In [12]:
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
import scipy
import scipy.spatial
from sklearn.cluster import KMeans
np.random.seed( 2503865 ) # We'll set the random number generator's seed so everyone generates the exact same dataset
In [7]:
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 )
Out[7]:
<matplotlib.collections.PathCollection at 0x109a1e790>
In [44]:
k = 3
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)
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
cluster_scatter( points, labels )
Out[44]:
16.645493271420985
In [36]:
Out[36]:
[0, 1, 2]
In [32]:
max_k = 5
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)
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
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],
[ 2.11223333e+00, 6.60157016e-01],
[ 1.98408430e+00, 6.83631951e-01],
[ 2.13513751e+00, 4.87602191e-01],
[ 1.93956947e+00, 6.23761234e-01],
[ 2.00975822e+00, 6.96550244e-01],
[ 2.15308740e+00, 8.31729008e-01],
[ 1.92965073e+00, 6.72554626e-01],
[ 1.92114652e+00, 8.53914940e-01],
[ 1.86404999e+00, 5.51826645e-01],
[ 1.82318042e+00, 4.58804470e-01],
[ 1.91736723e+00, 7.61003172e-01],
[ 2.09495992e+00, 7.78603595e-01],
[ 2.04921091e+00, 6.27055064e-01],
[ 2.07717925e+00, 4.02049715e-01],
[ 2.08331709e+00, 7.13072465e-01],
[ 1.84600737e+00, 7.89331420e-01],
[ 2.03949128e+00, 7.33684274e-01],
[ 2.00905880e+00, 8.24096268e-01],
[ 2.07157832e+00, 7.44459951e-01],
[ 1.96099922e+00, 7.31269533e-01],
[ 2.02074801e+00, 6.55721817e-01],
[ 2.03749619e+00, 1.04414088e+00],
[ 2.10161028e+00, 7.36176333e-01],
[ 2.00069486e+00, 9.07100856e-01],
[ 2.02208908e+00, 6.79150272e-01],
[ 2.00342619e+00, 5.01751999e-01],
[ 1.96555996e+00, 7.38894526e-01],
[ 1.81697010e+00, 6.09178452e-01],
[ 2.08585709e+00, 8.01563206e-01],
[ 1.95833452e+00, 6.14366306e-01],
[ 1.84588139e+00, 8.54159259e-01],
[ 1.75819570e+00, 4.85640836e-01],
[ 1.73420741e+00, 9.94309567e-01],
[ 1.74493908e+00, 5.28398176e-01],
[ 2.12250455e+00, 7.99575036e-01],
[ 1.84453320e+00, 8.12643454e-01],
[ 1.84735152e+00, 5.90249162e-01],
[ 1.94651833e+00, 9.03709737e-01],
[ 2.06189493e+00, 4.94530910e-01],
[ 1.95788857e+00, 6.79111231e-01],
[ 2.29331880e+00, 6.68290818e-01],
[ 1.86311989e+00, 7.60411828e-01],
[ 1.99573693e+00, 6.28194592e-01],
[ 2.14339821e+00, 8.73189931e-01],
[ 1.87887708e+00, 6.67047320e-01],
[ 1.76961640e+00, 9.27733211e-01],
[ 1.93998522e+00, 6.68487617e-01],
[ 2.00642717e+00, 5.70185837e-01],
[ 1.99432889e+00, 1.02935522e+00],
[ 2.00488319e+00, 5.62010053e-01],
[ 1.94424081e+00, 9.41974804e-01],
[ 1.87548204e+00, 6.97857382e-01],
[ 2.17590404e+00, 8.20991030e-01],
[ 1.81625515e+00, 5.77336053e-01],
[ 1.77250184e+00, 5.54013711e-01],
[ 1.92389365e+00, 4.01972538e-01],
[ 1.66429547e+00, 8.27031231e-01],
[ 1.92657862e+00, 5.86589127e-01],
[ 1.90896893e+00, 9.14167842e-01],
[ 2.00948183e+00, 9.49078642e-01],
[ 2.03277606e+00, 9.30968080e-01],
[ 2.12814188e+00, 8.77150724e-01],
[ 1.88034007e+00, 6.52158636e-01],
[ 1.90473185e+00, 8.28243677e-01],
[ 1.96273476e+00, 7.28454408e-01],
[ 2.22179400e+00, 6.63428941e-01],
[ 1.77164552e+00, 6.35915401e-01],
[ 2.09357835e+00, 9.27450271e-01],
[ 2.04260366e+00, 7.46850207e-01],
[ 2.12557165e+00, 9.16987123e-01],
[ 2.14556642e+00, 4.41624696e-01],
[ 1.93260495e+00, 8.58095616e-01],
[ 2.07846493e+00, 6.87302755e-01],
[ 2.06820621e+00, 7.62680108e-01],
[ 2.12812786e+00, 5.79714066e-01],
[ 1.72015800e+00, 8.01566989e-01],
[ 1.72291961e+00, 5.79014825e-01],
[ 1.88470556e+00, 7.30148168e-01],
[ 2.80957463e-01, 8.87458587e-01],
