Question

Ok, let’s suppose we have members table. There is a field called, let’s say, about_member. There will be a string like this 1-1-2-1-2 for everybody. Let’s suppose member_1 has this string 1-1-2-2-1 and he searches who has the similar string or as much similar as possible. For example if member_2 has string 1-1-2-2-1 it will be 100% match, but if member_3 has string like this 2-1-1-2-1 it will be 60% match. And it has to be ordered by match percent. What is the most optimal way to do it with MYSQL and PHP? It’s really hard to explain what I mean, but maybe you got it, if not, ask me. Thanks.

Edit: Please give me ideas without Levenshtein method. That answer will get bounty. Thanks. (bounty will be announced when I will be able to do that)

Answer 1

Jawa posted this idea originally; here is my attempt.

^ is the XOR function. It compares 2 binary numbers bit-by-bit and returns 0 if both bits are the same, and 1 otherwise.

    0 1 0 0 0 1 0 1 0 1 1 1  (number 1)
 ^  0 1 1 1 0 1 0 1 1 0 1 1  (number 2)
 =  0 0 1 1 0 0 0 0 1 1 0 0  (result)

How this applies to your problem:

  // In binary...
  1111 ^ 0111 = 1000 // (1 bit out of 4 didn't match: 75% match)
  1111 ^ 0000 = 1111 // (4 bits out of 4 didn't match: 0% match)

  // The same examples, except now in decimal...
    15 ^    7 = 8  (1000 in binary) // (1 bit out of 4 didn't match: 75% match)
    15 ^    0 = 15 (1111 in binary) // (4 bits out of 4 didn't match: 0% match)

How we can count these bits in MySQL:

BIT_COUNT(b'0111') = 3 // Bit count of binary '0111'
BIT_COUNT(7) = 3       // Bit count of decimal 7 (= 0111 in binary)
BIT_COUNT(b'1111' ^ b'0111') = 1 // (1 bit out of 4 didn't match: 75% match)

So to get the similarity…

// First we focus on calculating mismatch.
(BIT_COUNT(b'1111' ^ b'0111') / YOUR_TOTAL_BITS) = 0.25 (25% mismatch)
(BIT_COUNT(b'1111' ^ b'1111') / YOUR_TOTAL_BITS) = 0 (0% mismatch; 100% match)

// Now, getting the proportion of matched bits is easy
1 - (BIT_COUNT(b'1111' ^ b'0111') / YOUR_TOTAL_BITS) = 0.75 (75% match)
1 - (BIT_COUNT(b'1111' ^ b'1111') / YOUR_TOTAL_BITS) = 1.00 (100% match)

If we could just make your about_member field store data as bits (and be represented by an integer), we could do all of this easily! Instead of 1-2-1-1-1, use 0-1-0-0-0, but without the dashes.

Here’s how PHP can help us:

bindec('01000') == 8;
bindec('00001') == 1;
decbin(8) == '01000';
decbin(1) == '00001';

And finally, here’s the implementation:

// Setting a member's about_member property...
$about_member = '01100101';
$about_member_int = bindec($about_member);
$query = "INSERT INTO members (name,about_member) VALUES ($name,$about_member_int)";

// Getting matches...
$total_bits = 8; // The maximum length the member_about field can be (8 in this example)
$my_member_about = '00101100';
$my_member_about_int = bindec($my_member_about_int);
$query = "
    SELECT 
        *,
        (1 - (BIT_COUNT(member_about ^ $my_member_about_int) / $total_bits)) match 
    FROM members
    ORDER BY match DESC
    LIMIT 10";

This last query will have selected the 10 members most similar to me!

Now, to recap, in layman’s terms,

We use binary because it makes things easier; the binary number is like a long line of light switches. We want to save our “light switch configuration” as well as find members that have the most similar configurations.

The ^ operator, given 2 light switch configurations, does a comparison for us. The result is again a series of switches; a switch will be ON if the 2 original switches were in different positions, and OFF if they were in the same position.

BIT_COUNT tells us how many switches are ON–giving us a count of how many switches were different. YOUR_TOTAL_BITS is the total number of switches.

But binary numbers are still just numbers… and so a string of 1’s and 0’s really just represents a number like 133 or 94. But it’s a lot harder to visualize our “light switch configuration” if we use decimal numbers. That’s where PHP’s decbin and bindec come in.

Learn more about the binary numeral system.

Hope this helps!