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What are 3 clusters and their centers after one iteration? Show the detailed steps, same as  questions b and c.

What are 3 clusters and their centers after one iteration? Show the detailed steps, same as  questions b and c.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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  1. What are 3 clusters and their centers after one iteration? Show the detailed steps, same as  questions b and c.
  2. What are 3 clusters and their centers after two iterations?
  3. What are 3 clusters and their centers when the clustering converges?
  4. .How many iterations are required for the clusters to converge?
All data in X were plotted in Figure 1. The center of 3 clusters were initialized as ₁ = (6.2, 3.2) (red), C₂ = (6.6, 3.7) (green), 3 = (6.5,3.) (blue). X = [5.9 3.2 4.6 2.9 6.2 2.8 4.7 3.2 5.5 4.2 5.0 3.0 4.9 3.1 6.7 3.1 5.1 3.8 6.0 3.0
Transcribed Image Text:All data in X were plotted in Figure 1. The center of 3 clusters were initialized as ₁ = (6.2, 3.2) (red), C₂ = (6.6, 3.7) (green), 3 = (6.5,3.) (blue). X = [5.9 3.2 4.6 2.9 6.2 2.8 4.7 3.2 5.5 4.2 5.0 3.0 4.9 3.1 6.7 3.1 5.1 3.8 6.0 3.0
1. 4.4 4.2 4+ 3.8 3.6 3.4 3.2 3- 2.8 2.6 Implement K-means manually 4.5 A 44.7.322 (4.6, 2.9) (5.1, 3.8) (4.9.3.1) (5.0, 3.0) 5 45.5, 4.2) d = 5.5 n A (5.9, 3.2) (6.2, 3.2) i=1 A (6.0, 3.0) 6 (6.2, 2.8) (Pi 9₁)² Figure 1: Scatter plot of datasets and the initialized centers of 3 clusters Given the input matrix X whose rows represent different data points, please perform a k-means clustering on this dataset using the Euclidean distance as the distance function. Here is chosen as 3. The Euclidean distance d between input vector p E R" and q E R" is defined as (6.6, 3.7) 1 6.5 (6.7, 3.1) (6.5, 3.0)
Transcribed Image Text:1. 4.4 4.2 4+ 3.8 3.6 3.4 3.2 3- 2.8 2.6 Implement K-means manually 4.5 A 44.7.322 (4.6, 2.9) (5.1, 3.8) (4.9.3.1) (5.0, 3.0) 5 45.5, 4.2) d = 5.5 n A (5.9, 3.2) (6.2, 3.2) i=1 A (6.0, 3.0) 6 (6.2, 2.8) (Pi 9₁)² Figure 1: Scatter plot of datasets and the initialized centers of 3 clusters Given the input matrix X whose rows represent different data points, please perform a k-means clustering on this dataset using the Euclidean distance as the distance function. Here is chosen as 3. The Euclidean distance d between input vector p E R" and q E R" is defined as (6.6, 3.7) 1 6.5 (6.7, 3.1) (6.5, 3.0)
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