import pandas as pd
from sklearn.cluster import KMeans
import matplotlib.pyplot as plt
from sklearn.preprocessing import StandardScaler
# Sample data
data = {
 'Feature1': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
 'Feature2': [5, 8, 12, 15, 18, 24, 28, 30, 34, 40]
}
df = pd.DataFrame(data)
# Standardize the features
scaler = StandardScaler()
X = scaler.fit_transform(df)
# Elbow method for finding optimal k
inertia = []
K = range(1, 11)
for k in K:
 kmeans = KMeans(n_clusters=k, random_state=42)
 kmeans.fit(X)
 inertia.append(kmeans.inertia_)
plt.plot(K, inertia, 'bo-')
plt.xlabel('Number of clusters, k')
plt.ylabel('Inertia')
plt.title('Elbow Method For Optimal k')
plt.show()
# Apply K-Means with the chosen number of clusters (e.g., 3)
kmeans = KMeans(n_clusters=3, random_state=42)
df['Cluster'] = kmeans.fit_predict(X)
# Visualize the clusters
plt.scatter(X[:, 0], X[:, 1], c=df['Cluster'], cmap='viridis', marker='o', edgecolor='k',
s=100)
plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], s=200, c='red',
marker='X') # Cluster centers
plt.xlabel('Feature1')
plt.ylabel('Feature2')
plt.title('K-Means Clustering')
plt.show()