{"id":476450,"date":"2023-08-09T07:29:55","date_gmt":"2023-08-09T07:29:55","guid":{"rendered":""},"modified":"2023-09-05T11:12:45","modified_gmt":"2023-09-05T11:12:45","slug":"cosine-similarity","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/cosine-similarity\/","title":{"rendered":"\u0110\u1ed9 t\u01b0\u01a1ng t\u1ef1 cosin"},"content":{"rendered":"<p>\u0110\u1ed9 t\u01b0\u01a1ng t\u1ef1 cosine l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n trong to\u00e1n h\u1ecdc v\u00e0 x\u1eed l\u00fd ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean (NLP), \u0111o l\u01b0\u1eddng \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 gi\u1eefa hai vect\u01a1 kh\u00e1c 0 trong m\u1ed9t kh\u00f4ng gian t\u00edch b\u00ean trong. N\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau, bao g\u1ed3m truy xu\u1ea5t th\u00f4ng tin, khai th\u00e1c v\u0103n b\u1ea3n, h\u1ec7 th\u1ed1ng \u0111\u1ec1 xu\u1ea5t, v.v. B\u00e0i vi\u1ebft n\u00e0y s\u1ebd \u0111i s\u00e2u v\u00e0o l\u1ecbch s\u1eed, c\u1ea5u tr\u00fac b\u00ean trong, lo\u1ea1i, c\u00e1ch s\u1eed d\u1ee5ng v\u00e0 quan \u0111i\u1ec3m trong t\u01b0\u01a1ng lai v\u1ec1 s\u1ef1 t\u01b0\u01a1ng \u0111\u1ed3ng c\u1ee7a Cosine.<\/p>\n<h2>L\u1ecbch s\u1eed v\u1ec1 ngu\u1ed3n g\u1ed1c c\u1ee7a s\u1ef1 t\u01b0\u01a1ng t\u1ef1 Cosine v\u00e0 l\u1ea7n \u0111\u1ea7u ti\u00ean \u0111\u1ec1 c\u1eadp \u0111\u1ebfn n\u00f3<\/h2>\n<p>Kh\u00e1i ni\u1ec7m v\u1ec1 s\u1ef1 t\u01b0\u01a1ng t\u1ef1 Cosine c\u00f3 th\u1ec3 b\u1eaft ngu\u1ed3n t\u1eeb \u0111\u1ea7u th\u1ebf k\u1ef7 19 khi nh\u00e0 to\u00e1n h\u1ecdc Th\u1ee5y S\u0129 Adrien-Marie Legendre gi\u1edbi thi\u1ec7u n\u00f3 nh\u01b0 m\u1ed9t ph\u1ea7n trong c\u00f4ng tr\u00ecnh c\u1ee7a \u00f4ng v\u1ec1 t\u00edch ph\u00e2n elip. Sau \u0111\u00f3, v\u00e0o th\u1ebf k\u1ef7 20, \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine \u0111\u01b0\u1ee3c \u0111\u01b0a v\u00e0o l\u0129nh v\u1ef1c truy xu\u1ea5t th\u00f4ng tin v\u00e0 NLP nh\u01b0 m\u1ed9t th\u01b0\u1edbc \u0111o h\u1eefu \u00edch \u0111\u1ec3 so s\u00e1nh \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 c\u1ee7a t\u00e0i li\u1ec7u v\u00e0 v\u0103n b\u1ea3n.<\/p>\n<h2>Th\u00f4ng tin chi ti\u1ebft v\u1ec1 \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine. M\u1edf r\u1ed9ng ch\u1ee7 \u0111\u1ec1 T\u01b0\u01a1ng t\u1ef1 Cosine<\/h2>\n<p>\u0110\u1ed9 t\u01b0\u01a1ng t\u1ef1 cosine t\u00ednh to\u00e1n cosin c\u1ee7a g\u00f3c gi\u1eefa hai vect\u01a1, bi\u1ec3u th\u1ecb c\u00e1c t\u00e0i li\u1ec7u ho\u1eb7c v\u0103n b\u1ea3n \u0111\u01b0\u1ee3c so s\u00e1nh, trong kh\u00f4ng gian \u0111a chi\u1ec1u. C\u00f4ng th\u1ee9c t\u00ednh \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine gi\u1eefa hai vect\u01a1 A v\u00e0 B l\u00e0:<\/p>\n<pre><div