[ 4.41773126e-01, 9.20828306e-01],
[ 2.23380964e-01, 9.29675955e-01],
[ 2.39289275e-01, 1.05705364e+00],
[ 2.13257456e-01, 1.08489786e+00],
[ 3.09869936e-01, 9.56324715e-01],
[ 2.01637286e-02, 1.03725174e+00],
[ 2.42786101e-01, 9.36271476e-01],
[ 1.64706982e-01, 1.22490800e+00],
[ 8.59793429e-02, 9.79638645e-01],
[ 6.74392378e-02, 8.55484340e-01],
[ -1.48636574e-01, 1.04324959e+00],
[ 2.05631035e-01, 1.21051149e+00],
[ 2.55797575e-02, 1.02505086e+00],
[ 9.75004675e-02, 6.71627883e-01],
[ 1.04698107e-01, 1.12668860e+00],
[ 2.96155382e-01, 1.09267753e+00],
[ 3.21396501e-01, 9.31449825e-01],
[ -8.97990289e-02, 8.21702020e-01],
[ 2.86021750e-01, 1.00045520e+00],
[ 2.59575577e-01, 1.24024383e+00],
[ 1.96185241e-01, 1.04284005e+00],
[ 1.13427724e-01, 1.09723574e+00],
[ 1.54941931e-01, 7.55014516e-01],
[ 2.53949716e-01, 9.84817448e-01],
[ -2.35809581e-01, 8.55830891e-01],
[ 3.12151885e-01, 1.03264074e+00],
[ 2.52979503e-02, 9.46378793e-01],
[ 3.89009402e-02, 1.03865173e+00],
[ 3.73187613e-01, 1.29914482e+00],
[ 2.70973875e-01, 1.03623164e+00],
[ 3.23845473e-01, 5.57621391e-01],
[ 2.54049196e-01, 9.35961058e-01],
[ 3.84166697e-02, 9.27961741e-01],
[ -1.67514457e-02, 1.13573450e+00],
[ -1.26011851e-02, 1.11054194e+00],
[ -8.60893576e-03, 1.16873038e+00],
[ 2.26516612e-01, 8.94683981e-01],
[ 8.05881452e-02, 8.50077292e-01],
[ -8.97229216e-03, 1.20157182e+00],
[ 4.48434575e-02, 8.77640254e-01],
[ 1.45514282e-01, 8.92171146e-01],
[ 1.08999556e-01, 1.19031309e+00],
[ 3.38072428e-01, 1.14791933e+00],
[ 7.82520161e-02, 9.92283649e-01],
[ 8.88605217e-02, 1.28016550e+00],
[ 1.13193569e-01, 1.20754359e+00],
[ 5.52175751e-02, 8.36910730e-01],
[ 2.40835083e-01, 8.74562748e-01],
[ 2.92212463e-01, 1.10435069e+00],
[ 2.15626014e-01, 1.12912830e+00],
[ 2.50207000e-01, 8.32400621e-01],
[ 4.97521869e-02, 1.01713902e+00],
[ -3.34954679e-02, 1.01106239e+00],
[ 1.10702568e-01, 1.39845555e+00],
[ 1.88599472e-01, 1.09180008e+00],
[ 1.88775950e-01, 1.16205451e+00],
[ 1.07686258e-01, 9.59183420e-01],
[ 2.05300584e-01, 1.26262518e+00],
[ 3.00797928e-01, 8.16657185e-01],
[ -5.45269625e-02, 1.15502597e+00],
[ 1.57299054e-01, 1.00551022e+00],
[ 3.21295419e-01, 8.15025257e-01],
[ 1.96519468e-01, 1.20493201e+00],
[ -6.49628746e-02, 1.20808262e+00],
[ -5.24919173e-02, 9.82460172e-01],
[ 1.45319176e-01, 1.14614537e+00],
[ -1.66232827e-01, 8.86582793e-01],
[ 4.38253047e-02, 1.17267055e+00],
[ 1.54076120e-01, 1.02392269e+00],
[ 4.04318408e-01, 8.63541341e-01],
[ 2.57052902e-01, 1.29882069e+00],
[ 1.50279823e-01, 1.26945172e+00],
[ 3.93042329e-01, 8.36914749e-01],
[ 2.62179292e-01, 1.02602356e+00],
[ 2.60767904e-01, 1.04340278e+00],
[ 2.86020157e-01, 9.06978831e-01],
[ 2.28002143e-01, 1.21029112e+00],
[ 2.23314971e-01, 1.14647363e+00],
[ -9.79175744e-02, 1.22579131e+00],
[ -1.03949701e-01, 1.14837283e+00],
[ 3.61408875e-02, 8.30267905e-01],
[ 7.16907503e-02, 1.26765983e+00],
[ 2.45596265e-01, 9.44775218e-01],
[ 2.58105105e-01, 1.01040303e+00],
[ 7.10880922e-02, 1.05800973e+00],
[ 1.47011215e-01, 1.03099971e+00],
[ 2.60719714e-01, 9.36821705e-01],
[ 9.33609981e-02, 9.85537418e-01],
[ 2.78977172e-01, 1.32989670e+00],
[ -4.63465790e-02, 8.90650377e-01],
[ -2.23324749e-02, 1.16195985e+00],
[ 1.98697478e-01, 9.80688662e-01],
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In [22]:
labels
Out[22]:
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In [24]:
np.random.rand(3)
Out[24]:
array([ 0.66278854, 0.8080636 , 0.46854239])
In [ ]:
Content source: JoshuaW1990/TuftsCOMP135_Spring2016
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