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EM.py
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import numpy as np
from scipy.stats import multivariate_normal
from cluster import kMeanCluster
from time import time
reg_cov = 1e-6 # add to the diagonal of covariance for Non-negative regularization.
# judge whether the result converges.
def log_likelihood_sum(likelihood, weights):
# product = 1
# for i in range(len(likelihood_index)):
# product = product * likelihood[i][likelihood_index[i]]
# return np.log(product)
# max_likelihood_arr = likelihood[range(len(likelihood)), likelihood_index]
probability = (likelihood*weights).sum(axis=1)
log_prob_sum = np.log(probability).sum()
return log_prob_sum
def _estimate_gaussian_parameters(data, posterior):
post_sum = posterior.sum(axis=0) + 10 * np.finfo(posterior.dtype).eps # weights of component.
means = np.dot(posterior.T, data) / post_sum[:, np.newaxis]
covariances = _estimate_gaussian_covariances(posterior, data, post_sum, means)
post_sum /= data.shape[0]
return post_sum, means, covariances
def _estimate_gaussian_covariances(posterior, data, nk, means):
n_components, n_features = means.shape
covariances = np.empty((n_components, n_features, n_features))
for k in range(n_components):
diff = data - means[k]
covariances[k] = np.dot(posterior[:, k] * diff.T, diff) / nk[k]
covariances[k].flat[::n_features + 1] += reg_cov # add reg_cov on the diagonal line.
return covariances
class EM:
def __init__(self, max_iter=30, threshold=1e-2, random_seed=26, k=2, init_params='kmeans', verbose=False):
self.max_iter = max_iter
self.threshold = threshold # iteration stop threshold
self.random_seed = random_seed
self.init_params = init_params
self.n_components = k
self.verbose = verbose
def set_parameters(self, mean, covariance, weight):
self.means = mean
self.covariances = covariance
self.weights = weight
def initialize(self, data):
# Siyi's Part: Initialize the mean, the variance and the weight for each cluster
# Comment the following code and implement a better initialization algorithm
k = self.n_components
n_samples = data.shape[0]
if self.init_params == 'kmeans':
res = np.zeros((n_samples, self.n_components))
label = kMeanCluster(num_clusters=self.n_components, ).fit(data).label_
res[np.arange(n_samples), label] = 1
weights, means, covariances = _estimate_gaussian_parameters(data, res)
elif self.init_params == 'random':
means = np.ndarray(shape=(k, data.shape[1]), dtype=float)
covariances = np.ndarray(shape=(k, data.shape[1], data.shape[1]), dtype=float)
weights = np.ones(shape=k) / k
clusters = [None] * k
l = int(data.shape[0] / k)
for i in range(k - 1):
clusters[i] = data[i * l:(i + 1) * l]
clusters[k - 1] = data[(k - 1) * l:]
for i in range(k):
means[i] = np.mean(clusters[i], axis=0)
covariances[i] = np.cov(np.array(clusters[i]).T)
else:
print('set correct initial params')
return
self.set_parameters(means, covariances, weights)
def print_verbose(self, iter, change, end=False):
if self.verbose:
if iter % 10 == 0 or end:
print('%d iter\t time:%.1f\t change:%.2f' % (iter, time() - self.start_time, change))
def fit(self, data):
self.start_time = time()
k = self.n_components
n_samples = data.shape[0]
if len(data) < k:
print('Number of cluster exceeds size of data')
return
self.initialize(data)
# posterior: P(theta | X) likelihood: P(X | theta)
self.likelihood = np.ndarray(shape=(len(data), k), dtype=float)
self.posterior = np.ndarray(shape=(k, len(data)), dtype=float)
# old_likelihood = np.ndarray(shape=(len(data), k), dtype=float)
# old_maximum_likelihood_index = np.ndarray(shape=data.shape[0], dtype=int)
# new_maximum_likelihood_index = np.ndarray(shape=data.shape[0], dtype=int)
previous_likelihood_sum = 0
for iter in range(self.max_iter):
likelihood_T = np.ndarray(shape=(k, len(data)), dtype=float)
for i in range(k):
likelihood_T[i] = multivariate_normal.pdf(data, mean=self.means[i], cov=self.covariances[i])
self.likelihood = likelihood_T.T
# Expectation
evidence = np.dot(self.likelihood, self.weights) # size n of p(x_i).
for i in range(k):
self.posterior[i] = np.multiply(likelihood_T[i], self.weights[i]) / evidence
# for i in range(k):
# for j in range(len(data)):
# evidence = np.dot(self.likelihood[j], self.weight)
# self.posterior[i][j] = self.likelihood[j][i] * self.weight[i] / evidence
# Maximization Step
# for i in range(k):
# posterior_sum = np.sum(self.posterior[i])
# self.means[i] = np.dot(self.posterior[i], data) / posterior_sum
# diff = data - self.means[i]
# self.covariances[i] = np.zeros(shape=(data.shape[1], data.shape[1])) # ??
# for j in range(len(data)):
# self.covariances[i] += self.posterior[i][j] * diff[j] * diff[j].reshape(diff[j].shape[0], 1)
# self.covariances[i] = self.covariances[i] / posterior_sum
# # in case of singular matrix
# if not np.any(self.covariances[i]):
# self.covariances[i] = np.diag([1e-6] * data.shape[1])
# self.weights[i] = posterior_sum / len(data)
weights, means, covariances = _estimate_gaussian_parameters(data, self.posterior.T)
self.set_parameters(means, covariances, weights)
# log likelihood
if iter == 0:
previous_likelihood_sum = log_likelihood_sum(self.likelihood, weights)
else:
current_likelihood_sum = log_likelihood_sum(self.likelihood, weights)
change = abs(current_likelihood_sum - previous_likelihood_sum)
# if abs(current_likelihood_sum - previous_likelihood_sum) < 0.2:
previous_likelihood_sum = current_likelihood_sum
if change <= self.threshold:
self.print_verbose(iter, change, end=True)
break
self.print_verbose(iter, change)
# else:
# for i in range(len(data)):
# new_maximum_likelihood_index[i] = np.argmax(self.likelihood[i])
# old_log_likelihood = log_likelihood(old_likelihood, old_maximum_likelihood_index)
# new_log_likelihood = log_likelihood(self.likelihood, new_maximum_likelihood_index)
# if np.abs((new_log_likelihood - old_log_likelihood) / old_log_likelihood) < 0.2:
# print('stop update. iteration %i' % iter)
# break
# old_likelihood = self.likelihood.copy()
# old_maximum_likelihood_index = new_maximum_likelihood_index.copy()
# clusters = [None] * k
# for i in range(len(data)):
# if clusters[new_maximum_likelihood_index[i]] is None:
# clusters[new_maximum_likelihood_index[i]] = []
# clusters[new_maximum_likelihood_index[i]].append(i)
new_maximum_likelihood_index = np.argmax(self.likelihood, axis=1)
return new_maximum_likelihood_index