Lecture 52:-   K-Means Algo 1

Here's an explanation of the K-Means algorithm along with a basic Python code example using the scikit-learn library:

K-Means Algorithm:

K-Means is an unsupervised machine learning algorithm used for clustering data into groups or clusters based on their similarity. The algorithm aims to partition the data into K clusters, where each data point belongs to the cluster with the nearest mean (centroid). The centroids are updated iteratively until convergence.

Here's how the K-Means algorithm works:

1. Initialization: Choose the number of clusters K and initialize K centroids randomly (usually by selecting K data points from the dataset).

2. Assignment Step: Assign each data point to the nearest centroid based on a distance metric (usually Euclidean distance).

3. Update Step: Recalculate the centroids of each cluster based on the mean of the data points assigned to that cluster.

4. Repeat: Iterate steps 2 and 3 until convergence (when the centroids no longer change significantly) or until a maximum number of iterations is reached.

5. Final Clustering: Once the algorithm converges, the data points are assigned to their final clusters based on the centroids.

K-Means Code Example:

Here's a simple Python code example using the scikit-learn library to perform K-Means clustering on a synthetic dataset:

pythonCopy code

import numpy as np from sklearn.datasets import make_blobs from sklearn.cluster import KMeans import matplotlib.pyplot as plt # Generate synthetic data data, _ = make_blobs(n_samples=300, centers=4, random_state=42) # Create K-Means model k = 4 # Number of clusters model = KMeans(n_clusters=k, random_state=42) # Fit the model to the data model.fit(data) # Get cluster assignments and centroids cluster_assignments = model.labels_ centroids = model.cluster_centers_ # Plot the data and centroids plt.scatter(data[:, 0], data[:, 1], c=cluster_assignments, cmap='rainbow') plt.scatter(centroids[:, 0], centroids[:, 1], marker='X', s=200, c='black') plt.xlabel('Feature 1') plt.ylabel('Feature 2') plt.title('K-Means Clustering') plt.show()

This code snippet demonstrates the following steps:

1. Generate a synthetic dataset using make_blobs.
2. Create a K-Means model with the desired number of clusters.
3. Fit the model to the data.
4. Retrieve cluster assignments and centroids.
5. Plot the data points colored by cluster assignments and show the centroids.

This is a basic example, and in practice, you might need to preprocess your data and use techniques like elbow method or silhouette score to determine the optimal number of clusters (K).