def sample_cond_dist(self, Y, n_samples):
""" Returns conditional samples from the gaussian mixture model.
Keyword arguments:
Y -- A numpy vector of the same length as the input data samples with either
values or np.nan. A two dimensional input array could be
np.array([3, np.nan]). The gmm would be sampled with a fixed first
dimension of 3.
n_samples -- Number of requested samples
"""
# get the conditional distribution
(con_means, con_covariances, con_weights) = self.cond_dist(Y)
#sample from the conditional distribution
samples = pypr_gmm.sample_gaussian_mixture(con_means, con_covariances,
con_weights, n_samples)
# find the columns where the nans are
nan_cols = np.where(np.isnan(Y))[0]
# extend the input to the length of the samples
full_samples = np.tile(Y, (n_samples, 1))
#copy the sample columns
full_samples[:, nan_cols] = samples
return full_samples
def generateData(n):
mc = [0.4, 0.4, 0.2] # Mixing coefficients
centroids = [ array([0,0]), array([3,3]), array([0,4]) ]
ccov = [ array([[1,0.4],[0.4,1]]), diag((1,2)), diag((0.4,0.1)) ]
# Generate samples from the gaussian mixture model
X = gmm.sample_gaussian_mixture(centroids, ccov, mc, samples=n)
return X
def sample_cond_dist(self, Y, n_samples):
# get the conditional distribution
(con_means, con_covariances, con_weights) = self.cond_dist(Y)
#sample from the conditional distribution
samples = pypr_gmm.sample_gaussian_mixture(con_means, con_covariances,
con_weights, n_samples)
# find the columns where the nans are
nan_cols = np.where(np.isnan(Y))[0]
# extend the input to the length of the samples
full_samples = np.tile(Y, (n_samples, 1))
#copy the sample columns
full_samples[:, nan_cols] = samples
return full_samples
def generate_data(n_samples):
mc = [0.4, 0.4, 0.2] # Mixing coefficients
centroids = [
np.array([0, 0]),
np.array([3, 3]),
np.array([0, 4])
]
ccov = [
np.array([[1, 0.4], [0.4, 1]]),
np.diag((1, 2)),
np.diag((0.4, 0.1))
]
# Generate samples from the gaussian mixture model
samples = gmm.sample_gaussian_mixture(centroids, ccov, mc, samples=n_samples)
xs, ys = samples[:, 0], samples[:, 1]
probs = np.zeros([n_samples], dtype=np.float32)
for it in range(n_samples):
input_ = np.array([xs[it], np.nan])
con_cen, con_cov, new_p_k = gmm.cond_dist(input_, centroids, ccov, mc)
prob = gmm.gmm_pdf(ys[it], con_cen, con_cov, new_p_k)
probs[it] = prob
return xs, ys, probs
cen_lst = []
cov_lst = []
# Generate cluster centers, covariance, and mixing coefficients:
sigma_scl = 0.1
X = np.zeros((samples_pr_cluster * K_orig, D))
for k in range(K_orig):
mu = np.random.randn(D)
sigma = np.eye(D) * sigma_scl
cen_lst.append(mu)
cov_lst.append(sigma)
mc = np.ones(K_orig) / K_orig # All clusters equally probable
# Sample from the mixture:
N = 1000
X = gmm.sample_gaussian_mixture(cen_lst, cov_lst, mc, samples=N)
K_range = list(range(2, 10))
runs = 10
bic_table = np.zeros((len(K_range), runs))
for K_idx, K in enumerate(K_range):
print("Clustering for K=%d" % K)
for i in range(runs):
cluster_init_kw = {'cluster_init':'sample', 'max_init_iter':5, \
'cov_init':'var', 'verbose':True}
cen_lst, cov_lst, p_k, logL = gmm.em_gm(X, K = K, max_iter = 1000, \
delta_stop=1e-2, init_kw=cluster_init_kw, verbose=True, max_tries=10)
bic = stattest.bic_gmm(logL, N, D, K)
bic_table[K_idx, i] = bic
plot(K_range, bic_table)
def generate_samples(self):
self.samples = gmm.sample_gaussian_mixture(self.mean,
self.var,
self.weight,
samples=self.n_samples)
'''
def sample(self, nsamples=1):
'''
produce samples
'''
return gmm.sample_gaussian_mixture(self.mu, self.sigma, self.pi,
nsamples)
# Drawing samples from a Gaussian Mixture Model
from numpy import *
from matplotlib.pylab import *
import pypr.clustering.gmm as gmm
mc = [0.4, 0.4, 0.2] # Mixing coefficients
centroids = [ array([0,0]), array([3,3]), array([0,4]) ]
ccov = [ array([[1,0.4],[0.4,1]]), diag((1,2)), diag((0.4,0.1)) ]
# Covariance matrices
X = gmm.sample_gaussian_mixture(centroids, ccov, mc, samples=1000)
plot(X[:,0], X[:,1], '.')
for i in range(len(mc)):
x1, x2 = gmm.gauss_ellipse_2d(centroids[i], ccov[i])
plot(x1, x2, 'k', linewidth=2)
xlabel('$x_1$'); ylabel('$x_2$')
# Drawing samples from a Gaussian Mixture Model
from numpy import *
from matplotlib.pylab import *
import pypr.clustering.gmm as gmm
import pypr.stattest as stattest
seed(10)
mc = [0.4, 0.4, 0.2] # Mixing coefficients
centroids = [ array([0,0]), array([3,3]), array([0,4]) ]
ccov = [ array([[1,0.4],[0.4,1]]), diag((1,2)), diag((0.4,0.1)) ]
# Covariance matrices
T = gmm.sample_gaussian_mixture(centroids, ccov, mc, samples=500)
V = gmm.sample_gaussian_mixture(centroids, ccov, mc, samples=500)
plot(T[:,0], T[:,1], '.')