class=\"bg-black rounded-md mb-4\"><div class=\"flex items-center relative text-gray-200 bg-gray-800 px-4 py-2 text-xs font-sans justify-between rounded-t-md\"><span>css<\/span><button class=\"flex ml-auto gap-2\"><svg stroke=\"currentColor\" fill=\"none\" stroke-width=\"2\" viewbox=\"0 0 24 24\" stroke-linecap=\"round\" stroke-linejoin=\"round\" class=\"h-4 w-4\" height=\"1em\" width=\"1em\" ><path d=\"M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2\"><\/path><rect x=\"8\" y=\"2\" width=\"8\" height=\"4\" rx=\"1\" ry=\"1\"><\/rect><\/svg>Sao ch\u00e9p m\u00e3<\/button><\/div><div class=\"p-4 overflow-y-auto\"><code class=\"!whitespace-pre hljs language-css\" data-no-translation=\"\">Cosine Similarity(<span class=\"hljs-selector-tag\">A<\/span>, <span class=\"hljs-selector-tag\">B<\/span>) = (<span class=\"hljs-selector-tag\">A<\/span> \u00b7 <span class=\"hljs-selector-tag\">B<\/span>) \/ (||<span class=\"hljs-selector-tag\">A<\/span>|| * ||<span class=\"hljs-selector-tag\">B<\/span>||)\n<\/code><\/div><\/div><\/pre>\n<p>\u1ede \u0111\u00e2u <code data-no-translation=\"\">(A \u00b7 B)<\/code> \u0111\u1ea1i di\u1ec7n cho t\u00edch v\u00f4 h\u01b0\u1edbng c\u1ee7a vect\u01a1 A v\u00e0 B, v\u00e0 <code data-no-translation=\"\">||A||<\/code> V\u00e0 <code data-no-translation=\"\">||B||<\/code> l\u1ea7n l\u01b0\u1ee3t l\u00e0 \u0111\u1ed9 l\u1edbn (ho\u1eb7c chu\u1ea9n) c\u1ee7a vect\u01a1 A v\u00e0 B.<\/p>\n<p>\u0110\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine dao \u0111\u1ed9ng t\u1eeb -1 \u0111\u1ebfn 1, v\u1edbi -1 bi\u1ec3u th\u1ecb s\u1ef1 kh\u00e1c bi\u1ec7t ho\u00e0n to\u00e0n, 1 bi\u1ec3u th\u1ecb s\u1ef1 t\u01b0\u01a1ng t\u1ef1 tuy\u1ec7t \u0111\u1ed1i v\u00e0 0 bi\u1ec3u th\u1ecb t\u00ednh tr\u1ef1c giao (kh\u00f4ng t\u01b0\u01a1ng t\u1ef1).<\/p>\n<h2>C\u1ea5u tr\u00fac b\u00ean trong c\u1ee7a \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine. T\u00ednh t\u01b0\u01a1ng t\u1ef1 Cosine ho\u1ea1t \u0111\u1ed9ng nh\u01b0 th\u1ebf n\u00e0o<\/h2>\n<p>\u0110\u1ed9 t\u01b0\u01a1ng t\u1ef1 cosine ho\u1ea1t \u0111\u1ed9ng b\u1eb1ng c\u00e1ch chuy\u1ec3n \u0111\u1ed5i d\u1eef li\u1ec7u v\u0103n b\u1ea3n th\u00e0nh bi\u1ec3u di\u1ec5n s\u1ed1 (vect\u01a1) trong kh\u00f4ng gian nhi\u1ec1u chi\u1ec1u. M\u1ed7i th\u1ee9 nguy\u00ean t\u01b0\u01a1ng \u1ee9ng v\u1edbi m\u1ed9t thu\u1eadt ng\u1eef duy nh\u1ea5t trong t\u1eadp d\u1eef li\u1ec7u. \u0110\u1ed9 t\u01b0\u01a1ng t\u1ef1 gi\u1eefa hai t\u00e0i li\u1ec7u sau \u0111\u00f3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh d\u1ef1a tr\u00ean g\u00f3c gi\u1eefa c\u00e1c vect\u01a1 t\u01b0\u01a1ng \u1ee9ng c\u1ee7a ch\u00fang.