Calculating the relevance of a User based on Specific data

Question

I am currently in the process of trying to form an algorithm that will calculate the relevance of a user to another user based on certain bits of data.

Unfortunately, my Maths skills have deteriorated since leaving school almost a decade ago, and as such, I am very much struggling with this. I have found an algorithm online that pushes 'hot' posts to the top of a newsfeed and figure this is a good place to start. This is the algorithm/calculation I found online (in MySQL):

LOG10(ABS(activity) + 1) * SIGN(activity) + (UNIX_TIMESTAMP(created_at) / 300000)

What I am hoping to do is adapt the above concept to work with the data and models I have in my own application. Consider this user object (trimmed down):

{
    "id": 1
    "first_name": "Joe",
    "last_name": "Bloggs",
    "counts": {
        "connections": 21,
        "mutual_connections": 16
    },
    "mutual_objects": [
        {
            "created_at": "2017-03-26 13:30:47"
        },
        {
            "created_at": "2017-03-26 14:25:32"
        }
    ],
    "last_seen": "2017-03-26 14:25:32",
}

There are three bits of relevant information above that need to be considered in the algorithm:

• mutual_connections
• mutual_objects but taking into account that older objects should not drive up the relevance as much as newer objects, hence the created_at field.
• last_seen

Can anyone suggest a fairly simple (if that's possible) way of doing this?

This was my idea, but in all honesty, I have no idea what it is doing so I cannot be sure if it is a good solution and I have also missed out last_seen as I could not find a way to add this:

$mutual_date_sum = 0;

foreach ($user->mutual_objects as $mutual_object) {
    $mutual_date_sum =+ strtotime($mutual_object->created_at);
}

$mutual_date_thing = $mutual_date_sum / (300000 * count($user->mutual_objects));

$relevance = log10($user->counts->mutual_connections + 1) + $mutual_date_thing;

Just to be clear, I am not looking to implement some sort of government level AI, 50,000 line algorithm from a mathematical genius. I am merely looking for a relatively simple solution that will do the trick for the moment.

UPDATE

I have had a little play and have managed to build the following test. It seems the mutual_objects very much carries the weight in this particular algorithm as I would expect to see users 4 and 5 higher up the results list given their large number of mutual_connections.

I don't know if this makes it easier to amend/play with, but this is probably the best I can do. Please help if you have any suggestions :-)

$users = [
    [
        'id' => 1,
        'mutual_connections' => 15,
        'mutual_objects' => [
            [
                'created_at' => '2017-03-26 14:25:32'
            ],
            [
                'created_at' => '2017-03-26 14:25:32'
            ],
            [
                'created_at' => '2017-02-26 14:25:32'
            ],
            [
                'created_at' => '2017-03-15 14:25:32'
            ],
            [
                'created_at' => '2017-01-26 14:25:32'
            ],
            [
                'created_at' => '2017-03-26 14:25:32'
            ],
            [
                'created_at' => '2016-03-26 14:25:32'
            ],
            [
                'created_at' => '2017-03-26 14:25:32'
            ]
        ],
        'last_seen' => '2017-03-01 14:25:32'
    ],
    [
        'id' => 2,
        'mutual_connections' => 2,
        'mutual_objects' => [
            [
                'created_at' => '2016-03-26 14:25:32'
            ],
            [
                'created_at' => '2015-03-26 14:25:32'
            ],
            [
                'created_at' => '2017-02-26 14:25:32'
            ],
            [
                'created_at' => '2017-03-15 14:25:32'
            ],
            [
                'created_at' => '2017-01-26 14:25:32'
            ],
            [
                'created_at' => '2017-03-26 14:25:32'
            ],
            [
                'created_at' => '2016-03-26 14:25:32'
            ],
            [
                'created_at' => '2016-03-26 14:25:32'
            ],
            [
                'created_at' => '2016-03-26 14:25:32'
            ],
            [
                'created_at' => '2017-03-15 14:25:32'
            ],
            [
                'created_at' => '2017-02-26 14:25:32'
            ],
            [
                'created_at' => '2017-03-15 14:25:32'
            ],
            [
                'created_at' => '2017-01-26 14:25:32'
            ],
            [
                'created_at' => '2017-03-12 14:25:32'
            ],
            [
                'created_at' => '2016-03-13 14:25:32'
            ],
            [
                'created_at' => '2017-03-17 14:25:32'
            ]
        ],
        'last_seen' => '2015-03-25 14:25:32'
    ],
    [
        'id' => 3,
        'mutual_connections' => 30,
        'mutual_objects' => [
            [
                'created_at' => '2017-02-26 14:25:32'
            ],
            [
                'created_at' => '2017-03-26 14:25:32'
            ]
        ],
        'last_seen' => '2017-03-25 14:25:32'
    ],
    [
        'id' => 4,
        'mutual_connections' => 107,
        'mutual_objects' => [],
        'last_seen' => '2017-03-26 14:25:32'
    ],
    [
        'id' => 5,
        'mutual_connections' => 500,
        'mutual_objects' => [],
        'last_seen' => '2017-03-26 20:25:32'
    ],
    [
        'id' => 6,
        'mutual_connections' => 5,
        'mutual_objects' => [
            [
                'created_at' => '2017-03-26 20:55:32'
            ],
            [
                'created_at' => '2017-03-25 14:25:32'
            ]
        ],
        'last_seen' => '2017-03-25 14:25:32'
    ]
];

