In [1]:

    

%matplotlib inline


    

In [2]:

    

# difficult to tell the correct number of centroids.


    

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from sklearn.datasets import make_blobs
import numpy as np
from sklearn.cluster import KMeans
import matplotlib.pyplot as plt


    

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blobs, classes = make_blobs(500, centers=3)


    

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kmean = KMeans(n_clusters=3)
kmean.fit(blobs)


    

    
Out[14]:





KMeans(copy_x=True, init='k-means++', max_iter=300, n_clusters=3, n_init=10,
    n_jobs=1, precompute_distances='auto', random_state=None, tol=0.0001,
    verbose=0)

In [15]:

    

# Looking at Silhouette distance. It is the ratio of the
# difference between in-cluster dissimilarity, the closest
# out-of-cluster dissimilarity and the maximum of these
# two values. (The measure of how separate the clusters are)


    

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from sklearn import metrics


    

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silhouette_samples = metrics.silhouette_samples(blobs,
                                               kmean.labels_)


    

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np.column_stack((classes[:5], silhouette_samples[:5]))


    

    
Out[18]:





array([[ 2.        ,  0.74893892],
       [ 2.        ,  0.78156808],
       [ 2.        ,  0.7728649 ],
       [ 0.        ,  0.80882898],
       [ 2.        ,  0.74871458]])

In [19]:

    

f, ax = plt.subplots(figsize=(7.5, 7.5))
ax.hist(silhouette_samples)
ax.set_title('Hist of Silhouette Samples')


    

    
Out[19]:





<matplotlib.text.Text at 0x1069f9f50>






    

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# the average of silhouette coefficients is often used to
# describe the entire model's fit.


    

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silhouette_samples.mean()


    

    
Out[21]:





0.790784174912877

In [22]:

    

metrics.silhouette_score(blobs, kmean.labels_)


    

    
Out[22]:





0.790784174912877

In [23]:

    

# fit the models of several cluster counts to see the average
# silhouette score.


    

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blobs, classes = make_blobs(500, centers=10)


    

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silhouette_avgs = []
for k in range(2, 60):
    kmean = KMeans(n_clusters=k).fit(blobs)
    silhouette_avgs.append(metrics.silhouette_score(blobs,
                                                   kmean.labels_))


    

    




/usr/local/lib/python2.7/site-packages/numpy/core/_methods.py:59: RuntimeWarning: Mean of empty slice.
  warnings.warn("Mean of empty slice.", RuntimeWarning)
/usr/local/lib/python2.7/site-packages/numpy/core/_methods.py:71: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)

In [26]:

    

f, ax = plt.subplots(figsize=(7, 5))
ax.plot(silhouette_avgs)


    

    
Out[26]:





[<matplotlib.lines.Line2D at 0x106c76150>]






    

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''' This plot shows that the silhouette averages as the number of
centroids increased. It estimates that there were around 6 or
7 clusters ideally ( We know from the data creation process
that there were 3 clusters. )'''


    

    
Out[28]:





' This plot shows that the silhouette averages as the number of\ncentroids increased. It estimates that there were around 6 or\n7 clusters ideally ( We know from the data creation process\nthat there were 3 clusters. )'

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