<\/p>\n<p>Qu\u00e1 tr\u00ecnh t\u00ednh to\u00e1n \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine bao g\u1ed3m c\u00e1c b\u01b0\u1edbc sau:<\/p>\n<ol>\n<li>X\u1eed l\u00fd s\u01a1 b\u1ed9 v\u0103n b\u1ea3n: Lo\u1ea1i b\u1ecf c\u00e1c t\u1eeb d\u1eebng, k\u00fd t\u1ef1 \u0111\u1eb7c bi\u1ec7t v\u00e0 th\u1ef1c hi\u1ec7n t\u1eeb g\u1ed1c ho\u1eb7c t\u1eeb v\u1ef1ng \u0111\u1ec3 chu\u1ea9n h\u00f3a v\u0103n b\u1ea3n.<\/li>\n<li>T\u00ednh to\u00e1n t\u1ea7n s\u1ed1 thu\u1eadt ng\u1eef (TF): \u0110\u1ebfm t\u1ea7n su\u1ea5t c\u1ee7a t\u1eebng thu\u1eadt ng\u1eef trong t\u00e0i li\u1ec7u.<\/li>\n<li>T\u00ednh to\u00e1n t\u1ea7n s\u1ed1 t\u00e0i li\u1ec7u ngh\u1ecbch \u0111\u1ea3o (IDF): \u0110o l\u01b0\u1eddng t\u1ea7m quan tr\u1ecdng c\u1ee7a t\u1eebng thu\u1eadt ng\u1eef tr\u00ean t\u1ea5t c\u1ea3 c\u00e1c t\u00e0i li\u1ec7u \u0111\u1ec3 mang l\u1ea1i tr\u1ecdng s\u1ed1 cao h\u01a1n cho c\u00e1c thu\u1eadt ng\u1eef hi\u1ebfm.<\/li>\n<li>T\u00ednh to\u00e1n TF-IDF: K\u1ebft h\u1ee3p TF v\u00e0 IDF \u0111\u1ec3 c\u00f3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n s\u1ed1 cu\u1ed1i c\u00f9ng c\u1ee7a t\u00e0i li\u1ec7u.<\/li>\n<li>T\u00ednh to\u00e1n \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine: T\u00ednh to\u00e1n \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng vect\u01a1 TF-IDF c\u1ee7a t\u00e0i li\u1ec7u.<\/li>\n<\/ol>\n<h2>Ph\u00e2n t\u00edch c\u00e1c t\u00ednh n\u0103ng ch\u00ednh c\u1ee7a \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine<\/h2>\n<p>\u0110\u1ed9 t\u01b0\u01a1ng t\u1ef1 cosine cung c\u1ea5p m\u1ed9t s\u1ed1 t\u00ednh n\u0103ng ch\u00ednh khi\u1ebfn n\u00f3 tr\u1edf th\u00e0nh l\u1ef1a ch\u1ecdn ph\u1ed5 bi\u1ebfn cho c\u00e1c t\u00e1c v\u1ee5 so s\u00e1nh v\u0103n b\u1ea3n:<\/p>\n<ol>\n<li><strong>T\u1ec9 l\u1ec7 kh\u00f4ng thay \u0111\u1ed5i<\/strong>: \u0110\u1ed9 t\u01b0\u01a1ng t\u1ef1 cosine kh\u00f4ng b\u1ecb \u1ea3nh h\u01b0\u1edfng b\u1edfi \u0111\u1ed9 l\u1edbn c\u1ee7a vect\u01a1, khi\u1ebfn n\u00f3 tr\u1edf n\u00ean ch\u1eafc ch\u1eafn tr\u01b0\u1edbc nh\u1eefng thay \u0111\u1ed5i v\u1ec1 \u0111\u1ed9 d\u00e0i t\u00e0i li\u1ec7u.<\/li>\n<li><strong>Hi\u1ec7u qu\u1ea3<\/strong>: T\u00ednh to\u00e1n \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine mang l\u1ea1i hi\u1ec7u qu\u1ea3 v\u1ec1 m\u1eb7t t\u00ednh to\u00e1n, ngay c\u1ea3 \u0111\u1ed1i v\u1edbi c\u00e1c t\u1eadp d\u1eef li\u1ec7u v\u0103n b\u1ea3n l\u1edbn.<\/li>\n<li><strong>Kh\u1ea3 n\u0103ng gi\u1ea3i th\u00edch<\/strong>: \u0110i\u1ec3m t\u01b0\u01a1ng \u0111\u1ed3ng n\u1eb1m trong kho\u1ea3ng t\u1eeb -1 \u0111\u1ebfn 1, mang l\u1ea1i nh\u1eefng di\u1ec5n gi\u1ea3i tr\u1ef1c quan.<\/li>\n<li><strong>S\u1ef1 t\u01b0\u01a1ng \u0111\u1ed3ng v\u1ec1 ng\u1eef ngh\u0129a c\u1ee7a v\u0103n b\u1ea3n<\/strong>: \u0110\u1ed9 t\u01b0\u01a1ng t\u1ef1 cosine xem x\u00e9t s\u1ef1 t\u01b0\u01a1ng t\u1ef1 v\u1ec1 ng\u1eef ngh\u0129a gi\u1eefa c\u00e1c v\u0103n b\u1ea3n, l\u00e0m cho n\u00f3 ph\u00f9 h\u1ee3p v\u1edbi c\u00e1c \u0111\u1ec1 xu\u1ea5t v\u00e0 ph\u00e2n c\u1ee5m d\u1ef1a tr\u00ean n\u1ed9i dung.