def histgmm_main( mu0, sigma0, gamma, prior, w, x,
maxiters, minchange, minsigma, n, m ):
"""Do EM."""
mu = num.zeros( mu0.shape )
sigma = num.zeros( mu0.shape )
ischange = num.ones( m ).astype( num.bool )
if PRINT_PROGRESS: print "EM iterations:", ; sys.stdout.flush()
for iter in range( maxiters ):
if PRINT_PROGRESS: print iter, ; sys.stdout.flush()
# compute probability for each
p1 = normpdf( make_vect( x[:,ischange] ).T,
make_vect( kron( num.ones((n,1)), mu0[0,ischange] ) ).T,
make_vect( kron( num.ones((n,1)), sigma0[0,ischange] ) ) ) \
* make_vect( kron( num.ones((n,1)), prior[0,ischange] ) )
p2 = normpdf( make_vect( x[:,ischange] ).T,
make_vect( kron( num.ones((n,1)), mu0[1,ischange] ) ).T,
make_vect( kron( num.ones((n,1)), sigma0[1,ischange] ) ) ) \
* make_vect( kron( num.ones((n,1)), prior[1,ischange] ) )
tmp = p1 + p2
p1[tmp < eps] = 0.5
p2[tmp < eps] = 0.5
tmp[tmp < eps] = 1
gamma[:,ischange] = (p1/tmp).reshape( (n,len(ischange.nonzero()[0])) )
# update the mean, variance, and prior
tmp = w[:,ischange] * gamma[:,ischange]
prior[0,ischange] = tmp.sum( 0 )
tmp = tmp[:,prior[0,ischange] > 0]
isprior = prior[0,:] > 0
c_and_p = num.logical_and( ischange, isprior )
if c_and_p.any():
mu[0,c_and_p] = (tmp * x[:,c_and_p]).sum(0) / prior[0,c_and_p]
a = (x[:,c_and_p].T - \
kron( num.ones((n,1)), mu[0,c_and_p] )).T
sigma[0,c_and_p] = num.sqrt( (tmp * a**2).sum(0) / prior[0,c_and_p] )
tmp = w[:,ischange] * (1-gamma[:,ischange])
prior[1,ischange] = tmp.sum( 0 )
tmp = tmp[:,prior[1,ischange] > 0]
isprior = prior[1,:] > 0
c_and_p = num.logical_and( ischange, isprior )
if c_and_p.any():
mu[1,c_and_p] = (tmp * x[:,c_and_p]).sum(0) / prior[1,c_and_p]
a = (x[:,c_and_p].T - \
kron( num.ones((n,1)), mu[1,c_and_p] )).T
sigma[1,c_and_p] = num.sqrt( (tmp * a**2).sum(0) / prior[1,c_and_p] )
sigma[sigma < minsigma] = minsigma
# see if there is a change
ischange = num.logical_or( (num.abs( mu - mu0 ) >= minchange),
(num.abs( sigma - sigma0 ) >= minchange) ).any(0)
if not ischange.any(): break
mu0 = mu.copy()
sigma0 = sigma.copy()
# endfor: EM iterations
if PRINT_PROGRESS: print
p1 = normpdf( make_vect( x ).T,
make_vect( kron( num.ones((n,1)), mu[0,:] ) ).T,
make_vect( kron( num.ones((n,1)), sigma[0,:] ) ) ) \
* make_vect( kron( num.ones((n,1)), prior[0,:] ) )
p2 = normpdf( make_vect( x ).T,
make_vect( kron( num.ones((n,1)), mu[1,:] ) ).T,
make_vect( kron( num.ones((n,1)), sigma[1,:] ) ) ) \
* make_vect( kron( num.ones((n,1)), prior[1,:] ) )
p1.reshape( (n,m) )
p2.reshape( (n,m) )
a = make_vect(w) * (make_vect(gamma)*p1 + (1-make_vect(gamma))*p2)
score = a.sum( 0 )
return mu, sigma, prior, score
def histgmm( x, w, maxiters=100, minchange=None, minsigma=None ):
"""Gaussian mixture modeling using 2 clusters.
Returns 2-D arrays 'mu', 'sigma', 'prior'."""
if len(w.shape) == 1:
n = w.size
m = 1
w = w.reshape( (n,m) )
x = x.reshape( (n,m) )
else:
n,m = w.shape
w /= w.sum( 0 )
x = kron( num.ones((1,m)), x )
if minchange is None:
minchange = (x[-1]-x[0]) / n/2
if minsigma is None:
minsigma = (x[-1]-x[0]) / n/2
## initialize ##
# first initialization scheme
mu0 = num.zeros( (2,m) )
mu0[0,:] = x[0,:]
mu0[1,:] = x[-1,:]
sigma0 = (x[-1]-x[0]) / 4 * num.ones( (2,m) )
gamma = 0.5 * num.ones( (n,m) )
prior = 0.5 * num.ones( (2,m) )
mu, sigma, prior, score1 = histgmm_main( mu0, sigma0, gamma, prior, w, x,
maxiters, minchange, minsigma, n, m )
# second initialization scheme
c = num.r_[num.zeros(m), w.cumsum()]
gamma = (c[:-1] < 0.5).astype( num.float )
gamma.resize( (n,m) )
mu0 = num.zeros( (2,m) )
sigma0 = num.zeros( (2,m) )
tmp = w * gamma
prior[0,:] = tmp.sum( 0 )
isprior = prior[0,:] > 0
# the 'if' statement is necessary because sum( [] ) returns 0, not empty
if isprior.any():
mu0[0,isprior] = (tmp * x[:,isprior]).sum(0) / prior[0,isprior]
a = (x[:,isprior].T - \
kron( num.ones((n,1)), mu0[0,isprior] )).T
sigma0[0,isprior] = num.sqrt( (tmp * a**2).sum(0) / prior[0,isprior] )
tmp = w * (1.-gamma)
prior[1,:] = tmp.sum( 0 )
isprior = prior[1,:] > 0
if isprior.any():
mu0[1,isprior] = (tmp * x[:,isprior]).sum(0) / prior[1,isprior]
a = (x[:,isprior].T - \
kron( num.ones((n,1)), mu0[1,isprior] )).T
sigma0[1,isprior] = num.sqrt( (tmp * a**2).sum(0) / prior[1,isprior] )
sigma0[sigma0 < minsigma] = minsigma
mu2, sigma2, prior2, score2 = histgmm_main( mu0, sigma0, gamma, prior, w, x,
maxiters, minchange, minsigma, n, m )
## choose best of mu, mu2
# vectorize scores to allow indexing
inds2 = num.array((score2,0.)) > num.array((score1,1.))
if inds2.any():
mu[:,inds2] = mu2[:,inds2]
sigma[:,inds2] = sigma2[:,inds2]
prior[:,inds2] = prior2[:,inds2]
noprior = prior[0,:] < eps
if noprior.any():
mu[0,noprior] = mu[1,noprior]
sigma[0,noprior] = sigma[1,noprior]
noprior = prior[1,:] < eps
if noprior.any():
mu[1,noprior] = mu[0,noprior]
sigma[1,noprior] = sigma[0,noprior]
return mu, sigma, prior
