Before revision: 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.
After revision: 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 n / \log\log Var X ), which we show to be tight.