import matplotlib.pyplot as plt import numpy as np from sklearn.cluster import KMeans from sklearn.preprocessing import StandardScaler

1. Parameters

n_samples = 300 cluster_std = 0.15

1. Generate data

np.random.seed(0) cluster_centers_scales = (([-1, -1], 0.2), ([1, -1], 0.5), ([1.5, 1], 0.2), ([-0.5, 1], 0.5)) data = np.concatenate([

   np.random.normal(loc=center, scale=scale, size=(n_samples, 2))
   for center, scale in cluster_centers_scales

])

1. KMeans clustering

kmeans = KMeans(n_clusters=4, random_state=0)

1. Stretch along y-axis

data_stretched = data * np.array([1, 0.02])

1. KMeans on stretched data

labels_stretched = kmeans.fit_predict(data_stretched)

1. Z-score normalize data

scaler = StandardScaler() data_normalized = scaler.fit_transform(data_stretched)

1. KMeans on Z-score normalized data

labels_normalized = kmeans.fit_predict(data_normalized)

1. Plot both results as subplots within the same figure

plt.figure(figsize=(10, 5))

plt.subplot(1, 2, 1) plt.scatter(data_stretched[:, 0], data_stretched[:, 1], c=labels_stretched, marker='+') plt.title('Stretched Data')

plt.subplot(1, 2, 2) plt.scatter(data_normalized[:, 0], data_normalized[:, 1], c=labels_normalized, marker='+') plt.title('Z-score Normalized Data')

plt.savefig('z_score_normalization.svg') plt.show()