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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 <H1>K-means clustering (KMC) algorithm </H1>
<P>
Given a set $X$ of $n$ observations; $X = \{x_1, x_2, \cdots, x_n\}$, where every $i$ observation is a vector of measurements ($x_i \in R^d$). The K-means clustering aims to classify the observations into a set of $k$ clusters $C =\{c_1, c_2, \cdots, c_k\}$ that minimizes the following expression
Step1:  Consider the following data set consisting of the scores of two variables on each of 17 experiments
Step2:  This data set is to be grouped into two clusters. 
As a first step in finding a sensible initial partition, let the values of the measurements 1 and 2 of the two individuals
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Python Code:
%pylab inline
import matplotlib 
#matplotlib.rc('xtick', labelsize=20) 
#matplotlib.rc('ytick', labelsize=20) 
from scipy.spatial import distance
Explanation: <H1>K-means clustering (KMC) algorithm </H1>
<P>
Given a set $X$ of $n$ observations; $X = \{x_1, x_2, \cdots, x_n\}$, where every $i$ observation is a vector of measurements ($x_i \in R^d$). The K-means clustering aims to classify the observations into a set of $k$ clusters $C =\{c_1, c_2, \cdots, c_k\}$ that minimizes the following expression:
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$
\displaystyle{\operatorname{arg\,min}}  \sum_{\mathbf x \in C_i} \left\| \mathbf x - \boldsymbol\mu_i \right\|^2
$
End of explanation
x = np.loadtxt("data.txt", comments='//')
x.shape
print(x.shape)
# Plot 2 measurements
#for i in x:
#    plt.plot(i[0],i[1], 'ko');
plt.scatter(x[:,0], x[:,1], color='black')
plt.xlim(-0.5, 10);
plt.ylim(-0.5, 10);
plt.xlabel('Measurement 1');
plt.ylabel('Measurement 2');
Explanation: Consider the following data set consisting of the scores of two variables on each of 17 experiments
End of explanation
centroid1 = x[0] # first experiment 
centroid2 = x[3] # fourth experiment
print(centroid1, centroid2)
# calculate Euclidean distances from centroid 1
sample1= list()
for i, obs in enumerate(x):
    dist = distance.euclidean(obs, centroid1)
    sample1.append(dist)
    print("%2d -> %6f" %(i, dist))
# calculate Euclidean distances from centroid 2
sample2 = list()
for i, obs in enumerate(x):
    dist = distance.euclidean(obs, centroid2)
    sample2.append(dist)
    print("%2d -> %6f" %(i, dist))
group1 = x[np.array(sample1)<=np.array(sample2)]
print(group1)
group2 = x[np.array(sample2)<np.array(sample1)]
print(group2)
# Replot first categorization
# Plot 2 measurements
for i in group1:
    plt.plot(i[0],i[1], 'o',color='magenta');
for i in group2:
    plt.plot(i[0],i[1], 'o', color='cyan');
plt.plot(centroid1[0], centroid1[1], '*', color='magenta', ms=12)
plt.plot(centroid2[0], centroid2[1], '*', color='cyan', ms=12)
plt.xlim(-0.5, 10);
plt.ylim(-0.5, 10);
plt.xlabel('Measurement 1');
plt.ylabel('Measurement 2');
# recalculate centroids
centroid1 = np.average(group1, axis=0)
centroid2 = np.average(group2, axis=0)
print(centroid1, centroid2)
# calculate Euclidean distances from new centroid 1
sample1= list()
for i, obs in enumerate(x):
    dist = distance.euclidean(obs, centroid1)
    sample1.append(dist)
    print("%2d -> %6f" %(i, dist))
sample2= list()
for i, obs in enumerate(x):
    dist = distance.euclidean(obs, centroid2)
    sample2.append(dist)
    print("%2d -> %6f" %(i, dist))
# reasign the groups
group1 = x[np.array(sample1)<=np.array(sample2)]
print(group1)
group2 = x[np.array(sample2)<np.array(sample1)]
print(group2)
# Replot first categorization with new centrodis
# Plot 2 measurements
for i in group1:
    plt.plot(i[0],i[1], 'o', color='magenta');
for i in group2:
    plt.plot(i[0],i[1], 'o', color='cyan');
plt.plot(centroid1[0], centroid1[1], '*', color='magenta', ms=12)
plt.plot(centroid2[0], centroid2[1], '*', color='cyan', ms=12)
plt.xlim(-0.5, 10);
plt.ylim(-0.5, 10);
plt.xlabel('Measurement 1');
plt.ylabel('Measurement 2');
# recalculate centroids
centroid1 = np.average(group1, axis=0)
centroid2 = np.average(group2, axis=0)
print(centroid1, centroid2)
# calculate Euclidean distances from new centroid 1
sample1= list()
for i, obs in enumerate(x):
    dist = distance.euclidean(obs, centroid1)
    sample1.append(dist)
# calculate Euclidean distances from centroid 2
sample2 = list()
for i, obs in enumerate(x):
    dist = distance.euclidean(obs, centroid2)
    sample2.append(dist)
# reasign the groups
group1 = x[np.array(sample1)<=np.array(sample2)]
group2 = x[np.array(sample2)<np.array(sample1)]
# Replot first categorization with new centrodis
# Plot 2 measurements
for i in group1:
    plt.plot(i[0],i[1], 'o', color='magenta');
for i in group2:
    plt.plot(i[0],i[1], 'o', color='cyan');
plt.plot(centroid1[0], centroid1[1], '*', color='magenta', ms=12)
plt.plot(centroid2[0], centroid2[1], '*', color='cyan', ms=12)
plt.xlim(-0.5, 10);
plt.ylim(-0.5, 10);
plt.xlabel('Measurement 1');
plt.ylabel('Measurement 2');
# recalculate centroids
centroid1 = np.average(group1, axis=0)
centroid2 = np.average(group2, axis=0)
print(centroid1, centroid2)
Explanation: This data set is to be grouped into two clusters. 
As a first step in finding a sensible initial partition, let the values of the measurements 1 and 2 of the two individuals
End of explanation
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