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| 1 | <?php |
| 2 | /** |
| 3 | * Jingga |
| 4 | * |
| 5 | * PHP Version 8.1 |
| 6 | * |
| 7 | * @package phpOMS\Business\Recommendation |
| 8 | * @copyright Dennis Eichhorn |
| 9 | * @license OMS License 2.0 |
| 10 | * @version 1.0.0 |
| 11 | * @link https://jingga.app |
| 12 | */ |
| 13 | declare(strict_types=1); |
| 14 | |
| 15 | namespace phpOMS\Business\Recommendation; |
| 16 | |
| 17 | use phpOMS\Math\Topology\MetricsND; |
| 18 | |
| 19 | /** |
| 20 | * Memory based collaborative filtering |
| 21 | * |
| 22 | * Items or potential customers are found based on how much they like certain items. |
| 23 | * |
| 24 | * This requires a item/product rating of some sort in the backend. |
| 25 | * Such a rating could be either manual user ratings or a rating based on how often it is purchased or how long it is used. |
| 26 | * Most likely a combination is required. |
| 27 | * |
| 28 | * @package phpOMS\Business\Recommendation |
| 29 | * @license OMS License 2.0 |
| 30 | * @link https://jingga.app |
| 31 | * @see https://realpython.com/build-recommendation-engine-collaborative-filtering/ |
| 32 | * @since 1.0.0 |
| 33 | */ |
| 34 | final class MemoryCF |
| 35 | { |
| 36 | /** |
| 37 | * All rankings |
| 38 | * |
| 39 | * @var array<array> |
| 40 | * @since 1.0.0 |
| 41 | */ |
| 42 | private array $rankings = []; |
| 43 | |
| 44 | /** |
| 45 | * Constructor. |
| 46 | * |
| 47 | * @param array<array> $rankings Array of item ratings by users (or reverse to find users) |
| 48 | * |
| 49 | * @since 1.0.0 |
| 50 | */ |
| 51 | public function __construct(array $rankings) |
| 52 | { |
| 53 | $this->rankings = $this->normalizeRanking($rankings); |
| 54 | } |
| 55 | |
| 56 | /** |
| 57 | * Normalize all ratings. |
| 58 | * |
| 59 | * This is necessary because some users my give lower or higher ratings on average (bias). |
| 60 | * |
| 61 | * @param array<array> $rankings Item ratings/rankings |
| 62 | * |
| 63 | * @return array<array> |
| 64 | * |
| 65 | * @since 1.0.0 |
| 66 | */ |
| 67 | private function normalizeRanking(array $rankings) : array |
| 68 | { |
| 69 | foreach ($rankings as $idx => $items) { |
| 70 | $avg = \array_sum($items) / \count($items); |
| 71 | |
| 72 | foreach ($items as $idx2 => $_) { |
| 73 | $rankings[$idx][$idx2] -= $avg; |
| 74 | } |
| 75 | } |
| 76 | |
| 77 | return $rankings; |
| 78 | } |
| 79 | |
| 80 | /** |
| 81 | * Euclidean distance between users |
| 82 | * |
| 83 | * @param array $ranking Rating to find the distance for |
| 84 | * @param array<array> $rankings All ratings to find the distance to |
| 85 | * |
| 86 | * @return float[] |
| 87 | * |
| 88 | * @since 1.0.0 |
| 89 | */ |
| 90 | public function euclideanDistance(array $ranking, array $rankings) : array |
| 91 | { |
| 92 | $distances = []; |
| 93 | foreach ($rankings as $idx => $r) { |
| 94 | $distances[$idx] = \abs(MetricsND::euclidean($ranking, $r)); |
| 95 | } |
| 96 | |
| 97 | return $distances; |
| 98 | } |
| 99 | |
| 100 | /** |
| 101 | * Cosine distance between users |
| 102 | * |
| 103 | * @param array $ranking Rating to find the distance for |
| 104 | * @param array<array> $rankings All ratings to find the distance to |
| 105 | * |
| 106 | * @return float[] |
| 107 | * |
| 108 | * @since 1.0.0 |
| 109 | */ |
| 110 | public function cosineDistance(array $ranking, array $rankings) : array |
| 111 | { |
| 112 | $distances = []; |
| 113 | foreach ($rankings as $idx => $r) { |
| 114 | $distances[$idx] = \abs(MetricsND::cosine($ranking, $r)); |
| 115 | } |
| 116 | |
| 117 | return $distances; |
| 118 | } |
| 119 | |
