Another thing to look into is Devel::SmallProf which shows you how many times a line is run and how long your program spends running it, to help you find slowdowns.

You may also find a speedup if you can manage to create $Measure->new($wn) only once instead of at each call, but I'm not sure if the module will allow that, not being familiar with it.

Have a look at Profiling your code. Profiling will tell you what parts of your program use the most time, and you can focus your efforts there. If you find the results of profiling confusing, we can help with that.

You may be solving the wrong problem altogether. If your word list is very large (as I suspect it is), you'll be calculating a huge set of values. For many problems, you won't need the entire matrix. It may be better to compute them as needed and store them in the array when computed. That way, you compute only the ones you want, and once only. Something like:

sub get_similarity {
    my $i = shift;
    my $j = shift;

    # Matrix is symmetric around x==y
    ($i,$j) = ($j,$i) if $i > $j;

    return $sim[$i][$j] if defined $sim[$i][$j];

    $sim[$i][$j] = similarity($words[$i], $words[$j]);
}
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Extra credit if you:

• Use a hash instead of an array.
• Tie your array or hash to a dbm file so you keep your values between runs...

my $obj = $Measure->new($wn);
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Check your word list. Does it contain duplicated lines (you should never have to use Memoize)? Try this to spot errors:

sub similarity {
   my ( $w1, $w2 ) = @_;
   warn "'$w1' vs '$w2'";
   return $obj->getRelatedness($w1, $w2);
}
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thanks good advice for moving $obj from the loop.