In [2]:

    

%matplotlib inline

import numpy as np
import matplotlib.pyplot as plt
import scipy
import scipy.spatial
from sklearn.cluster import KMeans

np.random.seed( 2507365 ) # We'll set the random number generator's seed so everyone generates the exact same dataset


    

In [84]:

    

sigma = 1.5
cluster_sigma = 0.15

num_clumps = 5
clump_N = 100

clump_centers = [ ( np.random.normal(loc=0.5,scale=sigma), np.random.normal(loc=0.5,scale=sigma) ) for _ in range(num_clumps) ]

points = []
points = []

for clump_center in clump_centers:
    for _ in range( clump_N ):
        points += [ ( np.random.normal(loc=clump_center[0],scale=cluster_sigma), np.random.normal(loc=clump_center[1],scale=cluster_sigma) ) ]


points_x = [ point[0] for point in points ]
points_y = [ point[1] for point in points ]

clump1_color = 0
clump2_color = 1
clump_area = 75
#colors = [ clump1_color for i in range(clump1_N) ] + [ clump2_color for i in range(clump2_N) ]
areas = [ clump_area for i in range( len(points_x) ) ]

plt.scatter( points_x, points_y, s=areas )

#plt.savefig('../images/example_unclustered.png')


    

In [6]:

    

sigma = 1
cluster_sigma = 0.15

num_clumps = 2
clump_N = 100

clump_centers = [ ( np.random.normal(loc=0.5,scale=sigma), np.random.normal(loc=0.5,scale=sigma) ) for _ in range(num_clumps) ]

points = []
points = []
labels = []


#for clump_center in clump_centers:
for clump_idx in range(len(clump_centers)):
    clump_center = clump_centers[clump_idx]
    for _ in range( clump_N ):
        points += [ ( 10* np.random.normal(loc=clump_center[0],scale=cluster_sigma), np.random.normal(loc=clump_center[1],scale=cluster_sigma) ) ]
        labels += [clump_idx]


points_x = [ point[0] for point in points ]
points_y = [ point[1] for point in points ]

clump1_color = 0
clump2_color = 1
clump_area = 75
#colors = [ clump1_color for i in range(clump1_N) ] + [ clump2_color for i in range(clump2_N) ]
areas = [ clump_area for i in range( len(points_x) ) ]

plt.scatter( points_x, points_y, s=areas )

#plt.axes().set_title( 'Scatter = ' + str(cluster_scatter(points,labels)))

#plt.savefig('../images/example_feature_scaling.svg')


    

In [ ]:

    

def cluster_scatter( points, labels ):
    unique_clusters = list(set(labels))
    scatter = 0
    for cluster in unique_clusters:
        cluster_points = [ points[idx] for idx in range(len(labels)) if labels[idx]==cluster ]

        centroid_x = float( sum( [point[0] for point in cluster_points] ) ) / len(cluster_points)
        centroid_y = float( sum( [point[1] for point in cluster_points] ) ) / len(cluster_points)        

        centroid_distances = [ ( point[0] - centroid_x )**2 + ( point[1] - centroid_y )**2 for point in cluster_points ]
        scatter += sum(centroid_distances)
    return scatter


    

In [72]:

    

sigma = 1.5
cluster_sigma = 0.5

num_clumps = 2
clump_N = 100

clump_centers = [ ( np.random.normal(loc=0.5,scale=sigma), np.random.normal(loc=0.5,scale=sigma) ) for _ in range(num_clumps) ]

points = []
points = []
labels = []


#for clump_center in clump_centers:
for clump_idx in range(len(clump_centers)):
    clump_center = clump_centers[clump_idx]
    for _ in range( clump_N ):
        points += [ ( np.random.normal(loc=clump_center[0],scale=cluster_sigma), np.random.normal(loc=clump_center[1],scale=cluster_sigma) ) ]
        labels += [clump_idx]


points_x = [ point[0] for point in points ]
points_y = [ point[1] for point in points ]

clump1_color = 0
clump2_color = 1
clump_area = 75
#colors = [ clump1_color for i in range(clump1_N) ] + [ clump2_color for i in range(clump2_N) ]
areas = [ clump_area for i in range( len(points_x) ) ]

plt.scatter( points_x, points_y, s=areas )

plt.axes().set_title( 'Scatter = ' + str(cluster_scatter(points,labels)))

#plt.savefig('../images/example_high_scatter.png')


    

In [12]:

    

def cluster_distance( points, labels ):
    unique_clusters = list(set(labels))

    mean_x = float( sum( [point[0] for point in points] ) ) / len(points)
    mean_y = float( sum( [point[1] for point in points] ) ) / len(points)    
    
    cluster_distance = 0
    
    for cluster in unique_clusters:
        cluster_points = [ points[idx] for idx in range(len(labels)) if labels[idx]==cluster ]

        centroid_x = float( sum( [point[0] for point in cluster_points] ) ) / len(cluster_points)
        centroid_y = float( sum( [point[1] for point in cluster_points] ) ) / len(cluster_points)        

        cluster_distance += len(cluster_points) * ( ( centroid_x - mean_x )**2 + ( centroid_y - mean_y )**2 )

    return cluster_distance


    

In [80]:

