def _expectation_gauss2(data, theta, sigma, pi):
prob_cluster1 = (1-pi) * dmvnorm(data, mu=theta[0], sigma=sigma[0])
prob_cluster2 = pi * dmvnorm(data, mu=theta[1], sigma=sigma[1])
grouping = np.zeros_like(prob_cluster1, dtype=np.integer)
grouping[np.where(prob_cluster1<prob_cluster2)] = 1
responsibilities = prob_cluster2 / ( prob_cluster1 + prob_cluster2)
return grouping, responsibilities
def _expectation_gauss2(data, theta, sigma, pi):
prob_cluster1 = (1 - pi) * dmvnorm(data, mu=theta[0], sigma=sigma[0])
prob_cluster2 = pi * dmvnorm(data, mu=theta[1], sigma=sigma[1])
grouping = np.zeros_like(prob_cluster1, dtype=np.integer)
grouping[np.where(prob_cluster1 < prob_cluster2)] = 1
responsibilities = prob_cluster2 / (prob_cluster1 + prob_cluster2)
return grouping, responsibilities
def gaussian_mixture(x, y, theta, sigma, pi):
z = np.zeros((len(x), len(y)))
for i, xval in enumerate(x):
for j, yval in enumerate(y):
data = np.array([xval, yval]).reshape((1, 2))
z1 = dmvnorm(data, mu=theta[0], sigma=sigma[0])
z2 = dmvnorm(data, mu=theta[1], sigma=sigma[1])
z[j, i] = ((1-pi) * z1) + (pi * z2)
return z
def gaussian_mixture(x, y, theta, sigma, pi):
z = np.zeros((len(x), len(y)))
for i, xval in enumerate(x):
for j, yval in enumerate(y):
data = np.array([xval, yval]).reshape((1, 2))
z1 = dmvnorm(data, mu=theta[0], sigma=sigma[0])
z2 = dmvnorm(data, mu=theta[1], sigma=sigma[1])
z[j, i] = ((1 - pi) * z1) + (pi * z2)
return z
def __gaussian_mixture(x, y, pi, mu, sigma):
z = np.zeros((len(x), len(y)))
number_of_clusters = pi.shape[0]
p = mu.shape[1]
for i, xval in enumerate(x):
for j, yval in enumerate(y):
data = np.array([xval, yval]).reshape((1, p))
zval = 0
for k in range(number_of_clusters):
zval += pi[k] * dmvnorm(data, mu=mu[k], sigma=sigma[k])
z[i, j] = zval
return z
def __gaussian_mixture(x, y, pi, mu, sigma):
z = np.zeros((len(x), len(y)))
number_of_clusters = pi.shape[0]
p = mu.shape[1]
for i, xval in enumerate(x):
for j, yval in enumerate(y):
data = np.array([xval, yval]).reshape((1,p))
zval = 0
for k in range(number_of_clusters):
zval += pi[k] * dmvnorm(data, mu=mu[k], sigma=sigma[k])
z[i,j] = zval
return z
def run(self, data, k, iterations=100):
data = np.array(data)
num_observations = data.shape[0]
p = data.shape[1]
xi = np.median(data, axis=0)
dr = np.amax(data, axis=0) - np.amin(data, axis=0)
kappa = np.zeros((p, p))
for i in range(p):
kappa[i, i] = 1.0 / (dr[i]**2)
ikappa = la.inv(kappa)
h = (100.0 * self.__g / self.__alpha) * kappa
gibbs_pi = np.zeros((iterations, k), dtype=np.double)
gibbs_theta = np.zeros((iterations, k, p), dtype=np.double)
gibbs_sigma = np.zeros((iterations, k, p, p), dtype=np.double)
gibbs_beta = np.zeros((iterations, p, p), dtype=np.double)
for j in range(k):
gibbs_pi[0, j] = 1.0 / k
gibbs_theta[0, j] = np.mean(data, axis=0)
gibbs_sigma[0, j] = np.cov(data.T)
for i in range(1, iterations):
a = np.zeros((num_observations, k))
for m in range(k):
a[:, m] = gibbs_pi[i - 1, m] * dmvnorm(
data,
mu=gibbs_theta[i - 1, m],
