def main(ns):
global markers, components
res = []
for s in ns.sizes:
tgmm = TGMM(2, ns.bounds )
tgmm.means = ns.means
tgmm.covars = [1,1]
tgmm.weights = [.5,.5]
allsamples = tgmm.rvs((ns.reps, s))
tmp = []
for sample in allsamples:
gmm = GMM(components)
gmm.fit(sample[:,np.newaxis])
means = gmm.means.ravel()
means.sort()
tmp.append(np.abs(means - tgmm.means))
res.append(zip([s] * components, np.asarray(tmp).mean(axis=0)))
res = np.asarray(res).swapaxes(0,1)
for i in xrange(components):
hold(1)
x, y = res[i].T
if ns.loglog:
loglog(x, y, ':'+markers[i], c='k', label='$\mu_%d$' % (i+1))
else:
plot(x, y, ':'+markers[i], c='k', label='$\mu_%d$' % (i+1))
legend()
xlabel('sample size')
ylabel('average absolute error')
title(r'$\mu_1 = %g,\quad \mu_2 = %g,\quad x\in\left[%g,%g\right]$' %
(tuple(ns.means) + tuple(ns.bounds)))
show()
def main(args):
prng = np.random.RandomState(args.seed)
T = np.logspace(args.start, args.num + 1, base=args.base, num=args.num)
print 'sample size: %s' % map(int,T)
sys.stdout.flush()
resid = []
for t in T:
mresid, sresid, presid = [],[],[]
for m, s, p in zip(*sample_params(args, prng)):
gmm = GMM(args.components)
gmm.means = m
gmm.covars = s
gmm.weights = p
x = gmm.rvs(t)
gmm2 = GMM(args.components)
gmm2.fit(x, n_iter=20)
m, s, p = identify(m, s, p)
m2, s2, p2 = identify(gmm2.means, gmm2.covars, gmm2.weights)
mresid.extend(np.abs(m - m2))
sresid.extend(np.abs(s - s2))
presid.extend(np.abs(p - p2))
nsq = np.sqrt(args.reps)
mresid = (t, np.mean(mresid), np.std(mresid) / nsq)
sresid = (t, np.mean(sresid), np.std(sresid) / nsq)
presid = (t, np.mean(presid), np.std(presid) / nsq)
resid.append((mresid, sresid, presid))
resid = np.asarray(zip(*resid))
plot(args, resid)
return resid
def fit_gmm1(components,x): from scikits.learn.mixture import GMM, DPGMM, VBGMM x = np.asanyarray(x).reshape(-1,1) #gmm_baf = VBGMM(components,verbose=True,min_covar=0.01) gmm_baf = GMM(components) gmm_baf.fit(x) mu = np.array(gmm_baf.means, dtype=float).reshape(-1) order = mu.argsort() mu = mu[order] sd = np.array(gmm_baf.covars, dtype=float).reshape(-1)[order]**0.5 ws = np.array(gmm_baf.weights, dtype=float).reshape(-1)[order] logL = gmm_baf.score(x) return logL,mu,sd,ws
n = 10
l = 256
im = np.zeros((l, l))
points = l*np.random.random((2, n**2))
im[(points[0]).astype(np.int), (points[1]).astype(np.int)] = 1
im = ndimage.gaussian_filter(im, sigma=l/(4.*n))
mask = (im > im.mean()).astype(np.float)
img = mask + 0.3*np.random.randn(*mask.shape)
hist, bin_edges = np.histogram(img, bins=60)
bin_centers = 0.5*(bin_edges[:-1] + bin_edges[1:])
classif = GMM(n_components=2, cvtype='full')
classif.fit(img.reshape((img.size, 1)))
threshold = np.mean(classif.means)
binary_img = img > threshold
plt.figure(figsize=(11,4))
plt.subplot(131)
plt.imshow(img)
plt.axis('off')
plt.subplot(132)
plt.plot(bin_centers, hist, lw=2)
plt.axvline(0.5, color='r', ls='--', lw=2)
plt.text(0.57, 0.8, 'histogram', fontsize=20, transform = plt.gca().transAxes)
np.random.seed(1)
n = 10
l = 256
im = np.zeros((l, l))
