Dear Masters,
Suppose I have the following two variables: 
my @X = qw(s1 s2 s3 m1 m2 m3 w1 w2 w3);

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and 
my @sim = (
    # s1    s2    s3    m1    m2    m3    w1    w2     w3
    [1.00, 0.92, 0.56, 0.60, 0.45, 0.33, 0.23, 0.23, 0.33], # s1
    [0.92, 1.00, 0.50, 0.55, 0.40, 0.33, 0.23, 0.27, 0.36], # s2
    [0.56, 0.50, 1.00, 0.60, 0.57, 0.27, 0.20, 0.27, 0.40], # s3
    [0.60, 0.55, 0.60, 1.00, 0.82, 0.20, 0.30, 0.40, 0.50], # m1
    [0.45, 0.41, 0.57, 0.81, 1.00, 0.19, 0.30, 0.40, 0.50], # m2
    [0.33, 0.33, 0.27, 0.20, 0.19, 1.00, 0.25, 0.27, 0.23], # m3
    [0.23, 0.23, 0.20, 0.30, 0.30, 0.25, 1.00, 0.75, 0.60], # w1
    [0.23, 0.27, 0.27, 0.40, 0.40, 0.27, 0.75, 1.00, 0.80], # w2
    [0.33, 0.36, 0.40, 0.50, 0.50, 0.23, 0.60, 0.80, 1.00], # w3
);

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As you can see @sim is a pairwise similarity matrix of elements in X. So for example: 
sim(s1,s1) = 1 
sim(m1,s2) = 0.55

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The problem is how can we find a subset of @X, let's call it C(luster), such that the density and the size of that C is maximized? So the size of C can be varied, and we consider every point of X as a centroid.

By maximizing density and size I mean the member of that C should have high similarity among each other AND the member count should be as big as possible, in comparison to other C's. So the output is just 1 best C.

Can anybody suggest a simple algorithm to achieve that in Perl?

---
neversaint and everlastingly indebted.......

In reply to Finding The Best Cluster Problem by neversaint

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