I'm going to guess that this is a straight transfer of a C program to Perl --

First, you'd using a whole lot of for loops for tracking indexes to arrays:

In Perl, if you're just trying to iterate over a range, you can use the 'foreach' style loop, with the range operator:

Even if we were doing this in C, for the type of loops you're dealing with (starting at 0, order of operations doesn't matter), I'd still change the code, to reduce the number of comparisons against non-0 values:

In some cases, we can use the 'foreach' style loops to eliminate the need for index values, but because you're using them to index multiple arrays within the loop, that's not possible in your case.

...

Another change I might make is in how you deal with undefined values -- if the value must be defined, and can't be 0, (eg, $number_of_clusters), you can use the '||=' operator:

...

The only other thing is in how it's called -- if it were OO, you could inherit from it, and then replace the 'distance' function (or you could have it accept a coderef in for the distance function, if you didn't want to support inheritance), as some people prefer the manhatten distance when they're dealing with clusters:

sub distance {
  my ($vec1,$vec2) = @_;
  my $distance = 0;
  for my $i ( 0 .. (scalar @$vec1)-1 ) {
    $difference += abs( $vec1->[$i] - $vec2->[$i] );
  }
  return $difference;
}
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