def gmmmemberships(mu,S,priors,x,weights=1,initcovars=None):
if initcovars is None:
initcovars = S.copy()
# number of data points
n = x.shape[0]
# dimensionality of data
d = x.shape[1]
# number of clusters
k = mu.shape[0]
# allocate output
gamma = num.zeros((n,k))
# normalization constant
normal = (2.0*num.pi)**(num.double(d)/2.0)
#print 'd = %d, normal = %f' % (d,normal)
#print 'mu = '
#print mu
#print 'S = '
#for j in range(k):
# print S[:,:,j]
#print 'priors = '
#print priors
#print 'weights = '
#print weights
# compute the activation for each data point
for j in range(k):
#print 'j = %d' % j
#print 'mu[%d,:] = '%j + str(mu[j,:])
#print 'S[:,:,%d] = '%j + str(S[:,:,j])
diffs = x - mu[j,:]
#print 'diffs = '
#print diffs
try:
c = decomp.cholesky(S[:,:,j])
except num.linalg.linalg.LinAlgError:
if DEBUG: print 'S[:,:,%d] = '%j + str(S[:,:,j]) + ' is singular'
if DEBUG: print 'Reverting to initcovars[:,:,%d] = '%j + str(initcovars[:,:,j])
S[:,:,j] = initcovars[:,:,j]
c = decomp.cholesky(S[:,:,j])
#print 'chol(S[:,:,%d]) = '%j + str(c)
temp = num.transpose(num.linalg.solve(num.transpose(c),num.transpose(diffs)))
#print 'temp = '
#print temp
gamma[:,j] = num.exp(-.5*num.sum(temp**2,axis=1))/(normal*num.prod(num.diag(c)))
#print 'gamma[:,%d] = ' % j
#print gamma[:,j]
# include prior
gamma *= priors
#print 'after including prior, gamma = '
#print gamma
# compute negative log likelihood
e = -num.sum(num.log(num.sum(gamma,axis=1))*weights)
#print 'e = %f' % e
s = num.sum(gamma,axis=1)
#print 's = '
#print s
# make sure we don't divide by 0
s[s==0] = 1
gamma /= s.reshape(n,1)
#print 'gamma = '
#print gamma
return (gamma,e)
D = num.zeros((nclusts,n))
E = num.zeros((nclusts,n))
for i in range(nclusts):
D[i,:] = num.sum( (x - c[i,:])**2, axis=1 )
E[i,:] = num.sum((x - num.tile(c[i,:],[n,1]))**2,axis=1)
print "D[%d] = "%i + str(D[i,:])
print "E[%d] = "%i + str(E[i,:])
gamma1 = num.zeros((n,nclusts))
gamma2 = num.zeros((n,nclusts))
for j in range(nclusts):
print "j = " + str(j)
print "c.shape = " + str(c.shape)
diffs = x - c[j,:]
zz = S[0,0,j]*S[1,1,j] - S[0,1,j]**2
temp1 = (diffs[:,0]**2*S[1,1,j]
- 2*diffs[:,0]*diffs[:,1]*S[0,1,j]
+ diffs[:,1]**2*S[0,0,j]) / zz
print "temp1 = " + str(temp1)
ch = decomp.cholesky(S[:,:,j])
temp2 = num.transpose(num.linalg.solve(num.transpose(ch),num.transpose(diffs)))
temp2 = num.sum(temp2**2,axis=1)
gamma1[:,j] = num.exp(-.5*temp1)/(normal*num.sqrt(zz))
gamma2[:,j] = num.exp(-.5*temp2)/(normal*num.prod(num.diag(ch)))
print "temp2 = " + str(temp2)
print "sigma1 = " + str(num.sqrt(zz))
print "sigma2 = " + str(num.prod(num.diag(ch)))
print "gamma1 = " + str(gamma1[:,j])
print "gamma2 = " + str(gamma2[:,j])
def fixsmallpriors(x, mu, S, priors, initcovars, gamma=None):
# print 'calling fixsmallpriors with: '
# print 'mu = ' + str(mu)
# print 'S = '
# for i in range(S.shape[2]):
# print S[:,:,i]
# print 'priors = ' + str(priors)
# for i in range(initcovars.shape[2]):
# print 'initcovars[:,:,%d]: '%i
# print initcovars[:,:,i]
# print 'initcovars[:,:,%d].shape: '%i + str(initcovars[:,:,i].shape)
MINPRIOR = 0.01
issmall = priors < 0.01
if not issmall.any():
return
n = x.shape[0]
d = x.shape[1]
k = mu.shape[0]
normal = (2.0 * num.pi) ** (num.double(d) / 2.0)
if gamma is None:
# compute the density for each x from each mixture component
gamma = num.zeros((n, k))
for i in range(k):
diffs = x - num.tile(mu[i, :], [n, 1])
c = decomp.cholesky(S[:, :, i])
temp = num.transpose(num.linalg.solve(num.transpose(c), num.transpose(diffs)))
gamma[:, i] = num.exp(-0.5 * num.sum(temp ** 2, axis=1)) / (normal * num.prod(num.diag(c)))
# end gamma is None
# loop through all small priors
smalli, = num.where(issmall)
for i in smalli:
print "fixing cluster %d with small prior = %f: " % (i, priors[i])
# compute mixture density of each data point
p = num.sum(gamma * num.tile(priors, [n, 1]), axis=1)
# print 'samples: '
# print x
# print 'density of each sample: '
# print p
# choose the point with the smallest probability
j = p.argmin()
print "lowest density sample: x[%d] = " % j + str(x[j, :])
# create a new cluster
mu[i, :] = x[j, :]
S[:, :, i] = initcovars[:, :, i]
priors *= (1 - MINPRIOR) / (1.0 - priors[i])
priors[i] = MINPRIOR
print "reset cluster %d to: " % i
print "mu = " + str(mu[i, :])
print "S = "
print S[:, :, i]
print "S.shape: " + str(S[:, :, i].shape)
print "prior = " + str(priors[i])
# update gamma
diffs = x - num.tile(mu[i, :], [n, 1])
c = decomp.cholesky(S[:, :, i])
temp = num.transpose(num.linalg.solve(num.transpose(c), num.transpose(diffs)))
gamma[:, i] = num.exp(-0.5 * num.sum(temp ** 2, axis=1)) / (normal * num.prod(num.diag(c)))
