The document describes the k-means clustering algorithm, detailing the process of computing centroids, assigning clusters based on Euclidean distances, and achieving convergence with final clusters {1,2} and {3,4,5,6,7}. It highlights the algorithm's efficiency with a time complexity of O(tkn) and its applications in machine learning, data mining, speech understanding, image segmentation, and color palette selection. Overall, k-means is regarded as a simple yet powerful tool for various fields, including artificial intelligence and pattern recognition.

14. Now using the new centroids
we compute the new centroids,
we compute the Euclidean
distance of each object.
Step 3
Based on the lowest distance to the centroids the new
clusters are {1,2} and {3, 4, 5, 6, 7}
New centroids are again calculated
m1= (1.25, 1.5)
m2= (3.90, 5.1)

15. Previous step is repeated and
we can see that there is no
change in clusters.
The clusters are {1,2} and
{3,4,5,6,7}
Thus the algorithm has come to a convergence and the final
result consists of two clusters. {1, 2} and {3,4,5,6,7}

18. • It is relatively efficient and fast. It computes result at
O(tkn), where n is number of objects or points, k is
number of clusters and t is number of iterations.
• k-means clustering can be applied to machine
learning or data mining
• Used on acoustic data in speech understanding to
convert waveforms into one of k categories (known
as Vector Quantization)
• It can be used in Image Segmentation.
• Also used for choosing color palettes on old
fashioned graphical display devices and Image
Quantization.
Applications of K-Mean Clustering

19. CONCLUSION
• K-means algorithm is useful for undirected
knowledge discovery and is relatively simple.
• K-means has found wide spread usage in lot of
fields, ranging from unsupervised learning of
neural network, Pattern recognitions,
Classification analysis, Artificial intelligence,
image processing, machine vision, and many
others.