Merge pull request #42 from rflamary/linear_mapping

Linear mapping + tests

Author: rflamary

Makefile

@@ -1,6 +1,6 @@
 
 
-PYTHON=python
+PYTHON=python3
 
 help :
 	@echo "The following make targets are available:"
@@ -41,21 +41,26 @@ pep8 :
 	flake8 examples/ ot/ test/
 
 test : FORCE pep8
-	python -m py.test -v test/ --cov=ot --cov-report html:cov_html
+	$(PYTHON) -m pytest -v test/ --cov=ot --cov-report html:cov_html
 
 pytest : FORCE 
-	python -m py.test -v test/ --cov=ot
+	$(PYTHON) -m py.test -v test/ --cov=ot
 
 uploadpypi :
 	#python setup.py register
-	python setup.py sdist upload -r pypi
+	$(PYTHON) setup.py sdist upload -r pypi
 
 rdoc :
 	pandoc --from=markdown --to=rst --output=docs/source/readme.rst README.md
 
 
 notebook :
 	ipython notebook --matplotlib=inline  --notebook-dir=notebooks/
+	
+autopep8 :
+	autopep8 -ir test ot examples
 
+aautopep8 :
+	autopep8 -air test ot examples
 
 FORCE :

README.md

@@ -13,14 +13,14 @@ This open source Python library provide several solvers for optimization problem
 
 It provides the following solvers:
 
-* OT solver for the linear program/ Earth Movers Distance [1].
+* OT Network Flow solver for the linear program/ Earth Movers Distance [1].
 * Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2] and stabilized version [9][10] with optional GPU implementation (required cudamat).
 * Bregman projections for Wasserstein barycenter [3] and unmixing [4].
 * Optimal transport for domain adaptation with group lasso regularization [5]
 * Conditional gradient [6] and Generalized conditional gradient for regularized OT [7].
-* Joint OT matrix and mapping estimation [8].
+* Linear OT [14] and Joint OT matrix and mapping estimation [8].
 * Wasserstein Discriminant Analysis [11] (requires autograd + pymanopt).
-* Gromov-Wasserstein distances and barycenters [12]
+* Gromov-Wasserstein distances and barycenters ([13] and regularized [12])
 
 Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder.
 
@@ -195,14 +195,18 @@ You can also post bug reports and feature requests in Github issues. Make sure t
 
 [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). [Generalized conditional gradient: analysis of convergence and applications](https://arxiv.org/pdf/1510.06567.pdf). arXiv preprint arXiv:1510.06567.
 
-[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, [Mapping estimation for discrete optimal transport](http://remi.flamary.com/biblio/perrot2016mapping.pdf), Neural Information Processing Systems (NIPS), 2016.
+[8] M. Perrot, N. Courty, R. Flamary, A. Habrard (2016), [Mapping estimation for discrete optimal transport](http://remi.flamary.com/biblio/perrot2016mapping.pdf), Neural Information Processing Systems (NIPS).
 
 [9] Schmitzer, B. (2016). [Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems](https://arxiv.org/pdf/1610.06519.pdf). arXiv preprint arXiv:1610.06519.
 
 [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). [Scaling algorithms for unbalanced transport problems](https://arxiv.org/pdf/1607.05816.pdf). arXiv preprint arXiv:1607.05816.
 
 [11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). [Wasserstein Discriminant Analysis](https://arxiv.org/pdf/1608.08063.pdf). arXiv preprint arXiv:1608.08063.
 
-[12] Gabriel Peyré, Marco Cuturi, and Justin Solomon, [Gromov-Wasserstein averaging of kernel and distance matrices](http://proceedings.mlr.press/v48/peyre16.html)  International Conference on Machine Learning (ICML). 2016.
+[12] Gabriel Peyré, Marco Cuturi, and Justin Solomon (2016), [Gromov-Wasserstein averaging of kernel and distance matrices](http://proceedings.mlr.press/v48/peyre16.html)  International Conference on Machine Learning (ICML).
 