| 120 | /** |
| 121 | * Assign a item rank/rating based on the distance to other items |
| 122 | * |
| 123 | * @param string $itemId Id of the item to rank |
| 124 | * @param array $distances Distance to other users |
| 125 | * @param array<array> $users All user ratings |
| 126 | * @param int $size Only consider the top n distances (best matches with other users) |
| 127 | * |
| 128 | * @return float Estimated item rank/rating based on similarity to other users |
| 129 | * |
| 130 | * @since 1.0.0 |
| 131 | */ |
| 132 | private function weightedItemRank(string $itemId, array $distances, array $users, int $size) : float |
| 133 | { |
| 134 | $rank = 0.0; |
| 135 | $count = 0; |
| 136 | foreach ($distances as $uId => $_) { |
| 137 | if ($count >= $size) { |
| 138 | break; |
| 139 | } |
| 140 | |
| 141 | if (!isset($users[$itemId])) { |
| 142 | continue; |
| 143 | } |
| 144 | |
| 145 | ++$count; |
| 146 | $rank += $users[$uId][$itemId]; |
| 147 | } |
| 148 | |
| 149 | return $count === 0 ? 0.0 : $rank / $count; |
| 150 | } |
| 151 | |
| 152 | /** |
| 153 | * Find potential items/users which are a good match for a user/item. |
| 154 | * |
| 155 | * The algorithm uses the ratings of a a user and tries to find other users who have similar rating behavior and then searches for high rated items that the user doesn't have yet. |
| 156 | * |
| 157 | * This can be used to find items for a specific user (aka might be interested in) or to find users who might be interested in this item |
| 158 | * |
| 159 | * option 1 - find items |
| 160 | * ranking[itemId] = itemRank (how much does specific user like item) |
| 161 | * rankings[userId][itemId] = itemRank |
| 162 | * |
| 163 | * option 2 - find user |
| 164 | * ranking[userId] = itemRank (how much does user like specific item) |
| 165 | * rankings[itemId][userId] = itemRank |
| 166 | * option 1 searches for items, option 2 searches for users |
| 167 | * |
| 168 | * @param array $ranking Array of item ratings (e.g. products, movies, ...) |
| 169 | * |
| 170 | * @return array |
| 171 | * |
| 172 | * @since 1.0.0 |
| 173 | */ |
| 174 | public function bestMatch(array $ranking, int $size = 10) : array |
| 175 | { |
| 176 | $ranking = $this->normalizeRanking([$ranking]); |
| 177 | $ranking = $ranking[0]; |
| 178 | |
| 179 | $euclidean = $this->euclideanDistance($ranking, $this->rankings); |
| 180 | $cosine = $this->cosineDistance($ranking, $this->rankings); |
| 181 | |
| 182 | \asort($euclidean); |
| 183 | \asort($cosine); |
| 184 | |
| 185 | $size = \min($size, \count($this->rankings)); |
| 186 | $matches = []; |
| 187 | |
| 188 | $distancePointer = \array_keys($euclidean); |
| 189 | $anglePointer = \array_keys($cosine); |
| 190 | |
| 191 | // Inspect items of the top n comparable users |
| 192 | for ($i = 1; $i <= $size; ++$i) { |
| 193 | $index = (int) ($i / 2) - 1; |
| 194 | |
| 195 | $uId = $i % 2 === 1 ? $distancePointer[$index] : $anglePointer[$index]; |
| 196 | $distances = $i % 2 === 1 ? $euclidean : $cosine; |
| 197 | |
| 198 | foreach ($this->rankings[$uId] as $iId => $_) { |
| 199 | // Item is not already in dataset and not in historic dataset (we are only interested in new) |
| 200 | if (isset($matches[$iId]) || isset($ranking[$iId])) { |
| 201 | continue; |
| 202 | } |
| 203 | |
| 204 | // Calculate the expected rating the user would give based on what the best comparable users did |
| 205 | $matches[$iId] = $this->weightedItemRank($iId, $distances, $this->rankings, $size); |
| 206 | } |
| 207 | } |
| 208 | |
| 209 | \asort($matches); |
| 210 | |
| 211 | return \array_reverse($matches, true); |
| 212 | } |
| 213 | } |