Solution :

K-Means Clustering:

K-Means is a popular unsupervised machine learning algorithm used for partitioning a dataset into K clusters based on the similarity of their features. It works by minimizing the variance within each cluster and is widely used in applications such as market segmentation, image compression, and pattern recognition.

K means clustering, assigns data points to one of the K clusters depending on their distance from the center of the clusters. It starts by randomly assigning the clusters centroid in the space. Then each data point assign to one of the cluster based on its distance from centroid of the cluster. After assigning each point to one of the cluster, new cluster centroids are assigned. This process runs iteratively until it finds good cluster. In the analysis we assume that number of cluster is given in advanced and we have to put points in one of the group.

ALGORITHM:

1. Initialization:
   • Choose the number of clusters (k) to divide the data into.
   • Initialize the centroids (cluster centers) randomly or using specific techniques.
2. Assignment:
   • Assign each data point to the nearest centroid based on the distance (e.g., Euclidean distance).
   • Each data point is labeled as belonging to one of the k clusters.
3. Update:
   • Recalculate the centroids of the clusters by averaging the coordinates of all data points assigned to each cluster.
4. Repeat:
   • Repeat the Assignment and Update steps iteratively until the centroids stabilize (i.e., no significant changes in their positions) or a predefined number of iterations is reached.

Steps for Program:

1. Import Necessary Libraries:
   • numpy: For numerical computations.
   • matplotlib.pyplot: For visualizing the data points and clustering results.
   • KMeans from sklearn.cluster: To implement the K-Means algorithm.
   • make_blobs from sklearn.datasets: To generate synthetic data for clustering.
2. Generate Synthetic Data:
   • The make_blobs function generates 300 data points with 4 clusters. The points are distributed with a standard deviation of 0.60 around the cluster centers.
   • The dataset consists of:
     Features (X): A 2D array representing the data points' coordinates.
3. Visualize Raw Data:
   • A scatter plot is created to visualize the data points before clustering.
4. Apply K-Means Algorithm:
   • The K-Means model is initialized with n_clusters=4 to specify 4 clusters.
   • The model is fit to the data using the fit method.
5. Retrieve Cluster Information:
   • Cluster Centers: The coordinates of the centroids for each cluster are stored in kmeans.cluster_centers_.
   • Cluster Labels: Each data point is assigned a cluster label using kmeans.labels_.
6. Visualize Clustered Data:
   • A scatter plot shows the data points grouped into clusters, with colors representing different clusters.
   • Cluster centroids are displayed as red points to highlight their locations.

Library Installation:

To install required libraries, Open Command Prompt or Terminal and execute the following commands

$ pip install scikit-learn

$ pip install numpy

$ pip install matplotlib

Source Code:

File Name: kmeans.py

#Necessary Libraries
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.datasets import make_blobs

#Generate Data
X, _ = make_blobs(n_samples = 300, centers = 4 , cluster_std = 0.60,random_state = 0)

#Plot the data points
plt.scatter(X[:,0],X[:,1])
plt.title("Data Points")
plt.show()

#KMeans clustering
kmeans = KMeans(n_clusters = 4)
kmeans.fit(X)

#Getting the cluster centers and labels
centers = kmeans.cluster_centers_ #returns the coordinates of the

#cluster center found by the algorithm
labels = kmeans.labels_ #Returns the labels for each data point , indicating which cluster it has

#been assigned to.
#Plot the clustered data
plt.scatter(X[:,0],X[:,1],c = labels)
plt.scatter(centers[:,0],centers[:,1],alpha = 0.75,s=200,color = 'red')
plt.title("Clustered Data")
plt.show()

Output:

Sample Run:
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$ python3 kmeans.py