sigma=gibbs_sigma[i - 1, m])
asum = np.sum(a, axis=1)
z = np.zeros((num_observations, k), dtype=np.integer)
for j in range(num_observations):
z[j] = npr.multinomial(1, a[j] / asum[j])
gibbs_pi[i] = npr.dirichlet(np.sum(z, axis=0) + self.__delta)
gibbs_beta[i] = rwish(
2.0 * self.__g + 2.0 * k * self.__alpha,
la.inv(2.0 * h +
2.0 * self.__sum_isigma(gibbs_sigma[i - 1], k, p)))[0]
y = []
n = np.zeros(k, dtype=np.integer)
for m in range(k):
pos_data = data[np.where(z[:, m] == 1)]
y.append(pos_data)
n[m] = pos_data.shape[0]
assert len(y) == k
for m in range(k):
y_diff = y[m] - gibbs_theta[i - 1, m]
y_sum = np.zeros((p, p), dtype=np.double)
for l in range(n[m]):
y_sum = y_sum + y_diff[l].reshape((p, 1)) * y_diff[l]
cov = (2.0 * gibbs_beta[i]) + y_sum
gibbs_sigma[i, m] = la.inv(
rwish(2.0 * self.__alpha + n[m], la.inv(cov))[0])
for m in range(k):
cov = la.inv(n[m] * la.inv(gibbs_sigma[i, m]) + kappa)
mean_x = np.mean(y[m], axis=0)
mean = cov.dot(n[m] * la.inv(gibbs_sigma[i, m]).dot(mean_x) +
kappa.dot(xi))
gibbs_theta[i, m] = npr.multivariate_normal(mean, cov, size=1)
return (gibbs_pi, gibbs_theta, gibbs_sigma)
def run(self,data,k,iterations=100):
data = np.array(data)
num_observations = data.shape[0]
p = data.shape[1]
xi = np.median(data,axis=0)
dr = np.amax(data,axis=0) - np.amin(data,axis=0)
kappa = np.zeros((p,p))
for i in range(p):
kappa[i,i] = 1.0/(dr[i]**2)
ikappa = la.inv(kappa)
h = (100.0*self.__g/self.__alpha) * kappa
gibbs_pi = np.zeros((iterations,k),dtype=np.double)
gibbs_theta = np.zeros((iterations,k,p),dtype=np.double)
gibbs_sigma = np.zeros((iterations,k,p,p),dtype=np.double)
gibbs_beta = np.zeros((iterations,p,p),dtype=np.double)
for j in range(k):
gibbs_pi[0,j] = 1.0/k
gibbs_theta[0,j] = np.mean(data,axis=0)
gibbs_sigma[0,j] = np.cov(data.T)
for i in range(1,iterations):
a = np.zeros((num_observations,k))
for m in range(k):
a[:,m] = gibbs_pi[i-1,m] * dmvnorm(data, mu=gibbs_theta[i-1,m],sigma=gibbs_sigma[i-1,m])
asum = np.sum(a,axis=1)
z = np.zeros((num_observations,k),dtype=np.integer)
for j in range(num_observations):
z[j] = npr.multinomial(1,a[j]/asum[j])
gibbs_pi[i] = npr.dirichlet(np.sum(z,axis=0) + self.__delta)
gibbs_beta[i] = rwish(2.0*self.__g + 2.0*k*self.__alpha,
la.inv(2.0*h + 2.0*self.__sum_isigma(gibbs_sigma[i-1],k,p)))[0]
y = []
n = np.zeros(k,dtype=np.integer)
for m in range(k):
pos_data = data[np.where(z[:,m]==1)]
y.append(pos_data)
n[m] = pos_data.shape[0]
assert len(y) == k
for m in range(k):
y_diff = y[m] - gibbs_theta[i-1,m]
y_sum = np.zeros((p,p),dtype=np.double)
for l in range(n[m]):
y_sum = y_sum + y_diff[l].reshape((p,1)) * y_diff[l]
cov = (2.0 * gibbs_beta[i]) + y_sum
gibbs_sigma[i,m] = la.inv(rwish(2.0*self.__alpha + n[m], la.inv(cov))[0])
for m in range(k):
cov = la.inv(n[m] * la.inv(gibbs_sigma[i,m]) + kappa)
mean_x = np.mean(y[m],axis=0)
mean = cov.dot(n[m] * la.inv(gibbs_sigma[i,m]).dot(mean_x) + kappa.dot(xi))
gibbs_theta[i,m] = npr.multivariate_normal(mean,cov,size=1)
return (gibbs_pi,gibbs_theta,gibbs_sigma)