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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 numpy as np
#from ..utils import unif
from .bregman import sinkhorn
import cudamat
def pairwiseEuclideanGPU(a, b, returnAsGPU=False, squared=False):
"""
Compute the pairwise euclidean distance between matrices a and b.
Parameters
----------
a : np.ndarray (n, f)
first matrice
b : np.ndarray (m, f)
second matrice
returnAsGPU : boolean, optional (default False)
if True, returns cudamat matrix still on GPU, else return np.ndarray
squared : boolean, optional (default False)
if True, return squared euclidean distance matrice
Returns
-------
c : (n x m) np.ndarray or cudamat.CUDAMatrix
pairwise euclidean distance distance matrix
"""
# a is shape (n, f) and b shape (m, f). Return matrix c of shape (n, m).
# First compute in c_GPU the squared euclidean distance. And return its
# square root. At each cell [i,j] of c, we want to have
# sum{k in range(f)} ( (a[i,k] - b[j,k])^2 ). We know that
# (a-b)^2 = a^2 -2ab +b^2. Thus we want to have in each cell of c:
# sum{k in range(f)} ( a[i,k]^2 -2a[i,k]b[j,k] +b[j,k]^2).
a_GPU = cudamat.CUDAMatrix(a)
b_GPU = cudamat.CUDAMatrix(b)
# Multiply a by b transpose to obtain in each cell [i,j] of c the
# value sum{k in range(f)} ( a[i,k]b[j,k] )
c_GPU = cudamat.dot(a_GPU, b_GPU.transpose())
# multiply by -2 to have sum{k in range(f)} ( -2a[i,k]b[j,k] )
c_GPU.mult(-2)
# Compute the vectors of the sum of squared elements.
a_GPU = cudamat.pow(a_GPU, 2).sum(axis=1)
b_GPU = cudamat.pow(b_GPU, 2).sum(axis=1)
# Add the vectors in each columns (respectivly rows) of c.
# sum{k in range(f)} ( a[i,k]^2 -2a[i,k]b[j,k] )
c_GPU.add_col_vec(a_GPU)
# sum{k in range(f)} ( a[i,k]^2 -2a[i,k]b[j,k] +b[j,k]^2)
c_GPU.add_row_vec(b_GPU.transpose())
if not squared:
c_GPU = cudamat.sqrt(c_GPU)
if returnAsGPU:
return c_GPU
else:
return c_GPU.asarray()
def sinkhorn_lpl1_mm(a, labels_a, b, M_GPU, 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 weights in the target domain
M_GPU : cudamat.CUDAMatrix (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
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
Nfin = len(b)
indices_labels = []
classes = np.unique(labels_a)
for c in classes:
idxc, = np.where(labels_a == c)
indices_labels.append(cudamat.CUDAMatrix(idxc.reshape(1, -1)))
Mreg_GPU = cudamat.empty(M_GPU.shape)
W_GPU = cudamat.empty(M_GPU.shape).assign(0)
for cpt in range(numItermax):
Mreg_GPU.assign(M_GPU)
Mreg_GPU.add_mult(W_GPU, eta)
transp_GPU = sinkhorn(a, b, Mreg_GPU, reg, numItermax=numInnerItermax,
stopThr=stopInnerThr, returnAsGPU=True)
# the transport has been computed. Check if classes are really
# separated
W_GPU.assign(1)
W_GPU = W_GPU.transpose()
for (i, c) in enumerate(classes):
(_, nbRow) = indices_labels[i].shape
tmpC_GPU = cudamat.empty((Nfin, nbRow)).assign(0)
transp_GPU.transpose().select_columns(indices_labels[i], tmpC_GPU)
majs_GPU = tmpC_GPU.sum(axis=1).add(epsilon)
cudamat.pow(majs_GPU, (p - 1))
majs_GPU.mult(p)
tmpC_GPU.assign(0)
tmpC_GPU.add_col_vec(majs_GPU)
W_GPU.set_selected_columns(indices_labels[i], tmpC_GPU)
W_GPU = W_GPU.transpose()
return transp_GPU.asarray()
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