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[WIP] Implementation of FUGW and UCOOT (#677)
* implementation of FUGW and UCOOT * fix pep8 error * fix test_utils error * remove print * add documentation and fix bug * first code review * fix documentation
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,11 +1,16 @@ | ||
| # -*- coding: utf-8 -*- | ||
| r""" | ||
| =============================================================== | ||
| Learning sample marginal distribution with CO-Optimal Transport | ||
| =============================================================== | ||
| ====================================================================================================================================== | ||
| Detecting outliers by learning sample marginal distribution with CO-Optimal Transport and by using unbalanced Co-Optimal Transport | ||
| ====================================================================================================================================== | ||
| In this example, we illustrate how to estimate the sample marginal distribution which minimizes | ||
| the CO-Optimal Transport distance [47]_ between two matrices. More precisely, given a source data | ||
| In this example, we consider two point clouds living in different Euclidean spaces, where the outliers | ||
| are artifically injected into the target data. We illustrate two methods which allow to filter out | ||
| these outliers. | ||
| The first method requires learning the sample marginal distribution which minimizes | ||
| the CO-Optimal Transport distance [49] between two input spaces. | ||
| More precisely, given a source data | ||
| :math:`(X, \mu_x^{(s)}, \mu_x^{(f)})` and a target matrix :math:`Y` associated with a fixed | ||
| histogram on features :math:`\mu_y^{(f)}`, we want to solve the following problem | ||
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|
@@ -17,9 +22,19 @@ | |
| allows us to compute the CO-Optimal Transport distance with :func:`ot.coot.co_optimal_transport2` | ||
| with differentiable losses. | ||
| The second method simply requires direct application of unbalanced Co-Optimal Transport [71]. | ||
| More precisely, it is enough to use the sample and feature coupling from solving | ||
| .. math:: | ||
| \text{UCOOT}\left( (X, \mu_x^{(s)}, \mu_x^{(f)}), (Y, \mu_y^{(s)}, \mu_y^{(f)}) \right) | ||
| where all the marginal distributions are uniform. | ||
| .. [49] Redko, I., Vayer, T., Flamary, R., and Courty, N. (2020). | ||
| `CO-Optimal Transport <https://proceedings.neurips.cc/paper/2020/file/cc384c68ad503482fb24e6d1e3b512ae-Paper.pdf>`_. | ||
| Advances in Neural Information Processing Systems, 33. | ||
| .. [71] H. Tran, H. Janati, N. Courty, R. Flamary, I. Redko, P. Demetci & R. Singh (2023). [Unbalanced Co-Optimal Transport](https://dl.acm.org/doi/10.1609/aaai.v37i8.26193). | ||
| AAAI Conference on Artificial Intelligence. | ||
| """ | ||
|
|
||
| # Author: Remi Flamary <[email protected]> | ||
|
|
@@ -35,6 +50,7 @@ | |
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| from ot.coot import co_optimal_transport as coot | ||
| from ot.coot import co_optimal_transport2 as coot2 | ||
| from ot.gromov._unbalanced import unbalanced_co_optimal_transport | ||
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||
| # %% | ||
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@@ -148,3 +164,49 @@ | |
| con = ConnectionPatch( | ||
| xyA=xyA, xyB=xyB, coordsA=ax1.transData, coordsB=ax2.transData, color="blue") | ||
| fig.add_artist(con) | ||
|
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||
| # %% | ||
| # Now, let see if we can use unbalanced Co-Optimal Transport to recover the clean OT plans, | ||
| # without the need of learning the marginal distribution as in Co-Optimal Transport. | ||
| # ----------------------------------------------------------------------------------------- | ||
|
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||
| pi_sample, pi_feature = unbalanced_co_optimal_transport( | ||
| X=X, Y=Y_noisy, reg_marginals=(10, 10), epsilon=0, divergence="kl", | ||
| unbalanced_solver="mm", max_iter=1000, tol=1e-6, | ||