<\/li>\n<\/ol>\n<h2>C\u00e1c lo\u1ea1i t\u01b0\u01a1ng t\u1ef1 Cosine<\/h2>\n<p>C\u00f3 hai lo\u1ea1i t\u01b0\u01a1ng t\u1ef1 Cosine ch\u00ednh th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng:<\/p>\n<ol>\n<li><strong>T\u01b0\u01a1ng t\u1ef1 Cosine c\u1ed5 \u0111i\u1ec3n<\/strong>: \u0110\u00e2y l\u00e0 \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine ti\u00eau chu\u1ea9n \u0111\u00e3 th\u1ea3o lu\u1eadn tr\u01b0\u1edbc \u0111\u00f3, s\u1eed d\u1ee5ng c\u00e1ch bi\u1ec3u di\u1ec5n t\u00e0i li\u1ec7u TF-IDF.<\/li>\n<li><strong>T\u01b0\u01a1ng t\u1ef1 cosin nh\u1ecb ph\u00e2n<\/strong>: Trong bi\u1ebfn th\u1ec3 n\u00e0y, c\u00e1c vect\u01a1 l\u00e0 nh\u1ecb ph\u00e2n, bi\u1ec3u th\u1ecb s\u1ef1 hi\u1ec7n di\u1ec7n (1) ho\u1eb7c v\u1eafng m\u1eb7t (0) c\u1ee7a c\u00e1c thu\u1eadt ng\u1eef trong t\u00e0i li\u1ec7u.<\/li>\n<\/ol>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 b\u1ea3ng so s\u00e1nh c\u1ee7a hai lo\u1ea1i:<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th>T\u01b0\u01a1ng t\u1ef1 Cosine c\u1ed5 \u0111i\u1ec3n<\/th>\n<th>T\u01b0\u01a1ng t\u1ef1 cosin nh\u1ecb ph\u00e2n<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Bi\u1ec3u di\u1ec5n v\u00e9c t\u01a1<\/td>\n<td>TF-IDF<\/td>\n<td>nh\u1ecb ph\u00e2n<\/td>\n<\/tr>\n<tr>\n<td>Kh\u1ea3 n\u0103ng gi\u1ea3i th\u00edch<\/td>\n<td>Gi\u00e1 tr\u1ecb th\u1ef1c (-1 \u0111\u1ebfn 1)<\/td>\n<td>Nh\u1ecb ph\u00e2n (0 ho\u1eb7c 1)<\/td>\n<\/tr>\n<tr>\n<td>Ph\u00f9 h\u1ee3p v\u1edbi<\/td>\n<td>\u1ee8ng d\u1ee5ng d\u1ef1a tr\u00ean v\u0103n b\u1ea3n<\/td>\n<td>K\u1ecbch b\u1ea3n d\u1eef li\u1ec7u th\u01b0a th\u1edbt<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>C\u00e1c c\u00e1ch s\u1eed d\u1ee5ng Cosine t\u01b0\u01a1ng t\u1ef1, c\u00e1c v\u1ea5n \u0111\u1ec1 v\u00e0 gi\u1ea3i ph\u00e1p li\u00ean quan \u0111\u1ebfn vi\u1ec7c s\u1eed d\u1ee5ng<\/h2>\n<p>S\u1ef1 t\u01b0\u01a1ng t\u1ef1 cosine t\u00ecm th\u1ea5y c\u00e1c \u1ee9ng d\u1ee5ng trong c\u00e1c l\u0129nh v\u1ef1c kh\u00e1c nhau:<\/p>\n<ol>\n<li><strong>Truy xu\u1ea5t th\u00f4ng tin<\/strong>: \u0110\u1ed9 t\u01b0\u01a1ng t\u1ef1 cosine gi\u00fap x\u1ebfp h\u1ea1ng t\u00e0i li\u1ec7u d\u1ef1a tr\u00ean m\u1ee9c \u0111\u1ed9 li\u00ean quan \u0111\u1ebfn truy v\u1ea5n, h\u1ed7 tr\u1ee3 c\u00e1c c\u00f4ng c\u1ee5 t\u00ecm ki\u1ebfm hi\u1ec7u qu\u1ea3.<\/li>\n<li><strong>Ph\u00e2n c\u1ee5m t\u00e0i li\u1ec7u<\/strong>: N\u00f3 t\u1ea1o \u0111i\u1ec1u ki\u1ec7n nh\u00f3m c\u00e1c t\u00e0i li\u1ec7u t\u01b0\u01a1ng t\u1ef1 l\u1ea1i v\u1edbi nhau \u0111\u1ec3 t\u1ed5 ch\u1ee9c v\u00e0 ph\u00e2n t\u00edch t\u1ed1t h\u01a1n.