    

sigma = 0.5
cluster_sigma = 0.15

num_clumps = 2
clump_N = 100

clump_centers = [ ( np.random.normal(loc=0.5,scale=sigma), np.random.normal(loc=0.5,scale=sigma) ) for _ in range(num_clumps) ]

points = []
points = []
labels = []


#for clump_center in clump_centers:
for clump_idx in range(len(clump_centers)):
    clump_center = clump_centers[clump_idx]
    for _ in range( clump_N ):
        points += [ ( np.random.normal(loc=clump_center[0],scale=cluster_sigma), np.random.normal(loc=clump_center[1],scale=cluster_sigma) ) ]
        labels += [clump_idx]


points_x = [ point[0] for point in points ]
points_y = [ point[1] for point in points ]

clump1_color = 0
clump2_color = 1
clump_area = 75
#colors = [ clump1_color for i in range(clump1_N) ] + [ clump2_color for i in range(clump2_N) ]
areas = [ clump_area for i in range( len(points_x) ) ]

plt.scatter( points_x, points_y, s=areas )

plt.axes().set_title( 'Cluster distance = ' + str(cluster_distance(points,labels)))

#plt.savefig('../images/example_high_distance.png')


    

In [79]:

    

def cluster_summin_distance( points, labels ):
    unique_clusters = list(set(labels))

    clusters = {}

    # Make a dictionary storing all points with their cluster
    for cluster in unique_clusters:
        clusters[cluster] = [ points[idx] for idx in range(len(labels)) if labels[idx]==cluster ]

    cluster_spacing = 0
    for cluster_i in unique_clusters:
        for cluster_j in unique_clusters:
            if cluster_i != cluster_j: # Skip self-self
                distances = [ ]
                
                for point_i in clusters[cluster_i]:
                    for point_j in clusters[cluster_j]:
                        distances += [ ( point_i[0] - point_j[0] )**2 + ( point_i[1] - point_j[1] )**2 ]

                cluster_spacing += min( distances ) / ( len(unique_clusters)**2 )
                        
    return cluster_spacing


    

In [82]:

    

sigma = 2.5
cluster_sigma = 0.15

num_clumps = 2
clump_N = 100

clump_centers = [ ( np.random.normal(loc=0.5,scale=sigma), np.random.normal(loc=0.5,scale=sigma) ) for _ in range(num_clumps) ]

points = []
points = []
labels = []


#for clump_center in clump_centers:
for clump_idx in range(len(clump_centers)):
    clump_center = clump_centers[clump_idx]
    for _ in range( clump_N ):
        points += [ ( np.random.normal(loc=clump_center[0],scale=cluster_sigma), np.random.normal(loc=clump_center[1],scale=cluster_sigma) ) ]
        labels += [clump_idx]


points_x = [ point[0] for point in points ]
points_y = [ point[1] for point in points ]

clump1_color = 0
clump2_color = 1
clump_area = 75
#colors = [ clump1_color for i in range(clump1_N) ] + [ clump2_color for i in range(clump2_N) ]
areas = [ clump_area for i in range( len(points_x) ) ]

plt.scatter( points_x, points_y, s=areas )

plt.axes().set_title( 'Cluster spacing = ' + str(cluster_summin_distance(points,labels)))

#plt.savefig('../images/example_large_spacing.png')


    

In [65]:

    

k = 3

def run_with_k( k ):
    est = KMeans(n_clusters=k)

    plt.cla()
    est.fit( np.array(points) )
    labels = est.labels_

    color_map = [ np.random.rand(3) for _ in range( k ) ]
    colors = [ color_map[label] for label in labels ]

    #plt.scatter(points_x, points_y, c=colors)
    
    return cluster_scatter( points, labels )
    #return cluster_distance( points, labels )
    #return cluster_summin_distance( points, labels )

X = range( 2, 10 )
Y = []
for k in X:
    Y += [ run_with_k(k) ]

ax = plt.axes()

plt.plot( X, Y )

ax.set_xlabel('k')
ax.set_ylabel('Cluster scatter')

#plt.savefig('../images/kmeans_k_v_scatter.png')


    

    
Out[65]:





<matplotlib.text.Text at 0x10b725890>






    

In [36]:

    




    

    
Out[36]:





[0, 1, 2]

In [11]:

    

max_k = 7

plt.clf()

fignum = 0
for k in range( 2, max_k ):
    fig = plt.figure(fignum, figsize=(4, 3))
    plt.clf()
    ax = plt.axes()

    est = KMeans(n_clusters=k)
    
    plt.cla()
    est.fit( np.array(points) )
    labels = est.labels_

    color_map = [ np.random.rand(3) for _ in range( k ) ]
    colors = [ color_map[label] for label in labels ]
    
    ax.scatter(points_x, points_y, c=colors, s=areas)

    ax.set_title("K = " + str(k))
#    ax.xaxis.set_ticklabels([])
#    ax.yaxis.set_ticklabels([])
#    ax.set_xlabel('Petal width')
#    ax.set_ylabel('Sepal length')
    fignum = fignum + 1
    #plt.savefig('../images/kmeans_k=' + str(k) + '.png')


    

In [121]:

    

k = 4

num_steps = 10

plt.clf()

#centroids = [ ( np.random.normal(loc=0.5,scale=sigma), np.random.normal(loc=0.5,scale=sigma) ) for _ in range(k) ]

# Initialize centroids as random points from the dataset
centroids = [ points[i] for i in np.random.choice( len(points), k ) ]