| max_iter_ot=1000, tol_ot=1e-6, log=False, verbose=False | ||
| ) | ||
|
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||
| # %% | ||
| # Visualizing the row and column alignments learned by unbalanced Co-Optimal Transport. | ||
| # ----------------------------------------------------------------------------------------- | ||
| # | ||
| # Similar to Co-Optimal Transport, we are also be able to fully recover the clean OT plans. | ||
|
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||
| fig = pl.figure(4, (9, 7)) | ||
| pl.clf() | ||
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| ax1 = pl.subplot(2, 2, 3) | ||
| pl.imshow(X, vmin=-2, vmax=2) | ||
| pl.xlabel('$X$') | ||
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||
| ax2 = pl.subplot(2, 2, 2) | ||
| ax2.yaxis.tick_right() | ||
| pl.imshow(np.transpose(Y_noisy), vmin=-2, vmax=2) | ||
| pl.title("Transpose(Noisy $Y$)") | ||
| ax2.xaxis.tick_top() | ||
|
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||
| for i in range(n1): | ||
| j = np.argmax(pi_sample[i, :]) | ||
| xyA = (d1 - .5, i) | ||
| xyB = (j, d2 - .5) | ||
| con = ConnectionPatch(xyA=xyA, xyB=xyB, coordsA=ax1.transData, | ||
| coordsB=ax2.transData, color="black") | ||
| fig.add_artist(con) | ||
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||
| for i in range(d1): | ||
| j = np.argmax(pi_feature[i, :]) | ||
| xyA = (i, -.5) | ||
| xyB = (-.5, j) | ||
| con = ConnectionPatch( | ||
| xyA=xyA, xyB=xyB, coordsA=ax1.transData, coordsB=ax2.transData, color="blue") | ||
| fig.add_artist(con) | ||
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@@ -6,13 +6,16 @@ | |
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| # Author: Remi Flamary <[email protected]> | ||
| # Cedric Vincent-Cuaz <[email protected]> | ||
| # Quang Huy Tran <[email protected]> | ||
| # | ||
| # License: MIT License | ||
|
|
||
| # All submodules and packages | ||
| from ._utils import (init_matrix, tensor_product, gwloss, gwggrad, | ||
| init_matrix_semirelaxed, semirelaxed_init_plan, | ||
| update_barycenter_structure, update_barycenter_feature) | ||
| update_barycenter_structure, update_barycenter_feature, | ||
| div_between_product, div_to_product, fused_unbalanced_across_spaces_cost, | ||
| uot_cost_matrix, uot_parameters_and_measures) | ||
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| from ._gw import (gromov_wasserstein, gromov_wasserstein2, | ||
| fused_gromov_wasserstein, fused_gromov_wasserstein2, | ||
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@@ -63,9 +66,17 @@ | |
| quantized_fused_gromov_wasserstein_samples | ||
| ) | ||
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| from ._unbalanced import (fused_unbalanced_gromov_wasserstein, | ||
| fused_unbalanced_gromov_wasserstein2, | ||
| unbalanced_co_optimal_transport, | ||
| unbalanced_co_optimal_transport2, | ||
| fused_unbalanced_across_spaces_divergence) | ||
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| __all__ = ['init_matrix', 'tensor_product', 'gwloss', 'gwggrad', | ||
| 'init_matrix_semirelaxed', 'semirelaxed_init_plan', | ||
| 'update_barycenter_structure', 'update_barycenter_feature', | ||
| 'div_between_product', 'div_to_product', 'fused_unbalanced_across_spaces_cost', | ||
| 'uot_cost_matrix', 'uot_parameters_and_measures', | ||
| 'gromov_wasserstein', 'gromov_wasserstein2', 'fused_gromov_wasserstein', | ||
| 'fused_gromov_wasserstein2', 'solve_gromov_linesearch', 'gromov_barycenters', | ||
| 'fgw_barycenters', 'entropic_gromov_wasserstein', 'entropic_gromov_wasserstein2', | ||
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@@ -87,4 +98,7 @@ | |
| 'get_graph_representants', 'format_partitioned_graph', | ||
| 'quantized_fused_gromov_wasserstein', 'get_partition_and_representants_samples', | ||
| 'format_partitioned_samples', 'quantized_fused_gromov_wasserstein_samples', | ||
| 'fused_unbalanced_gromov_wasserstein', 'fused_unbalanced_gromov_wasserstein2', | ||
| 'unbalanced_co_optimal_transport', 'unbalanced_co_optimal_transport2', | ||
| 'fused_unbalanced_across_spaces_divergence' | ||
| ] | ||
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