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# -*- coding: utf-8 -*-
"""
Domain adaptation with optimal transport with GPU implementation
"""
# Author: Remi Flamary <remi.flamary@unice.fr>
# Nicolas Courty <ncourty@irisa.fr>
# Michael Perrot <michael.perrot@univ-st-etienne.fr>
# Leo Gautheron <https://github.com/aje>
#
# License: MIT License
import cupy as np # np used for matrix computation
import cupy as cp # cp used for cupy specific operations
import numpy as npp
from . import utils
from .bregman import sinkhorn
def sinkhorn_lpl1_mm(a, labels_a, b, M, reg, eta=0.1, numItermax=10,
numInnerItermax=200, stopInnerThr=1e-9, verbose=False,
log=False, to_numpy=True):
"""
Solve the entropic regularization optimal transport problem with nonconvex
group lasso regularization on GPU
If the input matrix are in numpy format, they will be uploaded to the
GPU first which can incur significant time overhead.
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega_e(\gamma)
+ \eta \Omega_g(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega_e` is the entropic regularization term
:math:`\Omega_e(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`\Omega_g` is the group lasso regulaization term
:math:`\Omega_g(\gamma)=\sum_{i,c} \|\gamma_{i,\mathcal{I}_c}\|^{1/2}_1`
where :math:`\mathcal{I}_c` are the index of samples from class c
in the source domain.
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the generalised conditional
gradient as proposed in [5]_ [7]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
labels_a : np.ndarray (ns,)
labels of samples in the source domain
b : np.ndarray (nt,)
samples weights in the target domain
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term for entropic regularization >0
eta : float, optional
Regularization term for group lasso regularization >0
numItermax : int, optional
Max number of iterations
numInnerItermax : int, optional
Max number of iterations (inner sinkhorn solver)
stopInnerThr : float, optional
Stop threshold on error (inner sinkhorn solver) (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
to_numpy : boolean, optional (default True)
If true convert back the GPU array result to numpy format.
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy,
"Optimal Transport for Domain Adaptation," in IEEE
Transactions on Pattern Analysis and Machine Intelligence ,
vol.PP, no.99, pp.1-1
.. [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015).
Generalized conditional gradient: analysis of convergence
and applications. arXiv preprint arXiv:1510.06567.
See Also
--------
ot.lp.emd : Unregularized OT
ot.bregman.sinkhorn : Entropic regularized OT
ot.optim.cg : General regularized OT
"""
a, labels_a, b, M = utils.to_gpu(a, labels_a, b, M)
p = 0.5
epsilon = 1e-3
indices_labels = []
labels_a2 = cp.asnumpy(labels_a)
classes = npp.unique(labels_a2)
for c in classes:
idxc = utils.to_gpu(*npp.where(labels_a2 == c))
indices_labels.append(idxc)
W = np.zeros(M.shape)
for cpt in range(numItermax):
Mreg = M + eta * W
transp = sinkhorn(a, b, Mreg, reg, numItermax=numInnerItermax,
stopThr=stopInnerThr, to_numpy=False)
# the transport has been computed. Check if classes are really
# separated
W = np.ones(M.shape)
for (i, c) in enumerate(classes):
majs = np.sum(transp[indices_labels[i]], axis=0)
majs = p * ((majs + epsilon)**(p - 1))
W[indices_labels[i]] = majs
if to_numpy:
return utils.to_np(transp)
else:
return transp
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