Rating normalization algorithm

Question

I have a rating system where users can vote between 1-6. I'd like to normalize the votes a bit to better accommodate for extreme voting, where individuals tend to vote as high or as low as possible. To do this, I have the following algorithm which seems to work well. However, it's extremely inefficient and not very well written.

What might I do to improve it?

protected function calculateWeightedAverage($ratings)
{
    $values = array_values($ratings);
    sort($values);

    $count = count($values);
    $weights = array_fill(0, $count, 1);

    $out = (int) ($count / 3);
    $out2 = pow($out + 1, 2);

    $max = $count - 1;
    $min = 0;

    for ($i = 0; $i < $out; $i++) {
        $j = $i + 1;
        $weights[$min + $i] = $j * $j / $out2;
        $weights[$max - $i] = $j * $j / $out2;
    }

    $sum = array_sum($weights);

    for ($i = 0; $i < $count; $i++) {
        $weights[$i] /= $sum;
    }

    $rating = 0;
    for ($i = 0; $i < $count; $i++) {
        $rating += $values[$i] * $weights[$i];
    }

    return $rating;
}

Answer 1

Your code is really good and I can't see any significant way to improve it. One minor improvement is to reduce the number of loops from 3 to 2:

protected function calculateWeightedAverage($ratings)
{
  $sum = 0;
  $rating = 0;

  $values = array_values($ratings);
  sort($values);

  $count = count($values);
  $out = (int) ($count / 3);
  $out2 = pow($out + 1, 2);

  for ($i=0; $i<$count; $i++) {
    if ($i < $out) {
      $weights[$i] = pow(($i+1),2)/$out2;
    } elseif ($i > $count-$out-1) {
      $weights[$i] = pow($count-$i,2)/$out2;
    } else {
      $weights[$i] = 1;
    }
    $sum += $weights[$i];
  }

  for ($i = 0; $i < $count; $i++) {
    $rating += $values[$i] * $weights[$i]/$sum;
  }

  return $rating;
}

Answer 2

protected function calculateWeightedAverage($ratings)
{
    $values = array_values($ratings);
    sort($values);

    $count = count($values);

    $out = (int) ($count / 3);
    $out2 = pow($out + 1, 2);

    $max = $count - 1;
    $min = 0;

    $weights = array_fill(0, $count, 1);
    for ($i = 0; $i < $out; $i++) {
        $j = $i + 1;
        $weights[$min + $i] = $j * $j / $out2;
        $weights[$max - $i] = $j * $j / $out2;
    }

Try removing the $min +. It is nice for the reader but may be slower for the computer to execute.

    $sum = array_sum($weights);

    for ($i = 0; $i < $count; $i++) {
        $weights[$i] /= $sum;
    }

This loop is unnecessary since you can simply return $rating / $sum.

    $rating = 0;
    for ($i = 0; $i < $count; $i++) {
        $rating += $values[$i] * $weights[$i];
    }

Since you are looping over the arrays anyway, you could also compute the $sum in this loop. Measure it which one is faster or more readable.

    return $rating;
}

Since this algorithm is pretty straight-forward and not really slow, maybe the slow part is the part where you get your $ratings from. When they come from a database, I would worry more about that part.

I don't know how well PHP optimizes the code. If it doesn't, it may even help to extract the $j * $j / $out2 (which you use twice) into a temporary variable.

As with all performance-related topics: measure, and make sure you measure the realistic and relevant things.

Answer 3

It's pretty hard to understand what this code does. There's a lot going on and the code doesn't communicate well what it's doing. Like the variable names $out and $out2 look completely arbitrary.

My main suggestion is to split this function into two:

• one where you calculate the weights, and
• another where you calculate the average using these weights.

This way it would become clear that the creation of $weights array only depends on the count of values, not on the values themselves.

Additionally the function only uses $ratings assoc-array to extract values from it - therefore I would recommend only passing in the values in the first place (it shouldn't be the job of the averaging function to extract the values to be worked on).