# Expectation-Maximization of Mixture of Gaussians
Krange = range(1, 20 + 1);
runs = 1
meanLogL_train = np.zeros((len(Krange), runs))
meanLogL_valid = np.zeros((len(Krange), runs))
for K in Krange:
print "Clustering for K = ", K; sys.stdout.flush()
for r in range(runs):
cen_lst, cov_lst, p_k, logL = gmm.em_gm(T, K = K, iter = 100)
meanLogL_train[K-1, r] = logL
meanLogL_valid[K-1, r] = gmm.gm_log_likelihood(V, cen_lst, cov_lst, p_k)
fig1 = figure()
subplot(1, 2, 1)
for r in range(runs):
if __name__ == '__main__':
# Generate data from two gaussians
alpha = 0.05
epsilon = 0.0
mu = 0.0
mu1 = mu - epsilon
mu2 = mu + epsilon
sigma1 = 0.05
sigma2 = 0.05
N = 1000
# Sample data from two gaussians
X = pygmm.sample_gaussian_mixture([np.array([mu1]), np.array([mu2])], [[[sigma1]], [[sigma2]]], [alpha, 1.-alpha], samples=N)[:, 0]
dx = 0.2
deltaX = dx*np.random.randn(N)
# Gradient epsilon
f1 = lambda x, epsilon: 1./(np.sqrt(2*np.pi)*sigma1)*np.exp(-0.5*(x - mu + epsilon)**2./sigma1**2.)
f2 = lambda x, epsilon: 1./(np.sqrt(2*np.pi)*sigma2)*np.exp(-0.5*(x - mu - epsilon)**2./sigma2**2.)
h = lambda x, epsilon: alpha*f1(x, epsilon) + (1.-alpha)*f2(x, epsilon)
g = lambda x, epsilon: (1.-alpha)*f2(x, epsilon)*(x - mu - epsilon)/sigma2**2. - alpha*f1(x, epsilon)*(x - mu + epsilon)/sigma1**2.
par_g_eps = lambda x, epsilon: alpha*f1(x, epsilon)*((x - mu + epsilon)**2. - sigma1**2.)/sigma1**4. + (1. - alpha)*f2(x, epsilon)*((x - mu - epsilon)**2. - sigma2**2.)/sigma2**4.
par_g_x = lambda x, epsilon: alpha*f1(x, epsilon)*(x-mu+epsilon)**2./sigma1**4.-alpha*f1(x, epsilon)/sigma1**2. + (1. - alpha)*f2(x, epsilon)/sigma2**2. - (1.-alpha)*f2(x, epsilon)*(x - mu - epsilon)**2./sigma2**4.
par_h_x = lambda x, epsilon: -(1.-alpha)*f2(x, epsilon)*(x - mu - epsilon)/sigma2**2. - alpha*f1(x, epsilon)*(x - mu + epsilon)/sigma1**2.
par_ll_eps_fct = lambda epsilon, x: g(x, epsilon)/h(x, epsilon)
par_ll_eps_sum_fct = lambda epsilon, x: np.sum(np.ma.masked_invalid(par_ll_eps_fct(epsilon, x)))
cen_lst = []
cov_lst = []
# Generate cluster centers, covariance, and mixing coefficients:
sigma_scl = 0.1
X = np.zeros((samples_pr_cluster * K_orig, D))
for k in range(K_orig):
mu = np.random.randn(D)
sigma = np.eye(D) * sigma_scl
cen_lst.append(mu)
cov_lst.append(sigma)
mc = np.ones(K_orig) / K_orig # All clusters equally probable
# Sample from the mixture:
N = 1000
X = gmm.sample_gaussian_mixture(cen_lst, cov_lst, mc, samples=N)
K_range = range(2, 10)
runs = 10
bic_table = np.zeros((len(K_range), runs))
for K_idx, K in enumerate(K_range):
print "Clustering for K=%d" % K
for i in range(runs):
cluster_init_kw = {"cluster_init": "sample", "max_init_iter": 5, "cov_init": "var", "verbose": True}
cen_lst, cov_lst, p_k, logL = gmm.em_gm(
X, K=K, max_iter=1000, delta_stop=1e-2, init_kw=cluster_init_kw, verbose=True, max_tries=10
)
bic = stattest.bic_gmm(logL, N, D, K)
bic_table[K_idx, i] = bic
plot(K_range, bic_table)
for i in range(len(cen_lst)):
x, y = gmm.gauss_ellipse_2d(cen_lst[i], cov_lst[i])
plot(x, y, 'k', linewidth=0.5)
seed(1)
mc = [0.4, 0.4, 0.2] # Mixing coefficients
centroids = [array([0, 0, 0]), array([3, 3, 2]), array([0, 4, 3])]
ccov = [
array([[1, 0.4, 0.4], [0.4, 1, 0.4], [0.4, 0.4, 1]]),
diag((1, 2, 0.4)),
diag((0.4, 0.1, 1))
]
# Generate samples from the gaussian mixture model
X = gmm.sample_gaussian_mixture(centroids, ccov, mc, samples=500)
fig = figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(X[:500, 0].tolist(),
X[:500, 1].tolist(),
X[:500, 2].tolist(),
alpha=0.4)
# Expectation-Maximization of Mixture of Gaussians
cen_lst, cov_lst, p_k, logL = gmm.em_gm(X,
K=4,
max_iter=400,
verbose=True,
iter_call=None)
print "Log likelihood (how well the data fits the model) = ", logL