points = l * np.random.random((2, n**2))
im[(points[0]).astype(np.int), (points[1]).astype(np.int)] = 1
im = ndimage.gaussian_filter(im, sigma=l / (4. * n))
mask = (im > im.mean()).astype(np.float)
img = mask + 0.3 * np.random.randn(*mask.shape)
hist, bin_edges = np.histogram(img, bins=60)
bin_centers = 0.5 * (bin_edges[:-1] + bin_edges[1:])
classif = GMM(n_components=2, cvtype='full')
classif.fit(img.reshape((img.size, 1)))
threshold = np.mean(classif.means)
binary_img = img > threshold
plt.figure(figsize=(11, 4))
plt.subplot(131)
plt.imshow(img)
plt.axis('off')
plt.subplot(132)
plt.plot(bin_centers, hist, lw=2)
plt.axvline(0.5, color='r', ls='--', lw=2)
plt.text(0.57, 0.8, 'histogram', fontsize=20, transform=plt.gca().transAxes)
plt.yticks([])
colors = 'rgbmc'
for i, mu in enumerate(c_mu):
A = np.linspace(mu - 10 * model_sigma, mu + 10 * model_sigma, 100)
B = 1 / np.sqrt(2 * np.pi * model_sigma**2) * np.exp(-(A - mu)**2 /
(2 * model_sigma**2))
B *= pi[i]
c = colors[i % len(colors)]
plt.plot(A, B, '%s-' % c)
plt.hist(X, bins=50, alpha=0.5, facecolor='lightgrey')
plt.show()
# burn-in
#estimated_c_X, estimated_c_mu = estimate_dpm_model( alpha, X, burn_in_iterations, prior_mu, prior_sigma, model_sigma )
gmm = GMM(K, 'full')
gmm.fit(X, 0, init_params='wmc')
while not gmm.converged_:
gmm.fit(X, 40, init_params='')
pi = gmm.weights
mu = gmm.means
sigma = gmm.covars
#print 'real components:'
#print c_mu
#print 'estimated components:'
#print estimated_c_mu
# Break up the dataset into non-overlapping training (75%) and testing
# (25%) sets.
skf = StratifiedKFold(iris.target, k=4)
# Only take the first fold.
train_index, test_index = skf.__iter__().next()
X_train = iris.data[train_index]
y_train = iris.target[train_index]
X_test = iris.data[test_index]
y_test = iris.target[test_index]
n_classes = len(np.unique(y_train))
# Try GMMs using different types of covariances.
classifiers = dict((x, GMM(n_states=n_classes, cvtype=x))
for x in ['spherical', 'diag', 'tied', 'full'])
n_classifiers = len(classifiers)
pl.figure(figsize=(3 * n_classifiers / 2, 6))
pl.subplots_adjust(bottom=.01,
top=0.95,
hspace=.15,
wspace=.05,
left=.01,
right=.99)
for index, (name, classifier) in enumerate(classifiers.iteritems()):
# Since we have class labels for the training data, we can
# initialize the GMM parameters in a supervised manner.
colors = 'rgbmc'
for i,mu in enumerate( c_mu ):
A = np.linspace( mu - 10*model_sigma, mu + 10*model_sigma, 100 )
B = 1/np.sqrt(2*np.pi*model_sigma**2)*np.exp(-(A-mu)**2/(2*model_sigma**2))
B *= pi[ i ]
c = colors[ i % len( colors ) ]
plt.plot( A, B, '%s-' % c )
plt.hist( X, bins=50, alpha=0.5, facecolor='lightgrey' )
plt.show()
# burn-in
#estimated_c_X, estimated_c_mu = estimate_dpm_model( alpha, X, burn_in_iterations, prior_mu, prior_sigma, model_sigma )
gmm = GMM( K, 'full' )
gmm.fit( X, 0, init_params='wmc' )
while not gmm.converged_:
gmm.fit( X, 40, init_params='' )
pi = gmm.weights
mu = gmm.means
sigma = gmm.covars
#print 'real components:'
#print c_mu
#print 'estimated components:'
#print estimated_c_mu
