We present a truly simple analysis of k-means|| (Bahmani et al., PVLDB 2012) -- a distributed variant of the k-means++ algorithm (Arthur and Vassilvitskii, SODA 2007) -- and improve it from O(\log Var X) , whereVar X is the variance of the input data set, to O(\log Var X / \log\log Var X ), which we show to be tight.
We present a simple analysis of k-means|| (Bahmani et al., PVLDB 2012) -- a distributed variant of the k-means++ algorithm (Arthur and Vassilvitskii, SODA 2007) . Moreover, the bound on the number of rounds is improved from O(\log n) to O(\log n / \log\log n ), which we show to be tight.
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