Case 1: Comparing objects and users

Comparing users and objects: normalization, Euclidean distance, and dot product

Let us consider a typical applied ML and recommender-systems task. We have users and items (products, services, subscriptions), each represented by a set of numeric features.

First, we normalize user features to a common range. Then we compute Euclidean distance between users and finish with a dot product between a user profile and an item.

Example of code:


<?php

function normalize(array $x, array $min, array $max): array {
    $result = [];

    foreach ($x as $i => $value) {
        $result[$i] = ($value - $min[$i]) / ($max[$i] - $min[$i]);
    }

    return $result;
}

function euclideanDistance(array $a, array $b): float {
    $n = count($a);

    if ($n !== count($b)) {
        throw new InvalidArgumentException('Vectors must have the same length');
    }

    $sum = 0.0;

    for ($i = 0; $i < $n; $i++) {
        $diff = $a[$i] - $b[$i];
        $sum += $diff ** 2;
    }

    return sqrt($sum);
}

function dotProduct(array $a, array $b): float {
    $n = count($a);

    if ($n !== count($b)) {
        throw new InvalidArgumentException('Vectors must have the same length');
    }

    $sum = 0.0;

    for ($i = 0; $i < $n; $i++) {
        $sum += $a[$i] * $b[$i];
    }

    return $sum;
}