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I'm trying to make sense of some mathematical notation I'm seeing in a common clustering algorithm I've been reading about. The algorithm is laid out here (as an image). I'm a bit confused about line 10, specifically, which reads:

$$k_1 \leftarrow \operatorname{argmax}_{\{k\,:\,I[k]=1\}} P[k].\mathrm{Max}().\mathrm{sim}$$

I'm having difficulty making sense of the notation. What I understand here is that we're assigning a value to $k_1$. Then we have an $\operatorname{argmax}$ function, and the set builder notation (in subscript) $\{k:I[k]=1\}$, meaning a set containing all $k$ where $I[k]=1$. But I don't understand how the set builder notation relates to the expression which follows it, where we take the max value in $P[k]$. How is the argmax and set-builder notation related to the $P[k].\operatorname{Max}()$ expression? There's no operator (is it multiplication?) so I don't know how to read what's going on here.

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  • $\begingroup$ What is the _.sim member at the end? $\endgroup$ Aug 28, 2016 at 21:59
  • $\begingroup$ It is a similarity value - (a distance between two points) - basically the maximum value in $P[k]$ $\endgroup$
    – Siler
    Aug 28, 2016 at 22:00
  • $\begingroup$ Do you know what argmax means without set builder notation? The meaning isn't different here. $\endgroup$
    – Mark S.
    Aug 28, 2016 at 22:43

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The line says "assign to $k_1$ a $k$ that satisfies both: $I[k]=1$ and maximizes $P[k].\max.\operatorname{sim}$".

(Without some parenthesis it is hard to say wether $.\operatorname{sim}$ is being applied to the argmax result or to the result of $\max$)

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