Consider k-means with Euclidean distance function. = {(-6,-2), (-5,2), (-4, –2)} U {(4,2), (5, –2), (6, 2)} and k = 2 give the optimal cluster centers that minimize the SSE. Next, choose initialization values for the two cluster centers such that k-means never converges to the optimal clustering. 1. Given the two-dimensional dataset S =
Consider k-means with Euclidean distance function. = {(-6,-2), (-5,2), (-4, –2)} U {(4,2), (5, –2), (6, 2)} and k = 2 give the optimal cluster centers that minimize the SSE. Next, choose initialization values for the two cluster centers such that k-means never converges to the optimal clustering. 1. Given the two-dimensional dataset S =
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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![Consider k-means with Euclidean distance function.
{(-6, –2), (-5, 2), (-4, –2)} U {(4, 2), (5, –2), (6, 2)}
1. Given the two-dimensional dataset S =
and k = 2 give the optimal cluster centers that minimize the SSE. Next, choose initialization
values for the two cluster centers such that k-means never converges to the optimal clustering.
2. Proof that there always exists an initialization for which k-means converges to the global op-
timum. Use the fact that an iteration of k-means can never increase the SSE (sum of squared
errors, i.e. distances between the cluster center and associated elements).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2aced0b0-9e84-4add-8f13-67e7b6c5c9ae%2F5d446a0f-2337-4dc8-ba29-b51fd8896a73%2F3wck027_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider k-means with Euclidean distance function.
{(-6, –2), (-5, 2), (-4, –2)} U {(4, 2), (5, –2), (6, 2)}
1. Given the two-dimensional dataset S =
and k = 2 give the optimal cluster centers that minimize the SSE. Next, choose initialization
values for the two cluster centers such that k-means never converges to the optimal clustering.
2. Proof that there always exists an initialization for which k-means converges to the global op-
timum. Use the fact that an iteration of k-means can never increase the SSE (sum of squared
errors, i.e. distances between the cluster center and associated elements).
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