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# -*- coding: utf-8 -*-
"""
Domain adaptation with optimal transport
"""
import numpy as np
from .bregman import sinkhorn
def indices(a, func):
return [i for (i, val) in enumerate(a) if func(val)]
def sinkhorn_lpl1_mm(a,labels_a, b, M, reg, eta=0.1,numItermax = 10,numInnerItermax = 200,stopInnerThr=1e-9,verbose=False,log=False):
"""
Solve the entropic regularization optimal transport problem with nonconvex group lasso regularization
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 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
Returns
-------
gamma: (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log: dict
log dictionary return only if log==True in parameters
Examples
--------
>>> a=[.5,.5]
>>> b=[.5,.5]
>>> M=[[0.,1.],[1.,0.]]
>>> ot.sinkhorn(a,b,M,1)
array([[ 0.36552929, 0.13447071],
[ 0.13447071, 0.36552929]])
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
"""
p=0.5
epsilon = 1e-3
# init data
Nini = len(a)
Nfin = len(b)
indices_labels = []
idx_begin = np.min(labels_a)
for c in range(idx_begin,np.max(labels_a)+1):
idxc = indices(labels_a, lambda x: x==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)
# the transport has been computed. Check if classes are really separated
W = np.ones((Nini,Nfin))
for t in range(Nfin):
column = transp[:,t]
all_maj = []
for c in range(idx_begin,np.max(labels_a)+1):
col_c = column[indices_labels[c-idx_begin]]
if c!=-1:
maj = p*((sum(col_c)+epsilon)**(p-1))
W[indices_labels[c-idx_begin],t]=maj
all_maj.append(maj)
# now we majorize the unlabelled by the min of the majorizations
# do it only for unlabbled data
if idx_begin==-1:
W[indices_labels[0],t]=np.min(all_maj)
return transp
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