<\/li>\n<li><strong>L\u1ecdc c\u1ed9ng t\u00e1c<\/strong>: H\u1ec7 th\u1ed1ng g\u1ee3i \u00fd s\u1eed d\u1ee5ng \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine \u0111\u1ec3 g\u1ee3i \u00fd c\u00e1c m\u1eb7t h\u00e0ng cho ng\u01b0\u1eddi d\u00f9ng c\u00f3 c\u00f9ng s\u1edf th\u00edch.<\/li>\n<li><strong>Ph\u00e1t hi\u1ec7n \u0111\u1ea1o v\u0103n<\/strong>: N\u00f3 c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh c\u00e1c \u0111o\u1ea1n v\u0103n b\u1ea3n t\u01b0\u01a1ng t\u1ef1 trong c\u00e1c t\u00e0i li\u1ec7u kh\u00e1c nhau.<\/li>\n<\/ol>\n<p>Tuy nhi\u00ean, \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine c\u00f3 th\u1ec3 g\u1eb7p ph\u1ea3i th\u00e1ch th\u1ee9c trong m\u1ed9t s\u1ed1 tr\u01b0\u1eddng h\u1ee3p, ch\u1eb3ng h\u1ea1n nh\u01b0:<\/p>\n<ul>\n<li><strong>th\u01b0a th\u1edbt<\/strong>: Khi x\u1eed l\u00fd d\u1eef li\u1ec7u th\u01b0a th\u1edbt nhi\u1ec1u chi\u1ec1u, \u0111i\u1ec3m t\u01b0\u01a1ng t\u1ef1 c\u00f3 th\u1ec3 \u00edt th\u00f4ng tin h\u01a1n.<\/li>\n<li><strong>S\u1ef1 ph\u1ee5 thu\u1ed9c ng\u00f4n ng\u1eef<\/strong>: \u0110\u1ed9 t\u01b0\u01a1ng t\u1ef1 cosin c\u00f3 th\u1ec3 kh\u00f4ng n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c ng\u1eef c\u1ea3nh trong c\u00e1c ng\u00f4n ng\u1eef c\u00f3 ng\u1eef ph\u00e1p ho\u1eb7c tr\u1eadt t\u1ef1 t\u1eeb ph\u1ee9c t\u1ea1p.<\/li>\n<\/ul>\n<p>\u0110\u1ec3 kh\u1eafc ph\u1ee5c nh\u1eefng v\u1ea5n \u0111\u1ec1 n\u00e0y, c\u00e1c k\u1ef9 thu\u1eadt nh\u01b0 gi\u1ea3m k\u00edch th\u01b0\u1edbc (v\u00ed d\u1ee5: s\u1eed d\u1ee5ng Ph\u00e2n t\u00e1ch gi\u00e1 tr\u1ecb s\u1ed1 \u00edt) v\u00e0 nh\u00fang t\u1eeb (v\u00ed d\u1ee5: Word2Vec) \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 n\u00e2ng cao hi\u1ec7u su\u1ea5t.<\/p>\n<h2>C\u00e1c \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh v\u00e0 so s\u00e1nh kh\u00e1c v\u1edbi c\u00e1c thu\u1eadt ng\u1eef t\u01b0\u01a1ng t\u1ef1<\/h2>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th>\u0110\u1ed9 t\u01b0\u01a1ng t\u1ef1 cosin<\/th>\n<th>S\u1ef1 t\u01b0\u01a1ng \u0111\u1ed3ng c\u1ee7a Jaccard<\/th>\n<th>Kho\u1ea3ng c\u00e1ch Euclide<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Lo\u1ea1i \u0111o<\/td>\n<td>S\u1ef1 t\u01b0\u01a1ng \u0111\u1ed3ng<\/td>\n<td>S\u1ef1 t\u01b0\u01a1ng \u0111\u1ed3ng<\/td>\n<td>S\u1ef1 kh\u00e1c bi\u1ec7t<\/td>\n<\/tr>\n<tr>\n<td>Ph\u1ea1m vi<\/td>\n<td>-1 \u0111\u1ebfn 1<\/td>\n<td>0 \u0111\u1ebfn 1<\/td>\n<td>0 \u0111\u1ebfn \u221e<\/td>\n<\/tr>\n<tr>\n<td>Kh\u1ea3 n\u0103ng \u1ee9ng d\u1ee5ng<\/td>\n<td>So s\u00e1nh v\u0103n b\u1ea3n<\/td>\n<td>\u0110\u1eb7t so s\u00e1nh<\/td>\n<td>Vect\u01a1 s\u1ed1<\/td>\n<\/tr>\n<tr>\n<td>chi\u1ec1u<\/td>\n<td>chi\u1ec1u cao<\/td>\n<td>chi\u1ec1u