#color_map = [ np.random.rand(3) for _ in range( k ) ]


fignum = 0
for step in range( num_steps ):
    plt.clf()
    ax = plt.axes()    
    
    plt.cla()

    labels = []
    for el in range(len(points_x)):
        labels += [ min( range(k), key=lambda cidx: ( (centroids[cidx][0] - points_x[el])**2 + (centroids[cidx][1] - points_y[el] )**2) ) ]

    colors = [ color_map[label] for label in labels ]
    
    # Draw points
    ax.scatter(points_x, points_y, c=colors, s=areas)

    # Draw centroids
    centroid_colors = [ color_map[i] for i in range(k) ]
    centroid_areas = [ 500 for _ in range(k) ]
    ax.scatter([p[0] for p in centroids], [p[1] for p in centroids], c=centroid_colors, s=centroid_areas)
    
    ax.set_title("K = " + str(k) + ', step=' + str(step))
    
    plt.savefig('../images/example_kmeans_step=' + str(step) + '.svg')

    # Update centroids
    for cidx in range(k):
        xs = [ points_x[i] for i in range(len(points_x)) if labels[i]==cidx ]
        ys = [ points_y[i] for i in range(len(points_y)) if labels[i]==cidx ]        
        if len(xs) > 0:
            centroids[cidx] = ( sum(xs)/float(len(xs)), sum(ys)/float(len(ys)) )


    

In [ ]:

    




    

In [17]:

    

from sklearn import datasets
iris = datasets.load_iris()
X = iris.data
y = iris.target
X


    

    
Out[17]:





array([[ 5.1,  3.5,  1.4,  0.2],
       [ 4.9,  3. ,  1.4,  0.2],
       [ 4.7,  3.2,  1.3,  0.2],
       [ 4.6,  3.1,  1.5,  0.2],
       [ 5. ,  3.6,  1.4,  0.2],
       [ 5.4,  3.9,  1.7,  0.4],
       [ 4.6,  3.4,  1.4,  0.3],
       [ 5. ,  3.4,  1.5,  0.2],
       [ 4.4,  2.9,  1.4,  0.2],
       [ 4.9,  3.1,  1.5,  0.1],
       [ 5.4,  3.7,  1.5,  0.2],
       [ 4.8,  3.4,  1.6,  0.2],
       [ 4.8,  3. ,  1.4,  0.1],
       [ 4.3,  3. ,  1.1,  0.1],
       [ 5.8,  4. ,  1.2,  0.2],
       [ 5.7,  4.4,  1.5,  0.4],
       [ 5.4,  3.9,  1.3,  0.4],
       [ 5.1,  3.5,  1.4,  0.3],
       [ 5.7,  3.8,  1.7,  0.3],
       [ 5.1,  3.8,  1.5,  0.3],
       [ 5.4,  3.4,  1.7,  0.2],
       [ 5.1,  3.7,  1.5,  0.4],
       [ 4.6,  3.6,  1. ,  0.2],
       [ 5.1,  3.3,  1.7,  0.5],
       [ 4.8,  3.4,  1.9,  0.2],
       [ 5. ,  3. ,  1.6,  0.2],
       [ 5. ,  3.4,  1.6,  0.4],
       [ 5.2,  3.5,  1.5,  0.2],
       [ 5.2,  3.4,  1.4,  0.2],
       [ 4.7,  3.2,  1.6,  0.2],
       [ 4.8,  3.1,  1.6,  0.2],
       [ 5.4,  3.4,  1.5,  0.4],
       [ 5.2,  4.1,  1.5,  0.1],
       [ 5.5,  4.2,  1.4,  0.2],
       [ 4.9,  3.1,  1.5,  0.1],
       [ 5. ,  3.2,  1.2,  0.2],
       [ 5.5,  3.5,  1.3,  0.2],
       [ 4.9,  3.1,  1.5,  0.1],
       [ 4.4,  3. ,  1.3,  0.2],
       [ 5.1,  3.4,  1.5,  0.2],
       [ 5. ,  3.5,  1.3,  0.3],
       [ 4.5,  2.3,  1.3,  0.3],
       [ 4.4,  3.2,  1.3,  0.2],
       [ 5. ,  3.5,  1.6,  0.6],
       [ 5.1,  3.8,  1.9,  0.4],
       [ 4.8,  3. ,  1.4,  0.3],
       [ 5.1,  3.8,  1.6,  0.2],
       [ 4.6,  3.2,  1.4,  0.2],
       [ 5.3,  3.7,  1.5,  0.2],
       [ 5. ,  3.3,  1.4,  0.2],
       [ 7. ,  3.2,  4.7,  1.4],
       [ 6.4,  3.2,  4.5,  1.5],
       [ 6.9,  3.1,  4.9,  1.5],
       [ 5.5,  2.3,  4. ,  1.3],
       [ 6.5,  2.8,  4.6,  1.5],
       [ 5.7,  2.8,  4.5,  1.3],
       [ 6.3,  3.3,  4.7,  1.6],
       [ 4.9,  2.4,  3.3,  1. ],
       [ 6.6,  2.9,  4.6,  1.3],
       [ 5.2,  2.7,  3.9,  1.4],
       [ 5. ,  2. ,  3.5,  1. ],
       [ 5.9,  3. ,  4.2,  1.5],
       [ 6. ,  2.2,  4. ,  1. ],
       [ 6.1,  2.9,  4.7,  1.4],
       [ 5.6,  2.9,  3.6,  1.3],
       [ 6.7,  3.1,  4.4,  1.4],
       [ 5.6,  3. ,  4.5,  1.5],
       [ 5.8,  2.7,  4.1,  1. ],
       [ 6.2,  2.2,  4.5,  1.5],
       [ 5.6,  2.5,  3.9,  1.1],
       [ 5.9,  3.2,  4.8,  1.8],
       [ 6.1,  2.8,  4. ,  1.3],
       [ 6.3,  2.5,  4.9,  1.5],
       [ 6.1,  2.8,  4.7,  1.2],
       [ 6.4,  2.9,  4.3,  1.3],
       [ 6.6,  3. ,  4.4,  1.4],
       [ 6.8,  2.8,  4.8,  1.4],
       [ 6.7,  3. ,  5. ,  1.7],
       [ 6. ,  2.9,  4.5,  1.5],
       [ 5.7,  2.6,  3.5,  1. ],
       [ 5.5,  2.4,  3.8,  1.1],
       [ 5.5,  2.4,  3.7,  1. ],
       [ 5.8,  2.7,  3.9,  1.2],
       [ 6. ,  2.7,  5.1,  1.6],
       [ 5.4,  3. ,  4.5,  1.5],
       [ 6. ,  3.4,  4.5,  1.6],
       [ 6.7,  3.1,  4.7,  1.5],
       [ 6.3,  2.3,  4.4,  1.3],
       [ 5.6,  3. ,  4.1,  1.3],
       [ 5.5,  2.5,  4. ,  1.3],
       [ 5.5,  2.6,  4.4,  1.2],
       [ 6.1,  3. ,  4.6,  1.4],
       [ 5.8,  2.6,  4. ,  1.2],
       [ 5. ,  2.3,  3.3,  1. ],
       [ 5.6,  2.7,  4.2,  1.3],
       [ 5.7,  3. ,  4.2,  1.2],
       [ 5.7,  2.9,  4.2,  1.3],
       [ 6.2,  2.9,  4.3,  1.3],
       [ 5.1,  2.5,  3. ,  1.1],
       [ 5.7,  2.8,  4.1,  1.3],
       [ 6.3,  3.3,  6. ,  2.5],
       [ 5.8,  2.7,  5.1,  1.9],
       [ 7.1,  3. ,  5.9,  2.1],
       [ 6.3,  2.9,  5.6,  1.8],
       [ 6.5,  3. ,  5.8,  2.2],
       [ 7.6,  3. ,  6.6,  2.1],
       [ 4.9,  2.5,  4.5,  1.7],
       [ 7.3,  2.9,  6.3,  1.8],
       [ 6.7,  2.5,  5.8,  1.8],
       [ 7.2,  3.6,  6.1,  2.5],
       [ 6.5,  3.2,  5.1,  2. ],
       [ 6.4,  2.7,  5.3,  1.9],
       [ 6.8,  3. ,  5.5,  2.1],
       [ 5.7,  2.5,  5. ,  2. ],
       [ 5.8,  2.8,  5.1,  2.4],
       [ 6.4,  3.2,  5.3,  2.3],
       [ 6.5,  3. ,  5.5,  1.8],
       [ 7.7,  3.8,  6.7,  2.2],
       [ 7.7,  2.6,  6.9,  2.3],
       [ 6. ,  2.2,  5. ,  1.5],
       [ 6.9,  3.2,  5.7,  2.3],
       [ 5.6,  2.8,  4.9,  2. ],
       [ 7.7,  2.8,  6.7,  2. ],
       [ 6.3,  2.7,  4.9,  1.8],
       [ 6.7,  3.3,  5.7,  2.1],
       [ 7.2,  3.2,  6. ,  1.8],
       [ 6.2,  2.8,  4.8,  1.8],
       [ 6.1,  3. ,  4.9,  1.8],
       [ 6.4,  2.8,  5.6,  2.1],
       [ 7.2,  3. ,  5.8,  1.6],
       [ 7.4,  2.8,  6.1,  1.9],
       [ 7.9,  3.8,  6.4,  2. ],
       [ 6.4,  2.8,  5.6,  2.2],
       [ 6.3,  2.8,  5.1,  1.5],
       [ 6.1,  2.6,  5.6,  1.4],
       [ 7.7,  3. ,  6.1,  2.3],
       [ 6.3,  3.4,  5.6,  2.4],
       [ 6.4,  3.1,  5.5,  1.8],
       [ 6. ,  3. ,  4.8,  1.8],
       [ 6.9,  3.1,  5.4,  2.1],
       [ 6.7,  3.1,  5.6,  2.4],
       [ 6.9,  3.1,  5.1,  2.3],
       [ 5.8,  2.7,  5.1,  1.9],
       [ 6.8,  3.2,  5.9,  2.3],
       [ 6.7,  3.3,  5.7,  2.5],
       [ 6.7,  3. ,  5.2,  2.3],
       [ 6.3,  2.5,  5. ,  1.9],
       [ 6.5,  3. ,  5.2,  2. ],
       [ 6.2,  3.4,  5.4,  2.3],
       [ 5.9,  3. ,  5.1,  1.8]])

In [18]:

    

np.array(points)


    

