A 'cluster' is a rectangular subset of @sim?

The density of the cluster is the average of the values in the cluster?

Which would make the problem: Find __some__ subset with the largest average value; and if two subsets have the same average, favour the largest subset?

Say C1 has average 0.8 but only 1 member (excluding centroid) , and C2 has average 0.7 with 5 members, we would weight C2 as better than C1.

The problem is, you aren't specifying how you are scoring that.

1. If you go for the highest average (as I was) then 0.8*1/1 > 0.7 *5/5.
2. If you go for the highest score, which makes 3.5 beat 0.8, then you will never remove anything from the set because it would reduce the (total) score.

Put another way:

• Allowing irregular subsets, the 'cluster' of 9 1.0s that form the major diagonal gives you an average of 1.0 and a size of 9. This can never be beaten, (scoring the average) as adding any lesser value than 1.0 value will decrease the average.
• But if you use the total, you'll never remove anything from the set as any removal will reduce that total.

Unless you introduce some other metric or heuristic, you don't have a scoring mechanism that reflects your stated goals?

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In the absence of evidence, opinion is indistinguishable from prejudice.

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the 'cluster' of 9 1.0s that form the major diagonal gives you an average of 1.0

As mentioned earlier, the self-edges don't count.

A word spoken in Mind will reach its own level, in the objective world, by its own weight

You beat me to it, but my reading of the requirement (inevitably) produces 9 equal subsets with an size of 1 and an average of 1. D'oh!

However, I'm now confused by how you can have a centroid of an irregularly shaped set, given discrete values?

Actually, I think I'm completely lost by your meaning now. Could you give an example of two subsets, their relative densities, and how you calculated them?

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Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.

"Too many [] have been sedated by an oppressive environment of political correctness and risk aversion."

Dear BrowserUK,


Could you give an example of two subsets, their relative densities, and how you calculated them?

Let's say we have two cluster C1 and C2

C1 = (s2,s3,m3,w3), with centroid(z) = s2

sim(s2,s3)=0.5
sim(s2,m3)=0.3
sim(s2,w3)=0.36
----------------+
   Total = 0.96
   |C1| = 4
Density = Total/|C1| = 0.96/4 = 0.24

we skip including this: sim(s2,s2)=1
We never compare a centroid with itself.
[download]

And C2

C2 = (s3,m1,w3), with centroid(z) = w3

sim(w3,s3)=0.4
sim(w3,m1)=0.5
----------------+
   Total = 0.9
   |C2| = 3
Density = Total/|C2| = 0.9/3= 0.3
[download]




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