th\u1ea5p<\/td>\n<td>chi\u1ec1u cao<\/td>\n<\/tr>\n<tr>\n<td>t\u00ednh to\u00e1n<\/td>\n<td>C\u00f3 hi\u1ec7u qu\u1ea3<\/td>\n<td>C\u00f3 hi\u1ec7u qu\u1ea3<\/td>\n<td>T\u00ednh to\u00e1n chuy\u00ean s\u00e2u<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>C\u00e1c quan \u0111i\u1ec3m v\u00e0 c\u00f4ng ngh\u1ec7 c\u1ee7a t\u01b0\u01a1ng lai li\u00ean quan \u0111\u1ebfn s\u1ef1 t\u01b0\u01a1ng \u0111\u1ed3ng c\u1ee7a Cosine<\/h2>\n<p>Khi c\u00f4ng ngh\u1ec7 ti\u1ebfp t\u1ee5c ph\u00e1t tri\u1ec3n, \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine d\u1ef1 ki\u1ebfn s\u1ebd v\u1eabn l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 c\u00f3 gi\u00e1 tr\u1ecb trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau. V\u1edbi s\u1ef1 ra \u0111\u1eddi c\u1ee7a ph\u1ea7n c\u1ee9ng v\u00e0 thu\u1eadt to\u00e1n m\u1ea1nh m\u1ebd h\u01a1n, \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 c\u1ee7a Cosine s\u1ebd c\u00e0ng tr\u1edf n\u00ean hi\u1ec7u qu\u1ea3 h\u01a1n trong vi\u1ec7c x\u1eed l\u00fd c\u00e1c t\u1eadp d\u1eef li\u1ec7u l\u1edbn v\u00e0 \u0111\u01b0a ra c\u00e1c \u0111\u1ec1 xu\u1ea5t ch\u00ednh x\u00e1c. Ngo\u00e0i ra, nghi\u00ean c\u1ee9u \u0111ang di\u1ec5n ra v\u1ec1 x\u1eed l\u00fd ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean v\u00e0 h\u1ecdc s\u00e2u c\u00f3 th\u1ec3 gi\u00fap c\u1ea3i thi\u1ec7n c\u00e1ch tr\u00ecnh b\u00e0y v\u0103n b\u1ea3n, n\u00e2ng cao h\u01a1n n\u1eefa \u0111\u1ed9 ch\u00ednh x\u00e1c c\u1ee7a c\u00e1c ph\u00e9p t\u00ednh t\u01b0\u01a1ng t\u1ef1.<\/p>\n<h2>C\u00e1ch s\u1eed d\u1ee5ng ho\u1eb7c li\u00ean k\u1ebft m\u00e1y ch\u1ee7 proxy v\u1edbi s\u1ef1 t\u01b0\u01a1ng \u0111\u1ed3ng c\u1ee7a Cosine<\/h2>\n<p>C\u00e1c m\u00e1y ch\u1ee7 proxy, do OneProxy cung c\u1ea5p, \u0111\u00f3ng m\u1ed9t vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c h\u1ed7 tr\u1ee3 truy c\u1eadp Internet \u1ea9n danh v\u00e0 an to\u00e0n. M\u1eb7c d\u00f9 h\u1ecd c\u00f3 th\u1ec3 kh\u00f4ng tr\u1ef1c ti\u1ebfp s\u1eed d\u1ee5ng t\u00ednh t\u01b0\u01a1ng t\u1ef1 Cosine nh\u01b0ng h\u1ecd c\u00f3 th\u1ec3 tham gia v\u00e0o c\u00e1c \u1ee9ng d\u1ee5ng s\u1eed d\u1ee5ng so s\u00e1nh v\u0103n b\u1ea3n ho\u1eb7c l\u1ecdc d\u1ef1a tr\u00ean n\u1ed9i dung. V\u00ed d\u1ee5: m\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 n\u00e2ng cao hi\u1ec7u su\u1ea5t c\u1ee7a h\u1ec7 th\u1ed1ng \u0111\u1ec1 xu\u1ea5t, s\u1eed d\u1ee5ng \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine \u0111\u1ec3 so s\u00e1nh t\u00f9y ch\u1ecdn c\u1ee7a ng\u01b0\u1eddi d\u00f9ng v\u00e0 \u0111\u1ec1 xu\u1ea5t n\u1ed9i dung c\u00f3 li\u00ean quan. H\u01a1n n\u1eefa, ch\u00fang c\u00f3 th\u1ec3 h\u1ed7 tr\u1ee3 c\u00e1c t\u00e1c v\u1ee5 truy xu\u1ea5t th\u00f4ng tin, t\u1ed1i \u01b0u h\u00f3a k\u1ebft qu\u1ea3 t\u00ecm ki\u1ebfm d\u1ef1a tr\u00ean \u0111i\u1ec3m t\u01b0\u01a1ng \u0111\u1ed3ng gi\u1eefa truy v\u1ea5n c\u1ee7a ng\u01b0\u1eddi d\u00f9ng v\u00e0 t\u00e0i li\u1ec7u \u0111\u01b0\u1ee3c l\u1eadp ch\u1ec9 m\u1ee5c.