K-means is an iterative algorithm that initializes the cluster centers randomly. Is Kmeans algorithm guaranteed to converge regardless of how the cluster centers are initialized? Why?
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molbdnilo
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bharath chandra
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4https://stats.stackexchange.com/questions/188087/proof-of-convergence-of-k-means – Igor Belkov May 07 '20 at 05:40
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Yes. It converges but not coverage to the same result and not coverage with the same speed. It proves mathematically that the iterated running of finding the centers in k-means is converges. The reason is that:
In every iteration of k-means, the sum-of-distances to the center is reduced. This is because of how the center is selected (center of cluster is the the mean of each cluster nodes) in each iteration. In this way, as the sum of distances is reduced in each iteration,(because you assign each node to the nearest center) the algorithm converge. as I said before, this convergence has a mathematical proof. K-means is a kind of Expectation-Maximization(EM) algorithm and every EM algorithm converges. (You can see this proof and if you are interested in I can explain it more using Mathematical formulas.)
Arefeh Yavary
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