Explain why this method will not only speed up the convergence of the k-means algorithm, but also guarantee the quality of the final clustering results 9.1

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
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For the k-means algorithm, it is interesting to
note that by choosing the initial cluster centers
carefully,
we may be able to not only speed up the
convergence of the algorithm, but also
guarantee the quality
of the final clustering. The k-means++
algorithm is a variant of k-means, which
chooses the initial
centers as follows. First, it selects one center
uniformly at random from the objects in the data
set.
Iteratively, for each object p other than the
chosen center, it chooses an object as the new
center. This
object is chosen at random with probability
proportional to dist(p)2, where dist(p)) is the
distance
from p) to the closest center that has already
been chosen. The iteration continues until k
centers are
selected.
Explain why this method will not only speed up
the convergence of the k-means algorithm, but
also
guarantee the quality of the final clustering
results
jo 9:15
Transcribed Image Text:For the k-means algorithm, it is interesting to note that by choosing the initial cluster centers carefully, we may be able to not only speed up the convergence of the algorithm, but also guarantee the quality of the final clustering. The k-means++ algorithm is a variant of k-means, which chooses the initial centers as follows. First, it selects one center uniformly at random from the objects in the data set. Iteratively, for each object p other than the chosen center, it chooses an object as the new center. This object is chosen at random with probability proportional to dist(p)2, where dist(p)) is the distance from p) to the closest center that has already been chosen. The iteration continues until k centers are selected. Explain why this method will not only speed up the convergence of the k-means algorithm, but also guarantee the quality of the final clustering results jo 9:15
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