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Is there an online learning algorithm for clustering that doesn't require storing historical data?

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Yes. It's even a historic algorithm, too.

Look up online computation of the mean.

MacQueen used this 1967 for online clustering. See page 283.

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  • $\begingroup$ Could you explain how that could be exploited to perform "clustering" (and what kind of clustering it would be)? $\endgroup$ – whuber Nov 11 '15 at 21:42
  • $\begingroup$ See MacQueen, 1967. $\endgroup$ – Has QUIT--Anony-Mousse Nov 11 '15 at 22:11
  • $\begingroup$ The paper in question is avaialble here. (You should have said it is a paper, reading the comment seems like you refer to a book.) $\endgroup$ – usεr11852 Nov 11 '15 at 23:00

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