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# %load ron_gmmtest.py
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
from sklearn import mixture
np.random.seed(1)
mleArr = []
bic = []
mleDifferences = []
def mle(GMM, X):
return 2 * GMM.score(X).sum()
def verifyConcavity(arr):
for x in xrange(0, len(arr) - 2):
if arr[x+2] - 2*arr[x +1] + arr[x] > 0:
return False
return True
numClusters = [i for i in range(1,10)]
for x in xrange(1,10):
g = mixture.GMM(n_components=x)
# generate random observations with two modes centered on 0 and 100
obs = np.concatenate((np.random.randn(100, 1), 100 + np.random.randn(300, 1)))
g.fit(obs)
print 'mle'
print mle(g, obs)
mleArr.append(mle(g, obs))
bic.append(g.bic(obs))
print mleArr
print bic
for x in xrange(1,len(mleArr) - 1):
mleDifferences.append(mleArr[x] - mleArr[x-1])
print mleDifferences
print verifyConcavity(mleDifferences)
#usually not true
plt.figure(1)
plt.plot(numClusters, bic)
plt.ylabel('BIC')
plt.xlabel('Number of Clusters')
plt.title('BIC plot')
plt.figure(2)
plt.plot(numClusters, mleArr)
plt.ylabel('Maximum Likelihood Estimator')
plt.xlabel('Number of Clusters')
plt.title('MLE plot')
plt.figure(3)
plt.plot(numClusters[0:-2], mleDifferences, 'o')
plt.title('MLE Differences')
plt.ylabel('Difference in Maximum Likelihood Estimator')
plt.xlabel('Number of Clusters')
plt.show()
#bic source code, using this to define MLE function
# def bic(self, X):
# """Bayesian information criterion for the current model fit
# and the proposed data
# Parameters
# ----------
# X : array of shape(n_samples, n_dimensions)
# Returns
# -------
# bic: float (the lower the better)
# """
# return (-2 * self.score(X).sum() +
# self._n_parameters() * np.log(X.shape[0]))
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