K-Mean Clustering

 K-means clustering is an unsupervised machine learning algorithm used to partition a dataset into distinct groups, or clusters. The goal is to group similar data points together while maximizing the differences between clusters. Here's how it works:

1.      Initialization: Choose the number of clusters $k$ and randomly initialize $k$ centroids (the center points of the clusters).

2.      Assignment Step: Assign each data point to the nearest centroid, forming $k$ clusters.

3.      Update Step: Recalculate the centroids by taking the mean of all data points in each cluster.

4.      Repeat: Continue the assignment and update steps until the centroids no longer change significantly or a set number of iterations is reached.

K-means is popular due to its simplicity and efficiency, but it has some limitations, such as sensitivity to the initial placement of centroids and difficulty with clusters of varying shapes and sizes.

Step 1: Import Libraries

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

Step 2: Load Your Data

You can load your dataset using Pandas. Make sure your data is numerical and does not contain missing values.

# Example: Load a CSV file
data = pd.read_csv('your_data.csv')
# Display the first few rows
print(data.head())

Step 3: Data Preprocessing

1. Handle Missing Values: Remove or impute missing values.
2. Feature Scaling: Standardize your data for better clustering performance.

# Handle missing values if any
data = data.dropna()  # or use imputation
# Standardize the features
scaler = StandardScaler()
scaled_data = scaler.fit_transform(data)

Step 4: Choose the Number of Clusters (K)

Using the Elbow Method, you can find an optimal value for K.

wcss = []
for i in range(1, 11):
    kmeans = KMeans(n_clusters=i, random_state=42)
    kmeans.fit(scaled_data)
    wcss.append(kmeans.inertia_)
# Plot the results
plt.figure(figsize=(10, 6))
plt.plot(range(1, 11), wcss)
plt.title('Elbow Method')
plt.xlabel('Number of clusters (K)')
plt.ylabel('WCSS')
plt.show()

Step 5: Apply K-means Clustering

Choose a value for K based on the Elbow Method and fit the model.

# Assuming the optimal K is found to be 3
k = 3
kmeans = KMeans(n_clusters=k, random_state=42)
clusters = kmeans.fit_predict(scaled_data)
 
# Add cluster labels to the original data
data['Cluster'] = clusters

Step 6: Visualize the Clusters

For visualization, you might want to reduce dimensions using PCA or simply plot the first two features.

# If you want to visualize the first two dimensions
plt.figure(figsize=(10, 6))
plt.scatter(scaled_data[:, 0], scaled_data[:, 1], c=clusters, cmap='viridis')
plt.title('K-means Clustering')
plt.xlabel('Feature 1')
plt.ylabel('Feature 2')
plt.colorbar(label='Cluster')
plt.show()

Step 7: Analyze Results

Evaluate the clustering results by analyzing the characteristics of each cluster. You can check the mean values of features per cluster or visualize them further.

# Analyze clusters
cluster_analysis = data.groupby('Cluster').mean()
print(cluster_analysis)