} + L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} Where : @@ -487,8 +489,8 @@ def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5, Computes the FGW transport between two graphs (see :ref:`[24] `) .. math:: - \gamma = \mathop{\arg \min}_\gamma (1 - \alpha) <\gamma, \mathbf{M}>_F + \alpha \sum_{i,j,k,l} - L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} + \gamma = \mathop{\arg \min}_\gamma \quad (1 - \alpha) \langle \gamma, \mathbf{M} \rangle_F + + \alpha \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} s.t. \ \mathbf{\gamma} \mathbf{1} &= \mathbf{p} @@ -569,7 +571,7 @@ def fused_gromov_wasserstein2(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5 Computes the FGW distance between two graphs see (see :ref:`[24] `) .. math:: - \min_\gamma (1 - \alpha) <\gamma, \mathbf{M}>_F + \alpha \sum_{i,j,k,l} + \min_\gamma \quad (1 - \alpha) \langle \gamma, \mathbf{M} \rangle_F + \alpha \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} s.t. \ \mathbf{\gamma} \mathbf{1} &= \mathbf{p} @@ -591,9 +593,9 @@ def fused_gromov_wasserstein2(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5 M : array-like, shape (ns, nt) Metric cost matrix between features across domains C1 : array-like, shape (ns, ns) - Metric cost matrix respresentative of the structure in the source space. + Metric cost matrix representative of the structure in the source space. C2 : array-like, shape (nt, nt) - Metric cost matrix espresentative of the structure in the target space. + Metric cost matrix representative of the structure in the target space. p : array-like, shape (ns,) Distribution in the source space. q : array-like, shape (nt,) @@ -612,8 +614,8 @@ def fused_gromov_wasserstein2(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5 Returns ------- - gamma : array-like, shape (ns, nt) - Optimal transportation matrix for the given parameters. + fgw-distance : float + Fused gromov wasserstein distance for the given parameters. log : dict Log dictionary return only if log==True in parameters. @@ -780,7 +782,8 @@ def pointwise_gromov_wasserstein(C1, C2, p, q, loss_fun, The function solves the following optimization problem: .. math:: - \mathbf{GW} = \mathop{\arg \min}_\mathbf{T} \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} + \mathbf{GW} = \mathop{\arg \min}_\mathbf{T} \quad \sum_{i,j,k,l} + L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} s.t. \ \mathbf{T} \mathbf{1} &= \mathbf{p} @@ -901,7 +904,8 @@ def sampled_gromov_wasserstein(C1, C2, p, q, loss_fun, The function solves the following optimization problem: .. math:: - \mathbf{GW} = \mathop{\arg \min}_\mathbf{T} \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} + \mathbf{GW} = \mathop{\arg \min}_\mathbf{T} \quad \sum_{i,j,k,l} + L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} s.t. \ \mathbf{T} \mathbf{1} &= \mathbf{p} @@ -1052,7 +1056,7 @@ def entropic_gromov_wasserstein(C1, C2, p, q, loss_fun, epsilon, The function solves the following optimization problem: .. math:: - \mathbf{GW} = \mathop{\arg\min}_\mathbf{T} \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} - \epsilon(H(\mathbf{T})) + \mathbf{GW} = \mathop{\arg\min}_\mathbf{T} \quad \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} - \epsilon(H(\mathbf{T})) s.t. \ \mathbf{T} \mathbf{1} &= \mathbf{p} @@ -1157,7 +1161,8 @@ def entropic_gromov_wasserstein2(C1, C2, p, q, loss_fun, epsilon, The function solves the following optimization problem: .. math:: - GW = \min_\mathbf{T} \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} - \epsilon(H(\mathbf{T})) + GW = \min_\mathbf{T} \quad \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) + \mathbf{T}_{i,j} \mathbf{T}_{k,l} - \epsilon(H(\mathbf{T})) Where : @@ -1223,7 +1228,7 @@ def entropic_gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun, epsilon, .. math:: - \mathbf{C} = \mathop{\arg \min}_{\mathbf{C}\in \mathbb{R}^{N \times N}} \sum_s \lambda_s \mathrm{GW}(\mathbf{C}, \mathbf{C}_s, \mathbf{p}, \mathbf{p}_s) + \mathbf{C} = \mathop{\arg \min}_{\mathbf{C}\in \mathbb{R}^{N \times N}} \quad \sum_s \lambda_s \mathrm{GW}(\mathbf{C}, \mathbf{C}_s, \mathbf{p}, \mathbf{p}_s) Where : @@ -1336,7 +1341,7 @@ def gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun, .. math:: - \mathbf{C} = \mathop{\arg \min}_{\mathbf{C}\in \mathbb{R}^{N \times N}} \sum_s \lambda_s \mathrm{GW}(\mathbf{C}, \mathbf{C}_s, \mathbf{p}, \mathbf{p}_s) + \mathbf{C} = \mathop{\arg \min}_{\mathbf{C}\in \mathbb{R}^{N \times N}} \quad \sum_s \lambda_s \mathrm{GW}(\mathbf{C}, \mathbf{C}_s, \mathbf{p}, \mathbf{p}_s) Where : -- cgit v1.2.3