<\/p>\n<h2>Li\u00ean k\u1ebft li\u00ean quan<\/h2>\n<p>\u0110\u1ec3 bi\u1ebft th\u00eam th\u00f4ng tin v\u1ec1 \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine, b\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o c\u00e1c t\u00e0i nguy\u00ean sau:<\/p>\n<ol>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Cosine_similarity\" target=\"_new\" rel=\"noopener nofollow\">Wikipedia - T\u01b0\u01a1ng t\u1ef1 cosine<\/a><\/li>\n<li><a href=\"https:\/\/scikit-learn.org\/stable\/modules\/generated\/sklearn.metrics.pairwise.cosine_similarity.html\" target=\"_new\" rel=\"noopener nofollow\">Scikit-learn \u2013 T\u01b0\u01a1ng t\u1ef1 Cosine<\/a><\/li>\n<li><a href=\"https:\/\/scikit-learn.org\/stable\/modules\/generated\/sklearn.feature_extraction.text.TfidfVectorizer.html\" target=\"_new\" rel=\"noopener nofollow\">TfidfVectorizer \u2013 T\u00e0i li\u1ec7u Sklearn<\/a><\/li>\n<li><a href=\"https:\/\/nlp.stanford.edu\/IR-book\/\" target=\"_new\" rel=\"noopener nofollow\">Gi\u1edbi thi\u1ec7u v\u1ec1 Truy xu\u1ea5t Th\u00f4ng tin \u2013 Manning, Raghavan, Sch\u00fctze<\/a><\/li>\n<\/ol>\n<p>T\u00f3m l\u1ea1i, \u0111\u1ed9 t\u01b0\u01a1ng t\u1ef1 Cosine l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m to\u00e1n h\u1ecdc m\u1ea1nh m\u1ebd v\u1edbi nhi\u1ec1u \u1ee9ng d\u1ee5ng trong NLP, truy xu\u1ea5t th\u00f4ng tin v\u00e0 h\u1ec7 th\u1ed1ng \u0111\u1ec1 xu\u1ea5t. T\u00ednh \u0111\u01a1n gi\u1ea3n, hi\u1ec7u qu\u1ea3 v\u00e0 kh\u1ea3 n\u0103ng di\u1ec5n gi\u1ea3i c\u1ee7a n\u00f3 khi\u1ebfn n\u00f3 tr\u1edf th\u00e0nh l\u1ef1a ch\u1ecdn ph\u1ed5 bi\u1ebfn cho c\u00e1c t\u00e1c v\u1ee5 d\u1ef1a tr\u00ean v\u0103n b\u1ea3n kh\u00e1c nhau v\u00e0 nh\u1eefng ti\u1ebfn b\u1ed9 li\u00ean t\u1ee5c trong c\u00f4ng ngh\u1ec7 d\u1ef1 ki\u1ebfn s\u1ebd n\u00e2ng cao h\u01a1n n\u1eefa kh\u1ea3 n\u0103ng c\u1ee7a n\u00f3 trong t\u01b0\u01a1ng lai. Khi c\u00e1c doanh nghi\u1ec7p v\u00e0 nh\u00e0 nghi\u00ean c\u1ee9u ti\u1ebfp t\u1ee5c t\u1eadn d\u1ee5ng ti\u1ec1m n\u0103ng t\u01b0\u01a1ng t\u1ef1 c\u1ee7a Cosine, c\u00e1c m\u00e1y ch\u1ee7 proxy nh\u01b0 OneProxy s\u1ebd \u0111\u00f3ng m\u1ed9t vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c h\u1ed7 tr\u1ee3 c\u00e1c \u1ee9ng d\u1ee5ng n\u00e0y \u0111\u1ed3ng th\u1eddi \u0111\u1ea3m b\u1ea3o truy c\u1eadp Internet \u1ea9n danh v\u00e0 an to\u00e0n.