v Simple Clustering With SciPy - Python

Simple Clustering With SciPy

Import modules

import numpy as np
%matplotlib inline
import matplotlib.pyplot as plt
from scipy.cluster import vq

Create coordinates for battles for each year of the war

# create 100 coordinate pairs (i.e. two values), then add 5 to all of them
year_1 = np.random.randn(100, 2) + 5

# create 30 coordinatee pairs (i.e. two values), then subtract 5 to all of them
year_2 = np.random.randn(30, 2) - 5

# create 50 coordinatee pairs (i.e. two values)
year_3 = np.random.randn(50, 2)

View the first 3 entries of each year of battles

print('year 1 battles:',  year_1[0:3])
print('year 2 battles:', year_2[0:3])
print('year 3 battles:', year_3[0:3])
year 1 battles: [[ 5.25720722  4.78051294]
 [ 4.11980541  6.24062638]
 [ 4.04612449  5.23819217]]
year 2 battles: [[-3.90607071 -5.20880154]
 [-4.14244415 -4.52520445]
 [-6.01162308 -5.53489708]]
year 3 battles: [[-0.54820297 -0.97483204]
 [ 0.12813873  0.55198748]
 [-0.55677223 -0.68900608]]

Pool all three years of coordinates

# vertically stack year_1, year_2, and year_3 elements
battles = np.vstack([year_1, year_2, year_3])

Cluster the battle locations into three groups

# calculate the centroid coordinates of each cluster 
# and the variance of all the clusters
centroids, variance  = vq.kmeans(battles, 3)

View the centroid coordinate for each of the three clusters

centroids
array([[ 5.02707263,  5.03041508],
       [-0.05392784,  0.12892838],
       [-4.88957266, -4.85051116]])

View the variance of the clusters (they all share the same)

variance
1.2948126660038406

Seperate the battle data into clusters

identified, distance = vq.vq(battles, centroids)

View the cluster of each battle

identified
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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)

View the distance of each individual battle from their cluster's centroid

distance
array([ 0.3397249 ,  1.51252941,  1.00271161,  0.7583883 ,  0.58103782,
        1.81905849,  1.45452846,  1.34523274,  0.69254441,  3.32123157,
        1.73900653,  1.01999434,  1.5392708 ,  0.64417605,  1.25822142,
        1.68913457,  1.09543587,  0.20750281,  2.90778804,  1.62549404,
        1.0224336 ,  1.05196193,  0.98434964,  0.25634371,  1.19779956,
        1.73517217,  2.69339667,  1.32792584,  0.97809768,  1.52654056,
        2.20554365,  1.0403091 ,  0.93698624,  1.53359041,  0.91717984,
        0.3008527 ,  0.42901893,  0.95824461,  1.93321831,  1.89139314,
        1.49982335,  0.63265951,  1.48579627,  1.04574742,  0.83477916,
        2.80489932,  1.50671741,  0.35230994,  1.18607368,  1.36078497,
        1.17298152,  0.95961251,  0.95348923,  1.41903574,  1.7816999 ,
        1.32087763,  0.94807163,  2.22741733,  0.66198152,  0.97404075,
        0.24009773,  1.22021557,  1.36298565,  1.77358477,  0.62586652,
        1.45234278,  1.87925214,  2.18673534,  0.97113871,  1.0436524 ,
        1.63491437,  1.43922603,  1.8066756 ,  2.55661988,  0.64905457,
        0.6939938 ,  1.41183181,  2.72140674,  1.70390906,  3.53986459,
        1.52044903,  1.98702847,  1.2488108 ,  2.61774172,  2.66067284,
        0.80078946,  0.79648259,  2.72215296,  1.26904383,  1.16048896,
        1.42571458,  1.18519189,  0.46592397,  0.63831379,  0.2294296 ,
        0.90199062,  0.99296186,  1.79154225,  0.23854105,  1.19095902,
        1.0467321 ,  0.81487758,  1.31429876,  0.14625493,  1.04421102,
        0.72132375,  2.2209666 ,  1.00145286,  1.30465026,  1.57217776,
        1.31999891,  0.80321763,  2.12942642,  0.81168612,  1.40294667,
        0.89994242,  1.70402817,  0.79621269,  1.29554062,  1.87340273,
        2.40582742,  2.99089606,  1.01348705,  0.54974364,  0.39367389,
        2.28343779,  1.51924388,  0.52095884,  1.54219385,  0.62972955,
        1.20937793,  0.46057272,  0.96014023,  0.2287637 ,  0.84009151,
        1.34393522,  1.5983523 ,  0.46066181,  0.49504327,  2.22788557,
        1.74688212,  1.99998478,  0.25864751,  1.06955924,  1.68029793,
        3.41862662,  1.9273365 ,  0.91580509,  0.94390424,  1.42991149,
        0.64314749,  0.26250126,  1.09000179,  0.42658645,  0.40866344,
        0.47829004,  0.47718204,  0.53641019,  1.42037169,  2.20413065,
        1.85270104,  1.9544685 ,  1.40727147,  0.85730366,  1.63316935,
        1.09642325,  1.36490331,  1.307389  ,  1.9727463 ,  1.35859479,
        2.43699622,  0.80833152,  2.50758584,  0.95216108,  0.16936114,
        0.98714981,  0.19962377,  1.13262204,  2.47056129,  2.00154513])

Index the battles data by the cluster to which they belong

cluster_1 = battles[identified == 0]
cluster_2 = battles[identified == 1]
cluster_3 = battles[identified == 2]

Print the first three coordinate pairs of each cluster

print(cluster_1[0:3])
print(cluster_2[0:3])
print(cluster_3[0:3])
[[ 5.25720722  4.78051294]
 [ 4.11980541  6.24062638]
 [ 4.04612449  5.23819217]]
[[-0.54820297 -0.97483204]
 [ 0.12813873  0.55198748]
 [-0.55677223 -0.68900608]]
[[-3.90607071 -5.20880154]
 [-4.14244415 -4.52520445]
 [-6.01162308 -5.53489708]]

Plot all the battles, color each battle by cluster

# create a scatter plot there the x-axis is the first column of battles
# the y-axis is the second column of battles, the size is 100, and
# the color of each point is determined by the indentified variable
plt.scatter(battles[:,0], battles[:,1], s=100, c=identified)
<matplotlib.collections.PathCollection at 0x10d43f588>

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