    
Out[18]:





array([[  1.93218767e+00,   7.91349228e-01],
       [  1.99088464e+00,   6.62294160e-01],
       [  1.77806580e+00,   6.78895335e-01],
       [  1.82383858e+00,   4.70783881e-01],
       [  2.06520952e+00,   8.11187979e-01],
       [  2.01959735e+00,   8.86689868e-01],
       [  2.25005558e+00,   1.03023621e+00],
       [  2.15483815e+00,   7.58466743e-01],
       [  1.81622240e+00,   7.67047008e-01],
       [  2.09157296e+00,   7.62246984e-01],
       [  1.86089627e+00,   4.65529507e-01],
       [  1.75245377e+00,   8.59309588e-01],
       [  2.00287027e+00,   6.70898034e-01],
       [  2.26778432e+00,   1.03746423e+00],
       [  1.90617537e+00,   3.61362055e-01],
       [  2.01715142e+00,   5.42212452e-01],
       [  1.81002092e+00,   5.44576129e-01],
       [  1.95308554e+00,   8.22389637e-01],
       [  1.91143890e+00,   6.52377559e-01],
       [  2.03762057e+00,   9.23894779e-01],
       [  1.82705147e+00,   3.68534687e-01],
       [  2.01513115e+00,   8.82471876e-01],
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       [  4.72943272e-01,   2.55053275e+00],
       [  8.50136562e-01,   2.81925414e+00],
       [  4.69056466e-01,   2.91770742e+00],
       [  4.19399960e-01,   2.82971728e+00],
       [  7.73566392e-01,   3.04139446e+00],
       [  2.98045210e-01,   2.66095617e+00],
       [  3.83977004e-01,   2.82937330e+00],
       [  4.69916476e-01,   2.43639825e+00],
       [  5.61626646e-01,   2.58547065e+00],
       [  4.13815679e-01,   2.59005090e+00],
       [  6.70819298e-01,   2.71490458e+00],
       [  8.26243151e-01,   2.76810133e+00],
       [  3.51787379e-01,   2.52821127e+00],
       [  5.35532378e-01,   2.85975017e+00],
       [  3.39597125e-01,   2.67480015e+00],
       [  4.72447256e-01,   2.86013953e+00],
       [  5.64037533e-01,   2.99831818e+00],
       [  3.30938207e-01,   2.84284145e+00],
       [  7.06151285e-01,   2.85197992e+00],
       [  1.87394943e-01,   2.95571176e+00],
       [  2.66511397e-01,   2.64713820e+00],
       [  2.49793850e-01,   2.83454641e+00],
       [  3.40306316e-01,   2.93834570e+00],
       [  5.95297542e-01,   2.72714822e+00],
       [  4.62185627e-01,   2.84475668e+00],
       [  8.31966541e-01,   2.78020757e+00],
       [  5.09886726e-01,   3.02243620e+00],
       [  5.37307665e-01,   2.96612103e+00],
       [  5.36956603e-01,   2.97348544e+00],
       [  3.25051266e-01,   2.89165497e+00],
       [  4.74857954e-01,   2.85976184e+00],
       [  6.74917989e-01,   2.81218876e+00],
       [  5.79152137e-01,   2.78261091e+00],
       [  7.99206058e-01,   2.71032193e+00],
       [  2.68379562e-01,   2.87443668e+00],
       [  4.36457441e-01,   2.61427699e+00],
       [  5.84966004e-01,   2.65212095e+00],
       [  3.22289780e-01,   2.99756299e+00],
       [  6.47775546e-01,   2.69771921e+00],
       [  4.06605093e-01,   2.80332832e+00],
       [  3.59521113e-01,   2.80163538e+00],
       [  6.64075153e-01,   2.60882440e+00],
       [  3.66928230e-01,   2.57457916e+00],
       [  2.24909037e-01,   2.68017285e+00],
       [  3.89276676e-01,   2.81327228e+00],
       [  5.05118496e-01,   2.57633098e+00],
       [  4.21862199e-01,   2.74194179e+00],
       [  5.79220283e-01,   2.98241310e+00],
       [  4.22884204e-01,   2.79945123e+00],
       [  6.26102035e-01,   2.79686747e+00],
       [  1.72951068e-02,   2.83292234e+00],
       [  1.43872221e+00,   6.29332496e-01],
       [  1.50721149e+00,   6.61882310e-01],
       [  1.48078161e+00,   5.22521088e-01],
       [  1.27066787e+00,   3.85689738e-01],
       [  1.67913379e+00,   5.29602806e-01],
       [  1.51316958e+00,   6.26844780e-01],
       [  1.38850266e+00,   6.64811708e-01],
       [  1.74796147e+00,   6.82918062e-01],
       [  1.57706312e+00,   2.99232213e-01],
       [  1.31463526e+00,   4.65515974e-01],
       [  1.35048369e+00,   3.33014922e-01],
       [  1.72334236e+00,   8.76705254e-01],
       [  1.36822068e+00,   5.87740885e-01],
