k-Means Clustering

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Goal

This post aims to introduce k-means clustering using artificial data. image

Libraries

In [1]:
from sklearn.cluster import KMeans
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline

Create artificial clustered data

Parameters

In [2]:
# 3 clusters in 2D
d_means = {'cluster 1': [0, 0], 
           'cluster 2': [4, 5], 
           'cluster 3': [5, 0]}
d_covs = {'cluster 1': [[1, 1], 
                        [1, 4]], 
          'cluster 2': [[1, 1], 
                        [1, 3]], 
          'cluster 3': [[4, 2], 
                        [2, 2]]}

Ground Truth Data

In [3]:
# Generate data based on the above parameters
df_data = pd.DataFrame(columns=['x', 'y'])
for i, (cluster, mean) in enumerate(d_means.items()):
    x, y = np.random.multivariate_normal(mean, d_covs[cluster], 1000).T
    df_data = df_data.append(pd.DataFrame({'x':x, 'y': y}))
    plt.plot(x, y, '.', label=cluster, alpha=0.5)
#     plt.axis('equal')
plt.legend()
plt.show()

Observed Data

In [4]:
df_data.head()
Out[4]:
x y
0 0.242205 -0.692402
1 -0.939536 -2.498377
2 1.554767 1.949266
3 0.460970 4.290747
4 1.235782 2.366659
In [5]:
df_data.plot(kind='scatter', x='x', y='y', s=0.5);

K-means clustering

In [6]:
cls = KMeans(init='k-means++', n_clusters=3, n_init=10)
cls.fit(df_data)
Out[6]:
KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,
    n_clusters=3, n_init=10, n_jobs=None, precompute_distances='auto',
    random_state=None, tol=0.0001, verbose=0)
In [7]:
df_data['predicted_label'] = cls.labels_.astype(int)
In [8]:
df_data.head(5)
Out[8]:
x y predicted_label
0 0.242205 -0.692402 0
1 -0.939536 -2.498377 0
2 1.554767 1.949266 0
3 0.460970 4.290747 1
4 1.235782 2.366659 0

Check the predicted label by plot

In [9]:
sns.scatterplot(x="x", y="y", hue="predicted_label", 
                data=df_data, palette='Paired', s=20);
plt.legend(loc='lower right');

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