15.2. K-Means Workflow

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import seaborn as sns
import matplotlib.pyplot as plt
%matplotlib inline

15.2.1. K-means in a nutshell

K-means partitions the data into “k” groups by minimizing the within-cluster sum of squares. It alternates between two steps until convergence:

1. Assign each point to the nearest cluster center.

2. Update each center to be the mean of its assigned points.

This process is fast and simple, but it assumes clusters are roughly spherical and similar in size.

from sklearn.datasets import make_blobs

15.2.2. Create Some Data

make_blobs generates synthetic Gaussian clusters for quick experiments. It returns the feature matrix and the cluster labels used to create the points. Because we generate the data ourselves, we know which group each point came from, so we can check whether k-means recovers those groups. Real data come without these labels; the next section clusters a customer data set.

# Create Data
data = make_blobs(n_samples=200, n_features=2, 
                           centers=4, cluster_std=1.8,random_state=101)

15.2.3. Visualize Data

plt.scatter(data[0][:,0],data[0][:,1],c=data[1],cmap='rainbow')

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15.2.4. Creating the Clusters

from sklearn.cluster import KMeans

K-means starts from randomly placed centers, so different runs can end in different clusters. n_init=10 runs the algorithm 10 times from different starting centers and keeps the best result, and random_state fixes the random starts so that the result is the same every time the page is built.

kmeans = KMeans(n_clusters=4, n_init=10, random_state=101)

kmeans.fit(data[0])

KMeans(n_clusters=4, n_init=10, random_state=101)

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kmeans.cluster_centers_

array([[-9.46941837, -6.56081545],
       [-0.0123077 ,  2.13407664],
       [ 3.71749226,  7.01388735],
       [-4.13591321,  7.95389851]])

kmeans.labels_

array([3, 2, 1, 2, 2, 0, 2, 1, 2, 1, 3, 1, 2, 2, 3, 1, 2, 1, 0, 3, 0, 1,
       1, 0, 3, 0, 0, 1, 2, 2, 3, 0, 2, 1, 1, 3, 0, 0, 0, 1, 0, 3, 3, 3,
       1, 2, 3, 1, 0, 1, 1, 3, 2, 1, 0, 3, 1, 1, 3, 2, 0, 2, 0, 3, 2, 1,
       0, 2, 2, 0, 2, 1, 0, 1, 0, 2, 2, 1, 3, 1, 1, 0, 2, 0, 1, 1, 1, 3,
       1, 0, 0, 0, 0, 1, 1, 0, 2, 3, 0, 2, 1, 0, 1, 1, 2, 1, 0, 2, 0, 0,
       2, 3, 3, 2, 0, 2, 3, 3, 2, 3, 1, 3, 1, 3, 1, 2, 3, 1, 0, 3, 3, 3,
       1, 0, 0, 3, 2, 3, 2, 1, 0, 2, 0, 3, 3, 2, 1, 0, 3, 3, 3, 3, 1, 2,
       1, 3, 2, 2, 2, 1, 2, 1, 1, 3, 0, 3, 1, 2, 3, 1, 2, 1, 3, 2, 1, 3,
       2, 2, 0, 2, 3, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 2, 2, 3, 0, 1, 2, 2,
       0, 1], dtype=int32)

f, (ax1, ax2) = plt.subplots(1, 2, sharey=True,figsize=(10,6))
ax1.set_title('K Means')
ax1.scatter(data[0][:,0],data[0][:,1],c=kmeans.labels_,cmap='rainbow')
ax2.set_title("Original")
ax2.scatter(data[0][:,0],data[0][:,1],c=data[1],cmap='rainbow')

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The two plots mostly agree, except where the original groups overlap. The colors need not match: k-means numbers its clusters in whatever order it finds them, so a group that is cluster 2 in the original labels may be cluster 0 in the k-means result. Cluster numbers are names, not rankings.

15.2.5. Section Practice

Use this short exercise to check the main workflow from this section.

### Exercise: Practice K-Means Workflow
# Run one round of k-means by hand on six customers' monthly spend (one feature).
#   1. Assign each value to the nearer of the two centers (0 or 1).
#   2. Update each center to the mean of the values assigned to it.
# Print exactly:
# Assignments: [0, 0, 0, 1, 1, 1]
# New centers: [22.0, 71.0]
spend = [12, 20, 34, 58, 70, 85]
centers = [20, 60]
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### Your code ends here

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### Solution
spend = [12, 20, 34, 58, 70, 85]
centers = [20, 60]

assignments = []
for value in spend:
    if abs(value - centers[0]) <= abs(value - centers[1]):
        assignments.append(0)
    else:
        assignments.append(1)

new_centers = []
for cluster in [0, 1]:
    members = [v for v, a in zip(spend, assignments) if a == cluster]
    new_centers.append(sum(members) / len(members))

print('Assignments:', assignments)
print('New centers:', new_centers)

Assignments: [0, 0, 0, 1, 1, 1]
New centers: [22.0, 71.0]