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alignf.py
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alignf.py
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# A python implementation of ALIGNF
# Author: Huibin Shen
# 20.03.2015
import numpy as np
from scipy.sparse import isspmatrix_csr
import mosek
def f_dot(X,Y):
if isspmatrix_csr(X):
t = X*Y
return sum(t.data)
else:
return sum(sum(X*Y))
def center(km):
"""Center km if km is dense matrix"""
if isspmatrix_csr(km):
print "Centering a sparse matrix!!! Break the sparsity."
m = len(km)
I = np.eye(m)
one = np.ones((m,1))
t = I - np.dot(one,one.T)/m
return np.dot(np.dot(t,km),t)
def streamprinter(text):
sys.stdout.write(text)
sys.stdout.flush()
def ALIGNF(km_list, ky, centering=True):
"""
Parameters:
-----------
km_list, a list of kernel matrices, list of 2d array
ky, target kernel, 2d array
Returns:
--------
xx, the weight for each kernels
"""
n_feat = len(km_list)
km_list_copy = []
# center the kernel first
for i in range(n_feat):
if centering:
km_list_copy.append(center(km_list[i].copy()))
else:
km_list_copy.append(km_list[i].copy())
if centering:
ky_copy = center(ky.copy())
else:
ky_copy = ky.copy()
a = np.zeros(n_feat)
for i in range(n_feat):
a[i] = f_dot(km_list_copy[i], ky_copy)
M = np.zeros((n_feat, n_feat))
for i in range(n_feat):
for j in range(i,n_feat):
M[i,j] = f_dot(km_list_copy[i],km_list_copy[j])
M[j,i] = M[i,j]
Q = 2*M
C = -2*a
Q = Q + np.diag(np.ones(n_feat)*1e-10)
################################################
# Using mosek to solve the quadratice programming
# Set upper diagonal element to zeros, mosek only accept lower triangle
iu = np.triu_indices(n_feat,1)
Q[iu] = 0
# start solving with mosek
inf = 0.0
env = mosek.Env()
env.set_Stream(mosek.streamtype.log, streamprinter)
# Create a task
task = env.Task()
task.set_Stream(mosek.streamtype.log, streamprinter)
# Set up bound for variables
bkx = [mosek.boundkey.lo]* n_feat
blx = [0.0] * n_feat
bux = [+inf]* n_feat
numvar = len(bkx)
task.appendvars(numvar)
for j in range(numvar):
task.putcj(j,C[j])
task.putvarbound(j,bkx[j],blx[j],bux[j])
# Set up quadratic objective
inds = np.nonzero(Q)
qsubi = inds[0].tolist()
qsubj = inds[1].tolist()
qval = Q[inds].tolist()
# Input quadratic objective
task.putqobj(qsubi,qsubj,qval)
# Input objective sense (minimize/mximize)
task.putobjsense(mosek.objsense.minimize)
task.optimize()
# Print a summary containing information
# about the solution for debugging purposes
task.solutionsummary(mosek.streamtype.msg)
solsta = task.getsolsta(mosek.soltype.itr)
if (solsta == mosek.solsta.optimal or
solsta == mosek.solsta.near_optimal):
# Output a solution
xx = np.zeros(numvar, float)
task.getxx(mosek.soltype.itr, xx)
#xx = xx/np.linalg.norm(xx)
return xx
else:
print "Solution not optimal or near optimal"
print solsta
return None
# test
#km_list = []
#for i in range(5):
# A = np.random.rand(5,5)
# km_list.append(np.dot(A.T,A))
#B = np.random.rand(5,5)
#ky = np.dot(B.T,B)
#w = ALIGNF(km_list, ky)
#print w