-[13] Mémoli, Facundo. [Gromov–Wasserstein distances and the metric approach to object matching](https://media.adelaide.edu.au/acvt/Publications/2011/2011-Gromov%E2%80%93Wasserstein%20Distances%20and%20the%20Metric%20Approach%20to%20Object%20Matching.pdf). Foundations of computational mathematics 11.4 (2011): 417-487.
+[13] Mémoli, Facundo (2011). [Gromov–Wasserstein distances and the metric approach to object matching](https://media.adelaide.edu.au/acvt/Publications/2011/2011-Gromov%E2%80%93Wasserstein%20Distances%20and%20the%20Metric%20Approach%20to%20Object%20Matching.pdf). Foundations of computational mathematics 11.4 : 417-487.
+
+[14] Knott, M. and Smith, C. S. (1984).[On the optimal mapping of distributions](https://link.springer.com/article/10.1007/BF00934745), Journal of Optimization Theory and Applications Vol 43.
+
+[15] Peyré, G., & Cuturi, M. (2018). [Computational Optimal Transport](https://arxiv.org/pdf/1803.00567.pdf) .

docs/source/readme.rst

@@ -1,16 +1,17 @@
 POT: Python Optimal Transport
 =============================
 
-|PyPI version| |Build Status| |Documentation Status| |Anaconda Cloud|
-|License| |Anaconda downloads|
+|PyPI version| |Anaconda Cloud| |Build Status| |Documentation Status|
+|Anaconda downloads| |License|
 
 This open source Python library provide several solvers for optimization
 problems related to Optimal Transport for signal, image processing and
 machine learning.
 
 It provides the following solvers:
 
--  OT solver for the linear program/ Earth Movers Distance [1].
+-  OT Network Flow solver for the linear program/ Earth Movers Distance
+   [1].
 -  Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2]
    and stabilized version [9][10] with optional GPU implementation
    (required cudamat).
@@ -19,10 +20,11 @@ It provides the following solvers:
    regularization [5]
 -  Conditional gradient [6] and Generalized conditional gradient for
    regularized OT [7].
--  Joint OT matrix and mapping estimation [8].
+-  Linear OT [14] and Joint OT matrix and mapping estimation [8].
 -  Wasserstein Discriminant Analysis [11] (requires autograd +
    pymanopt).
--  Gromov-Wasserstein distances and barycenters [12]
+-  Gromov-Wasserstein distances and barycenters ([13] and regularized
+   [12])
 
 Some demonstrations (both in Python and Jupyter Notebook format) are
 available in the examples folder.
@@ -281,10 +283,10 @@ conditional gradient: analysis of convergence and
 applications <https://arxiv.org/pdf/1510.06567.pdf>`__. arXiv preprint
 arXiv:1510.06567.
 
-[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, `Mapping estimation
-for discrete optimal
+[8] M. Perrot, N. Courty, R. Flamary, A. Habrard (2016), `Mapping
+estimation for discrete optimal
 transport <http://remi.flamary.com/biblio/perrot2016mapping.pdf>`__,
-Neural Information Processing Systems (NIPS), 2016.
+Neural Information Processing Systems (NIPS).
 
 [9] Schmitzer, B. (2016). `Stabilized Sparse Scaling Algorithms for
 Entropy Regularized Transport
@@ -301,25 +303,32 @@ arXiv:1607.05816.
 Analysis <https://arxiv.org/pdf/1608.08063.pdf>`__. arXiv preprint
 arXiv:1608.08063.
 
-[12] Gabriel Peyré, Marco Cuturi, and Justin Solomon,
+[12] Gabriel Peyré, Marco Cuturi, and Justin Solomon (2016),
 `Gromov-Wasserstein averaging of kernel and distance
 matrices <http://proceedings.mlr.press/v48/peyre16.html>`__
-International Conference on Machine Learning (ICML). 2016.
+International Conference on Machine Learning (ICML).
 
-[13] Mémoli, Facundo. `Gromov–Wasserstein distances and the metric
-approach to object
+[13] Mémoli, Facundo (2011). `Gromov–Wasserstein distances and the
+metric approach to object
 matching <https://media.adelaide.edu.au/acvt/Publications/2011/2011-Gromov%E2%80%93Wasserstein%20Distances%20and%20the%20Metric%20Approach%20to%20Object%20Matching.pdf>`__.
-Foundations of computational mathematics 11.4 (2011): 417-487.
+Foundations of computational mathematics 11.4 : 417-487.
+
+[14] Knott, M. and Smith, C. S. (1984).`On the optimal mapping of
+distributions <https://link.springer.com/article/10.1007/BF00934745>`__,
+Journal of Optimization Theory and Applications Vol 43.
+
+[15] Peyré, G., & Cuturi, M. (2018). `Computational Optimal
+Transport <https://arxiv.org/pdf/1803.00567.pdf>`__ .
 
