

In [1]:

    
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
%load_ext autoreload
%autoreload 2

Data Generation



In [2]:

    
from numpy.random import rand, randn



In [3]:

    
n, d, k = 100, 2, 2



In [4]:

    
np.random.seed(20)
X = rand(n, d)

# means = [rand(d)  for _ in range(k)]  # works for any k
means = [rand(d) * 0.5 + 0.5 , - rand(d)  * 0.5 + 0.5]  # for better plotting when k = 2

S = np.diag(rand(d))

sigmas = [S]*k # we'll use the same Sigma for all clusters for better visual results

print(means)
print(sigmas)









    



[array([ 0.69872366,  0.75176984]), array([ 0.25997411,  0.14504062])]
[array([[ 0.01764816,  0.        ],
       [ 0.        ,  0.06360523]]), array([[ 0.01764816,  0.        ],
       [ 0.        ,  0.06360523]])]

Solution



In [1]:

    
def compute_log_p(X, mean, sigma):
    dxm = X - mean
    exponent = -0.5 * np.sum(dxm * np.dot(dxm, np.linalg.inv(sigma)), axis=1)
    return exponent - np.log(2 * np.pi) * (d / 2) - 0.5 * np.log(np.linalg.det(sigma))



In [2]:

    
log_ps = [compute_log_p(X, m, s) for m, s in zip(means, sigmas)]  # exercise: try to do this without looping









    



---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-2-40f202c2927a> in <module>()
----> 1 log_ps = [compute_log_p(X, m, s) for m, s in zip(means, sigmas)]  # exercise: try to do this without looping

NameError: name 'means' is not defined



In [3]:

    
assignments = np.argmax(log_ps, axis=0)
print(assignments)









    



---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-3-a8f92fc562b5> in <module>()
----> 1 assignments = np.argmax(log_ps, axis=0)
      2 print(assignments)

NameError: name 'np' is not defined



In [8]:

    
colors = np.array(['red', 'green'])[assignments]
plt.scatter(X[:, 0], X[:, 1], c=colors, s=100)
plt.scatter(np.array(means)[:, 0], np.array(means)[:, 1], marker='*', s=200)
plt.show()









    Out[8]:





<matplotlib.collections.PathCollection at 0x10fb2ac18>