$relevance = [];

foreach ($users as $user) {

    $mutual_date_sum = 0;

    foreach ($user['mutual_objects'] as $bubble) {
        $mutual_date_sum =+ strtotime($bubble['created_at']);
    }

    $mutual_date_thing = empty($mutual_date_sum) ? 1 : $mutual_date_sum / (300000 * count($user['mutual_objects']));

    $relevance[] = [
        'id' => $user['id'],
        'relevance' => log10($user['mutual_connections'] + 1) + $mutual_date_thing
    ];
}

$relevance = collect($relevance)->sortByDesc('relevance');

print_r($relevance->values()->all());

This prints out:

Array
(
    [0] => Array
        (
            [id] => 3
            [relevance] => 2485.7219150272
        )

    [1] => Array
        (
            [id] => 6
            [relevance] => 2484.8647045837
        )

    [2] => Array
        (
            [id] => 1
            [relevance] => 622.26175831599
        )

    [3] => Array
        (
            [id] => 2
            [relevance] => 310.84394042139
        )

    [4] => Array
        (
            [id] => 5
            [relevance] => 3.6998377258672
        )

    [5] => Array
        (
            [id] => 4
            [relevance] => 3.0334237554869
        )

)

Answer 1

This problem is a candidate for machine learning. Look for an introductory book, because I think that it is not very complex and you could do it. If not, depending on the income you make with your website, you might consider hiring someone who does it for you.

If you prefer to do it "manually"; you will build your own model with specific weights to different factors. Be aware that our brains deceive us very often and what you think is a perfect model might be far from optimal.

I would suggest you to start right away storing data on which users each user interacts more with; so you can compare your results with real data. Also, in the future you will have a foundation to build a proper machine learning system.

Having said that, here is my proposal:

In the end, you want a list like this (with 3 users):

A->B: relevance
----------------
User1->User2: 0.59
User1->User3: 0.17
User2->User1: 0.78
User2->User3: 0.63
User3->User1: 0.76
User3->User2: 0.45

1) For each user

1.1) Compute and cache the age of every user's 'last_seen', in days, integer rounding down (floor).

1.2) Store max(age(last_seen)) -let's call it just max-. This is one value, not one per user. But you can only compute it once you have previously computed the age of every user

1.3) For each user, change the stored age value with the result of (max-age)/max to get a value between 0 and 1.

1.4) Compute and cache also every object's 'created_at', in days.

2) For each user, comparing with every other user

2.1) Regarding mutual connections, think of this: if A has 100 connections, 10 of them shared with B, and C has 500 connections, 10 of them shared with D, do you really take 10 as the value for the calculation in both cases? I would take the percentage. For A->B it would be 10 and for C->D it would be 2. And then /100 to have a value between 0 and 1.

2.2) Pick a maximum age for mutual objects to be relevant. Let's take 365 days.

2.3) In user A, remove objects older than 365 days. Do not really remove them, just filter them out for the sake of these calculations.

2.4) From the remaining objects, compute the percentage of mutual objects with each of the other users.

2.5) For each one of these other users, compute the average age of the objects in common from the previous step. Take the maximum age (365), subtract the computed average and /365 to have a value between 0 and 1.

2.6) Retrieve the age value of the other user.

So, for each combination of A->B, you have four values between 0 and 1:

• MC: mutual connections A-B
• MO: mutual objects A-B
• OA: avg mutual object age A-B
• BA: age of B

Now you have to assign weights to each one of them in order to find the optimal solution. Assign percentages which sum 100 to make your life easier:

Relevance = 40 * MC + 30 * MO + 10 * OA + 20 * BA

In this case, since OA is so related to MO, you can mix them:

Relevance = 40 * MC + 20 * MO + 20 * MO * OA + 20 * BA

I would suggest running this overnight, every day. There are many ways to improve and optimize the process... have fun!