       [  1.48236372e+00,   4.59506084e-01],
       [  1.55077468e+00,   5.17676831e-01],
       [  1.59222975e+00,   7.07726137e-01],
       [  1.48971284e+00,   6.42754962e-01],
       [  1.45389003e+00,   3.84317808e-01],
       [  1.21389626e+00,   6.81176877e-01],
       [  1.47606694e+00,   6.91003497e-01],
       [  1.50381340e+00,   3.81195750e-01],
       [  1.63454613e+00,   4.24290730e-01],
       [  1.51639660e+00,   3.83045272e-01],
       [  1.58962706e+00,   6.10418697e-01],
       [  1.52490829e+00,   1.24443220e-01],
       [  1.39889593e+00,   4.21376285e-01],
       [  1.65646473e+00,   6.01147019e-01],
       [  1.53173531e+00,   5.25514486e-01],
       [  1.34066289e+00,   6.12541985e-01],
       [  1.32695441e+00,   4.86285344e-01],
       [  1.35680712e+00,   4.65064887e-01],
       [  1.41977189e+00,   6.44032277e-01],
       [  1.44540377e+00,   5.35858005e-01],
       [  1.66867820e+00,   9.25913468e-01],
       [  1.67949078e+00,   3.07588418e-01],
       [  1.36576898e+00,   5.91367897e-01],
       [  1.53264865e+00,   8.36402661e-01],
       [  1.29982542e+00,   3.88295082e-01],
       [  1.21689431e+00,   6.52230117e-01],
       [  1.51122243e+00,   7.57602665e-01],
       [  1.42559904e+00,   9.69431529e-02],
       [  1.40615911e+00,   4.94799226e-01],
       [  1.49697022e+00,   6.17675664e-01],
       [  1.49713164e+00,   7.69930590e-01],
       [  1.55323444e+00,   5.82765549e-01],
       [  1.28073406e+00,   4.83426276e-01],
       [  1.71708848e+00,   5.40888994e-01],
       [  1.33937427e+00,   7.31106217e-01],
       [  1.48497978e+00,   6.59123971e-01],
       [  1.38715411e+00,   7.94944941e-01],
       [  1.42077666e+00,   6.77829994e-01],
       [  1.47332070e+00,   6.57975151e-01],
       [  1.56769800e+00,   5.22765467e-01],
       [  1.41115358e+00,   7.63544471e-01],
       [  1.39891516e+00,   4.69046562e-01],
       [  1.72092760e+00,   3.60455368e-01],
       [  1.46089959e+00,   3.87750095e-01],
       [  1.34078802e+00,   6.04306413e-01],
       [  1.53673910e+00,   3.74516431e-01],
       [  1.47942118e+00,   5.08050959e-01],
       [  1.16848898e+00,   4.92719271e-01],
       [  1.40566649e+00,   6.58501379e-01],
       [  1.62717590e+00,   6.73523405e-01],
       [  1.42244865e+00,   5.02125292e-01],
       [  1.74270369e+00,   4.07008898e-01],
       [  1.34998348e+00,   4.74294904e-01],
       [  1.48309270e+00,   6.36602040e-01],
       [  1.45572700e+00,   4.99204364e-01],
       [  1.28159664e+00,   6.52634814e-01],
       [  1.59300473e+00,   5.17577880e-01],
       [  1.71982391e+00,   6.78217206e-01],
       [  1.32347278e+00,   6.14911251e-01],
       [  1.44790951e+00,   4.21607118e-01],
       [  1.35945375e+00,   7.63526601e-01],
       [  2.05484502e+00,   7.50570883e-01],
       [  1.45763776e+00,   4.05828033e-01],
       [  1.28797667e+00,   5.18270153e-01],
       [  1.31632462e+00,   4.99038663e-01],
       [  1.44224635e+00,   7.43485269e-01],
       [  1.62889446e+00,   6.42788432e-01],
       [  1.50040157e+00,   5.73146180e-01],
       [  1.39104273e+00,   5.18268870e-01],
       [  1.42248864e+00,   7.21562311e-01],
       [  1.36229474e+00,   6.53812365e-01],
       [  1.34716093e+00,   4.75184132e-01],
       [  1.56886464e+00,   6.07464689e-01],
       [  1.37351325e+00,   9.22798998e-01],
       [  1.51527931e+00,   6.24496427e-01],
       [  1.73406893e+00,   5.27116183e-01],
       [  1.49484621e+00,   4.01203141e-01],
       [  1.51951781e+00,   8.52856424e-01],
       [  1.24640055e+00,   5.55131369e-01],
       [  1.49715438e+00,   5.21103915e-01],
       [  1.39964100e+00,   6.99337966e-01],
       [  1.39495737e+00,   5.51746088e-01],
       [  1.35621434e+00,   3.46390965e-01],
       [  1.50874292e+00,   7.71332793e-01],
       [  1.56600153e+00,   3.48576028e-01],
       [  1.72592450e+00,   4.48087106e-01],
       [  1.49827454e+00,   7.98979063e-01]])