 .. |PyPI version| image:: https://badge.fury.io/py/POT.svg
    :target: https://badge.fury.io/py/POT
+.. |Anaconda Cloud| image:: https://anaconda.org/conda-forge/pot/badges/version.svg
+   :target: https://anaconda.org/conda-forge/pot
 .. |Build Status| image:: https://travis-ci.org/rflamary/POT.svg?branch=master
    :target: https://travis-ci.org/rflamary/POT
 .. |Documentation Status| image:: https://readthedocs.org/projects/pot/badge/?version=latest
    :target: http://pot.readthedocs.io/en/latest/?badge=latest
-.. |Anaconda Cloud| image:: https://anaconda.org/conda-forge/pot/badges/version.svg
+.. |Anaconda downloads| image:: https://anaconda.org/conda-forge/pot/badges/downloads.svg
    :target: https://anaconda.org/conda-forge/pot
 .. |License| image:: https://anaconda.org/conda-forge/pot/badges/license.svg
    :target: https://github.com/rflamary/POT/blob/master/LICENSE
-.. |Anaconda downloads| image:: https://anaconda.org/conda-forge/pot/badges/downloads.svg
-   :target: https://anaconda.org/conda-forge/pot

examples/plot_otda_linear_mapping.py

@@ -0,0 +1,138 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Mar 20 14:31:15 2018
+
+@author: rflamary
+"""
+
+import numpy as np
+import pylab as pl
+import ot
+
+##############################################################################
+# Generate data
+# -------------
+
+n = 1000
+d = 2
+sigma = .1
+
+# source samples
+angles = np.random.rand(n, 1) * 2 * np.pi
+xs = np.concatenate((np.sin(angles), np.cos(angles)),
+                    axis=1) + sigma * np.random.randn(n, 2)
+xs[:n // 2, 1] += 2
+
+
+# target samples
+anglet = np.random.rand(n, 1) * 2 * np.pi
+xt = np.concatenate((np.sin(anglet), np.cos(anglet)),
+                    axis=1) + sigma * np.random.randn(n, 2)
+xt[:n // 2, 1] += 2
+
+
+A = np.array([[1.5, .7], [.7, 1.5]])
+b = np.array([[4, 2]])
+xt = xt.dot(A) + b
+
+##############################################################################
+# Plot data
+# ---------
+
+pl.figure(1, (5, 5))
+pl.plot(xs[:, 0], xs[:, 1], '+')
+pl.plot(xt[:, 0], xt[:, 1], 'o')
+
+
+##############################################################################
+# Estimate linear mapping and transport
+# -------------------------------------
+
+Ae, be = ot.da.OT_mapping_linear(xs, xt)
+
+xst = xs.dot(Ae) + be
+
+
+##############################################################################
+# Plot transported samples
+# ------------------------
+
+pl.figure(1, (5, 5))
+pl.clf()
+pl.plot(xs[:, 0], xs[:, 1], '+')
+pl.plot(xt[:, 0], xt[:, 1], 'o')
+pl.plot(xst[:, 0], xst[:, 1], '+')
+
+pl.show()
+
+##############################################################################
+# Load image data
+# ---------------
+
+
+def im2mat(I):
+    """Converts and image to matrix (one pixel per line)"""
+    return I.reshape((I.shape[0] * I.shape[1], I.shape[2]))
+
+
+def mat2im(X, shape):
+    """Converts back a matrix to an image"""
+    return X.reshape(shape)
+
+
+def minmax(I):
+    return np.clip(I, 0, 1)
+
+
+# Loading images
+I1 = pl.imread('../data/ocean_day.jpg').astype(np.float64) / 256
+I2 = pl.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256
+
+
+X1 = im2mat(I1)
+X2 = im2mat(I2)
+
+##############################################################################
+# Estimate mapping and adapt
+# ----------------------------
+
+mapping = ot.da.LinearTransport()
+
+mapping.fit(Xs=X1, Xt=X2)
+
+
+xst = mapping.transform(Xs=X1)
+xts = mapping.inverse_transform(Xt=X2)
+
+I1t = minmax(mat2im(xst, I1.shape))
+I2t = minmax(mat2im(xts, I2.shape))
+
+# %%
+
+
+##############################################################################
+# Plot transformed images
+# -----------------------
+
+pl.figure(2, figsize=(10, 7))
+
+pl.subplot(2, 2, 1)
+pl.imshow(I1)
+pl.axis('off')
+pl.title('Im. 1')
+
+pl.subplot(2, 2, 2)
+pl.imshow(I2)
+pl.axis('off')
+pl.title('Im. 2')
+
+pl.subplot(2, 2, 3)
+pl.imshow(I1t)
+pl.axis('off')
+pl.title('Mapping Im. 1')
+
+pl.subplot(2, 2, 4)
+pl.imshow(I2t)
+pl.axis('off')
+pl.title('Inverse mapping Im. 2')