<\/p>","protected":false},"featured_media":468030,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-476450","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Cosine Similarity: A Comprehensive Guide<\/mark>","faq_items":[{"question":"What is Cosine similarity?","answer":"<p>Cosine similarity is a mathematical concept used to measure the similarity between two vectors in a multi-dimensional space. It is commonly applied in text analysis, recommendation systems, and information retrieval tasks.<\/p>"},{"question":"How does Cosine similarity work?","answer":"<p>Cosine similarity calculates the cosine of the angle between two vectors, representing the documents being compared. It ranges from -1 to 1, where -1 indicates complete dissimilarity, 1 indicates absolute similarity, and 0 indicates orthogonality (no similarity).<\/p>"},{"question":"What are the key features of Cosine similarity?","answer":"<p>Cosine similarity offers scale invariance, efficiency, interpretability, and the ability to measure textual semantic similarity.<\/p>"},{"question":"What types of Cosine similarity exist?","answer":"<p>There are two primary types: Classic Cosine Similarity, which uses TF-IDF representation, and Binary Cosine Similarity, which utilizes binary vectors.<\/p>"},{"question":"How can Cosine similarity be used?","answer":"<p>Cosine similarity finds applications in various fields, including information retrieval, document clustering, collaborative filtering, and plagiarism detection.<\/p>"},{"question":"What challenges does Cosine similarity face?","answer":"<p>Cosine similarity may encounter issues with sparsity and language dependence in certain scenarios. Techniques like dimensionality reduction and word embeddings can address these challenges.<\/p>"},{"question":"How does Cosine similarity compare to other similarity measures?","answer":"<p>Cosine similarity is distinct from Jaccard similarity and Euclidean distance in terms of range, applicability, dimensionality, and computation.<\/p>"},{"question":"What are the future perspectives of Cosine similarity?","answer":"<p>As technology advances, Cosine similarity is expected to remain a valuable tool with enhanced efficiency and accuracy in similarity calculations.<\/p>"},{"question":"How are proxy servers associated with Cosine similarity?","answer":"<p>While proxy servers like OneProxy don't directly utilize Cosine similarity, they can support applications that involve text comparison and content-based filtering, such as recommendation systems and information retrieval tasks. They also ensure secure internet access during these operations.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/476450","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/476450\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media\/468030"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media?parent=476450"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}