In [22]:

    

labels


    

    
Out[22]:





array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)

In [24]:

    

np.random.rand(3)


    

    
Out[24]:





array([ 0.66278854,  0.8080636 ,  0.46854239])

In [54]:

    

# Z-normalized Iris dataset

from sklearn import datasets
iris = datasets.load_iris()

X = iris.data
Y = iris.target

classes = [ 1 if el == 1 else 0 for el in Y ]

normX = (X - X.mean(axis=0)) / X.std(axis=0)
    
for line in normX:
    print line


    

    




[-0.90068117  1.03205722 -1.3412724  -1.31297673]
[-1.14301691 -0.1249576  -1.3412724  -1.31297673]
[-1.38535265  0.33784833 -1.39813811 -1.31297673]
[-1.50652052  0.10644536 -1.2844067  -1.31297673]
[-1.02184904  1.26346019 -1.3412724  -1.31297673]
[-0.53717756  1.95766909 -1.17067529 -1.05003079]
[-1.50652052  0.80065426 -1.3412724  -1.18150376]
[-1.02184904  0.80065426 -1.2844067  -1.31297673]
[-1.74885626 -0.35636057 -1.3412724  -1.31297673]
[-1.14301691  0.10644536 -1.2844067  -1.4444497 ]
[-0.53717756  1.49486315 -1.2844067  -1.31297673]
[-1.26418478  0.80065426 -1.227541   -1.31297673]
[-1.26418478 -0.1249576  -1.3412724  -1.4444497 ]
[-1.87002413 -0.1249576  -1.51186952 -1.4444497 ]
[-0.05250608  2.18907205 -1.45500381 -1.31297673]
[-0.17367395  3.11468391 -1.2844067  -1.05003079]
[-0.53717756  1.95766909 -1.39813811 -1.05003079]
[-0.90068117  1.03205722 -1.3412724  -1.18150376]
[-0.17367395  1.72626612 -1.17067529 -1.18150376]
[-0.90068117  1.72626612 -1.2844067  -1.18150376]
[-0.53717756  0.80065426 -1.17067529 -1.31297673]
[-0.90068117  1.49486315 -1.2844067  -1.05003079]
[-1.50652052  1.26346019 -1.56873522 -1.31297673]
[-0.90068117  0.56925129 -1.17067529 -0.91855782]
[-1.26418478  0.80065426 -1.05694388 -1.31297673]
[-1.02184904 -0.1249576  -1.227541   -1.31297673]
[-1.02184904  0.80065426 -1.227541   -1.05003079]
[-0.7795133   1.03205722 -1.2844067  -1.31297673]
[-0.7795133   0.80065426 -1.3412724  -1.31297673]
[-1.38535265  0.33784833 -1.227541   -1.31297673]
[-1.26418478  0.10644536 -1.227541   -1.31297673]
[-0.53717756  0.80065426 -1.2844067  -1.05003079]
[-0.7795133   2.42047502 -1.2844067  -1.4444497 ]
[-0.41600969  2.65187798 -1.3412724  -1.31297673]
[-1.14301691  0.10644536 -1.2844067  -1.4444497 ]
[-1.02184904  0.33784833 -1.45500381 -1.31297673]
[-0.41600969  1.03205722 -1.39813811 -1.31297673]
[-1.14301691  0.10644536 -1.2844067  -1.4444497 ]
[-1.74885626 -0.1249576  -1.39813811 -1.31297673]
[-0.90068117  0.80065426 -1.2844067  -1.31297673]
[-1.02184904  1.03205722 -1.39813811 -1.18150376]
[-1.62768839 -1.74477836 -1.39813811 -1.18150376]
[-1.74885626  0.33784833 -1.39813811 -1.31297673]
[-1.02184904  1.03205722 -1.227541   -0.78708485]
[-0.90068117  1.72626612 -1.05694388 -1.05003079]
[-1.26418478 -0.1249576  -1.3412724  -1.18150376]
[-0.90068117  1.72626612 -1.227541   -1.31297673]
[-1.50652052  0.33784833 -1.3412724  -1.31297673]
[-0.65834543  1.49486315 -1.2844067  -1.31297673]
[-1.02184904  0.56925129 -1.3412724  -1.31297673]
[ 1.40150837  0.33784833  0.53529583  0.26469891]
[ 0.67450115  0.33784833  0.42156442  0.39617188]
[ 1.2803405   0.10644536  0.64902723  0.39617188]
[-0.41600969 -1.74477836  0.1372359   0.13322594]
[ 0.79566902 -0.58776353  0.47843012  0.39617188]
[-0.17367395 -0.58776353  0.42156442  0.13322594]
[ 0.55333328  0.56925129  0.53529583  0.52764485]
[-1.14301691 -1.51337539 -0.26082403 -0.26119297]
[ 0.91683689 -0.35636057  0.47843012  0.13322594]
[-0.7795133  -0.8191665   0.08037019  0.26469891]
[-1.02184904 -2.43898725 -0.14709262 -0.26119297]
[ 0.06866179 -0.1249576   0.25096731  0.39617188]
[ 0.18982966 -1.97618132  0.1372359  -0.26119297]
[ 0.31099753 -0.35636057  0.53529583  0.26469891]
[-0.29484182 -0.35636057 -0.09022692  0.13322594]
[ 1.03800476  0.10644536  0.36469871  0.26469891]
[-0.29484182 -0.1249576   0.42156442  0.39617188]
[-0.05250608 -0.8191665   0.1941016  -0.26119297]
[ 0.4321654  -1.97618132  0.42156442  0.39617188]
[-0.29484182 -1.28197243  0.08037019 -0.12972   ]
[ 0.06866179  0.33784833  0.59216153  0.79059079]
