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;
}

• Ozan Kurt: Please provide how you store $ratings and give us something concrete.
• user1960364: Well, $ratings comes in as an array [userid => vote, ... ] but we're using array_values() so $values is just an array of integers 1-6.
• Ozan Kurt: Okay now it makes sense. I will have a look asap.
• user1149: Although I realize we should be able to divine it from your code, any chance you could give us a brief description of what the function is doing?
• user1960364: It sorts them and then applies a weight to the upper third (count / 3) and lower third items in the array, giving majority weight to values in the middle. For instance, if the votes were [1, 4, 7], the weight of the 1 and 7 would be decreased before calculating the average. If it were [2, 2, 3, 4, 4, 7] the weights of the 2, 2, second 4, and 7 would be lowered.

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).