{"id":19505,"date":"2025-08-31T15:45:32","date_gmt":"2025-08-31T07:45:32","guid":{"rendered":"https:\/\/www.orczhou.com\/?p=19505"},"modified":"2025-12-16T15:56:29","modified_gmt":"2025-12-16T07:56:29","slug":"understanding-word-embedding-some-way","status":"publish","type":"post","link":"https:\/\/www.orczhou.com\/index.php\/2025\/08\/understanding-word-embedding-some-way\/","title":{"rendered":"Word Embedding \u7684\u53ef\u89e3\u91ca\u6027\u63a2\u7d22"},"content":{"rendered":"\n\n\n\n<p>\u8fd9\u5927\u6982\u662f\u4e00\u4e2a\u6709\u8da3\u3001\u4e5f\u7565\u6df1\u523b\u7684\u53d1\u73b0\u3002<\/p>\n\n\n\n<p>Word Embedding\u662f\u6bd4\u8f83\u62bd\u8c61\u7684\uff0c\u4f46\u662f\u8fd9\u4e9b\u62bd\u8c61\u80cc\u540e\u662f\u4e00\u4e9b\u201c\u5177\u8c61\u201d\u7684\u542b\u4e49\u7684\uff0c\u672c\u6587\u901a\u8fc7\u4e00\u4e9b\u7b80\u5355\u7684\u8ba1\u7b97\uff08\u53d8\u6362\uff09\u6765\u5c06Embedding\u7684\u67d0\u4e9b\u7ef4\u5ea6\/\u5c5e\u6027\u5177\u8c61\u5316\u3002\u5177\u4f53\u7684\uff0c\u672c\u6587\u5c55\u793a\u4e86\u5728Embedding\u7a7a\u95f4\u4e2d\uff0c\u627e\u5230\u4e00\u4e2a\u4ee3\u8868\u201c\u52a8\u7269\u201d\u5c5e\u6027\u7684\u65b9\u5411\u3002\u611f\u5174\u8da3\u7684\u8bdd\uff0c\u53ef\u4ee5\u901a\u8fc7\u8fd9\u4e2a\u7b80\u5355\u7684\u65b9\u6cd5\uff0c\u627e\u5230\u4f60\u611f\u5174\u8da3\u7684\u5c5e\u6027\u65b9\u5411\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">TL;DR<\/h3>\n\n\n\n<p>\u901a\u5e38\uff0c\u5728\u67d0\u4e2a\u5177\u4f53\u7684Word Embedding\u5b9e\u73b0\u4e2d\uff0c\u5148\u7ed9\u51fa\u4e00\u7ec4\u5177\u6709\u201c\u5171\u540c\u5c5e\u6027\u201d\u7684\u8bcd\u8bed\uff0c\u7136\u540e\u8ba1\u7b97\u8fd9\u7ec4\u8bcd\u8bedEmbedding\u5411\u91cf\u7684\u5e73\u5747\u65b9\u5411\uff0c\u5c31\u53ef\u4ee5\u4ee3\u8868\u8fd9\u4e2a\u201c\u5171\u540c\u5c5e\u6027\u201d\u3002<\/p>\n\n\n\n<p>\u4f8b\u5982\uff0c\u627e\u5230\u4e00\u7ec4\u201c\u52a8\u7269\u201d\uff0c\u7136\u540e\u5bf9\u8fd9\u4e9b\u8bcd\u8bed\u7684Embedding\u5411\u91cf\u8ba1\u7b97\u5e73\u5747\u65b9\u5411\uff0c\u90a3\u4e48\u8fd9\u4e2a\u65b9\u5411\u5c31\u662f\u201c\u52a8\u7269\u201d\u8fd9\u4e2a\u5c5e\u6027\u7684\u65b9\u5411\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6982\u8ff0<\/h3>\n\n\n\n\n\n\n<p>\u5982\u679c\u4f60\u4e5f\u5c1d\u8bd5\u8fc7\u53bb\u7406\u89e3 Embedding \u5404\u4e2a\u7ef4\u5ea6\u7684\u542b\u4e49\u7684\u8bdd\uff0c\u5927\u6982\u90fd\u542c\u8fc7\u8fd9\u6837\u4e00\u79cd\u8bf4\u6cd5\uff1aEmbedding\u6bcf\u4e2a\u7ef4\u5ea6\u53ef\u4ee5\u7406\u89e3\u4e3a\u8fd9\u4e2a\u8bcd\u8bed\u7684\u67d0\u79cd\u5c5e\u6027\uff0c\u4f8b\u5982\uff0c\u201c\u6027\u522b\u5c5e\u6027\u201d\u3001\u201c\u7687\u5ba4\u76f8\u5173\u5ea6\u201d\u7b49\uff0c\u8fd9\u662f\u6700\u4e3a\u7ecf\u5178\u7684<code>man - woman = king - queue<\/code>\u7684\u4f8b\u5b50\u4e2d\u7684\u4e00\u4e9b\u89e3\u91ca\u3002<\/p>\n\n\n\n<p>\u5f53\u4f60\u771f\u7684\u62ff\u5230\u4e00\u4e2a\u8bcd\u8bed\u7684 Embedding \u7684\u65f6\u5019\uff0c\u5b83\u53ef\u80fd\u6709768\u7ef4\uff0c\u4f46\u662f\uff0c\u4f3c\u4e4e\u6ca1\u6709\u4e00\u4e2a\u7ef4\u5ea6\u6709\u4e0a\u8ff0\u7684\u6e05\u6670\u7684\u5c5e\u6027\u542b\u4e49\u3002\u800c\u5b9e\u9645\u4e0a\uff0c\u8fd9\u4e9b\u5c5e\u6027\u542b\u4e49\u662f\u786e\u5b9e\u5b58\u5728\u7684\uff0c\u53ea\u662f\u8fd9\u4e9b\u5c5e\u6027\u65b9\u5411\u5e76\u4e0d\u5b58\u5728\u4e8e\u201c\u6807\u51c6\u57fa\u201d\u7684\u65b9\u5411\u4e0a\u3002<\/p>\n\n\n\n<p>\u90a3\u5982\u679c\u5b58\u5728\uff0c\u6211\u4eec\u5e94\u8be5\u5982\u4f55\u627e\u5230\u8fd9\u4e2a\u65b9\u5411\u5462\uff1f\u672c\u6587\u5c55\u793a\u5e76\u9a8c\u8bc1\u4e86\u4e00\u4e2a\u975e\u5e38\u7b80\u5355\u7684\u65b9\u6cd5\uff0c\u8ba9\u4f60\u5feb\u901f\u627e\u5230\u67d0\u79cd\u5c5e\u6027\u7684\u65b9\u5411\uff0c\u5e76\u4e14\u8fdb\u884c\u4e00\u4e9b\u9a8c\u8bc1\u3002\u4ece\u800c\u53ef\u4ee5\u5927\u5927\u52a0\u6df1\u5bf9\u4e8e Embedding \u7684\u7406\u89e3\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5bfb\u627e\u67d0\u4e2a\u5173\u5fc3\u7684\u65b9\u5411<\/h3>\n\n\n\n<p>\u8fd9\u91cc\u5c55\u793a\u4e86\u4ee5\u5bfb\u627e\u201c\u52a8\u7269\u201d\u5c5e\u6027\u65b9\u5411\u4e3a\u4f8b\uff0c\u5c55\u793a\u5982\u4f55\u5bfb\u627e\u5e76\u9a8c\u8bc1\u8be5\u65b9\u5411\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u5217\u51fa\u6700\u5177\u4ee3\u8868\u6027\u7684\u8bcd\u8bed<\/h4>\n\n\n\n<p>\u6211\u4eec\u8fd9\u6837\u8003\u8651\u8fd9\u4e2a\u95ee\u9898\uff0c\u5982\u679c\u6709\u4e00\u4e2a\u65b9\u5411\u8868\u793a\u4e00\u4e2a\u8bcd\u8bed\u7684\u201c\u52a8\u7269\u201d\u5c5e\u6027\uff0c\u90a3\u4e48\u8fd9\u4e2a\u65b9\u5411\u4f1a\u662f\u54ea\u4e2a\u65b9\u5411\uff1f\u8fd9\u91cc\u4ee5<code>all-MiniLM-L6-v2<\/code>\u6a21\u578b\u63d0\u4f9b\u7684<code>Sentence