[ 0.31099753 -0.58776353  0.1372359   0.13322594]
[ 0.55333328 -1.28197243  0.64902723  0.39617188]
[ 0.31099753 -0.58776353  0.53529583  0.00175297]
[ 0.67450115 -0.35636057  0.30783301  0.13322594]
[ 0.91683689 -0.1249576   0.36469871  0.26469891]
[ 1.15917263 -0.58776353  0.59216153  0.26469891]
[ 1.03800476 -0.1249576   0.70589294  0.65911782]
[ 0.18982966 -0.35636057  0.42156442  0.39617188]
[-0.17367395 -1.05056946 -0.14709262 -0.26119297]
[-0.41600969 -1.51337539  0.02350449 -0.12972   ]
[-0.41600969 -1.51337539 -0.03336121 -0.26119297]
[-0.05250608 -0.8191665   0.08037019  0.00175297]
[ 0.18982966 -0.8191665   0.76275864  0.52764485]
[-0.53717756 -0.1249576   0.42156442  0.39617188]
[ 0.18982966  0.80065426  0.42156442  0.52764485]
[ 1.03800476  0.10644536  0.53529583  0.39617188]
[ 0.55333328 -1.74477836  0.36469871  0.13322594]
[-0.29484182 -0.1249576   0.1941016   0.13322594]
[-0.41600969 -1.28197243  0.1372359   0.13322594]
[-0.41600969 -1.05056946  0.36469871  0.00175297]
[ 0.31099753 -0.1249576   0.47843012  0.26469891]
[-0.05250608 -1.05056946  0.1372359   0.00175297]
[-1.02184904 -1.74477836 -0.26082403 -0.26119297]
[-0.29484182 -0.8191665   0.25096731  0.13322594]
[-0.17367395 -0.1249576   0.25096731  0.00175297]
[-0.17367395 -0.35636057  0.25096731  0.13322594]
[ 0.4321654  -0.35636057  0.30783301  0.13322594]
[-0.90068117 -1.28197243 -0.43142114 -0.12972   ]
[-0.17367395 -0.58776353  0.1941016   0.13322594]
[ 0.55333328  0.56925129  1.27454998  1.71090158]
[-0.05250608 -0.8191665   0.76275864  0.92206376]
[ 1.52267624 -0.1249576   1.21768427  1.1850097 ]
[ 0.55333328 -0.35636057  1.04708716  0.79059079]
[ 0.79566902 -0.1249576   1.16081857  1.31648267]
[ 2.12851559 -0.1249576   1.6157442   1.1850097 ]
[-1.14301691 -1.28197243  0.42156442  0.65911782]
[ 1.76501198 -0.35636057  1.44514709  0.79059079]
[ 1.03800476 -1.28197243  1.16081857  0.79059079]
[ 1.64384411  1.26346019  1.33141568  1.71090158]
[ 0.79566902  0.33784833  0.76275864  1.05353673]
[ 0.67450115 -0.8191665   0.87649005  0.92206376]
[ 1.15917263 -0.1249576   0.99022146  1.1850097 ]
[-0.17367395 -1.28197243  0.70589294  1.05353673]
[-0.05250608 -0.58776353  0.76275864  1.57942861]
[ 0.67450115  0.33784833  0.87649005  1.44795564]
[ 0.79566902 -0.1249576   0.99022146  0.79059079]
[ 2.24968346  1.72626612  1.67260991  1.31648267]
[ 2.24968346 -1.05056946  1.78634131  1.44795564]
[ 0.18982966 -1.97618132  0.70589294  0.39617188]
[ 1.2803405   0.33784833  1.10395287  1.44795564]
[-0.29484182 -0.58776353  0.64902723  1.05353673]
[ 2.24968346 -0.58776353  1.67260991  1.05353673]
[ 0.55333328 -0.8191665   0.64902723  0.79059079]
[ 1.03800476  0.56925129  1.10395287  1.1850097 ]
[ 1.64384411  0.33784833  1.27454998  0.79059079]
[ 0.4321654  -0.58776353  0.59216153  0.79059079]
[ 0.31099753 -0.1249576   0.64902723  0.79059079]
[ 0.67450115 -0.58776353  1.04708716  1.1850097 ]
[ 1.64384411 -0.1249576   1.16081857  0.52764485]
[ 1.88617985 -0.58776353  1.33141568  0.92206376]
[ 2.4920192   1.72626612  1.50201279  1.05353673]
[ 0.67450115 -0.58776353  1.04708716  1.31648267]
[ 0.55333328 -0.58776353  0.76275864  0.39617188]
[ 0.31099753 -1.05056946  1.04708716  0.26469891]
[ 2.24968346 -0.1249576   1.33141568  1.44795564]
[ 0.55333328  0.80065426  1.04708716  1.57942861]
[ 0.67450115  0.10644536  0.99022146  0.79059079]
[ 0.18982966 -0.1249576   0.59216153  0.79059079]
[ 1.2803405   0.10644536  0.93335575  1.1850097 ]
[ 1.03800476  0.10644536  1.04708716  1.57942861]
[ 1.2803405   0.10644536  0.76275864  1.44795564]
[-0.05250608 -0.8191665   0.76275864  0.92206376]
[ 1.15917263  0.33784833  1.21768427  1.44795564]
[ 1.03800476  0.56925129  1.10395287  1.71090158]
[ 1.03800476 -0.1249576   0.81962435  1.44795564]
[ 0.55333328 -1.28197243  0.70589294  0.92206376]
[ 0.79566902 -0.1249576   0.81962435  1.05353673]
[ 0.4321654   0.80065426  0.93335575  1.44795564]
[ 0.06866179 -0.1249576   0.76275864  0.79059079]

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