Embedding<\/code>\u4e3a\u4f8b\uff0c\u6211\u770b\u770b\u5982\u4f55\u627e\u5230\u8be5Embedding\u6240\u5904\u7684\u5411\u91cf\u7a7a\u95f4\u4e2d\u6700\u53ef\u80fd\u4ee3\u8868\u201c\u52a8\u7269\u201d\u5c5e\u6027\u7684\u65b9\u5411\u662f\u54ea\u4e2a\uff1f\u5177\u4f53\u7684\u65b9\u6cd5\u63cf\u8ff0\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9996\u5148\uff0c\u627e\u5230\u88ab\u8ba4\u4e3a\u6700\u5178\u578b\u7684\u4e0e\u201c\u52a8\u7269\u201d\u5c5e\u6027\u76f8\u5173\u7684\u8bcd\u8bed\\( n \\)\u4e2a\uff0c\u8fd9\u91cc\u53d6\\( n=50 \\)<\/li>\n\n\n\n<li>\u7136\u540e\u8ba1\u7b97\u4e0a\u8ff0\\( n \\)\u4e2a\u8bcd\u8bed\u7684\u5e73\u5747\u65b9\u5411 <code>avg_vector<\/code>\uff0c\u8be5\u65b9\u5411\u5219\u8ba4\u4e3a\u8981\u5bfb\u627e\u7684\u65b9\u5411<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u91cc\uff0c\u7ed9\u51fa\u768450\u4e2a\u52a8\u7269\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"python\" class=\"language-python\">animals = [\n    \"tiger\", \"lion\", \"elephant\", \"giraffe\", \"zebra\",\n    \"rhinoceros\", \"hippopotamus\",\"crocodile\", \"monkey\",\n    \"panda\", \"koala\", \"kangaroo\",\"whale\", \"dolphin\",\n    \"seal\", \"penguin\", \"shark\", \"snake\", \"lizard\",\n    \"turtle\", \"frog\", \"butterfly\", \"bee\", \"ant\", \"eagle\",\n    \"sparrow\", \"pigeon\", \"parrot\", \"owl\", \"duck\", \"chicken\",\n    \"dog\", \"cat\", \"pig\", \"cow\", \"sheep\", \"horse\", \"donkey\",\n    \"rabbit\", \"squirrel\", \"fox\", \"wolf\", \"bear\", \"deer\",\n    \"hedgehog\", \"bat\", \"mouse\", \"chameleon\", \"snail\", \"jellyfish\"\n]<\/code><\/pre>\n\n\n\n<h4 class=\"wp-block-heading\">\u8ba1\u7b97Embedding\u7684\u5e73\u5747\u65b9\u5411<\/h4>\n\n\n\n<p>\u8be5\u5e73\u5747\u65b9\u5411\uff0c\u5373\u4e3a\u6211\u4eec\u8981\u5bfb\u627e\u7684\u201c\u52a8\u7269\u201d\u5c5e\u6027\u65b9\u5411\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"python\" class=\"language-python\">animals_embeddings = model.encode(animals)\navg_animals_embeddings = np.mean(animals_embeddings, axis=0)<\/code><\/pre>\n\n\n\n<h4 class=\"wp-block-heading\">\u9a8c\u8bc1\u8be5\u65b9\u5411<\/h4>\n\n\n\n<p>\u518d\u9009\u53d6\u4e24\u7ec4\u8bcd\uff0c\u4e00\u7ec4\u8ba4\u4e3a\u662f\u4e0e\u201c\u52a8\u7269\u201d\u975e\u5e38\u76f8\u5173\u7684\u8bcd\uff0c\u53e6\u4e00\u7ec4\u5219\u662f\u4e0e\u52a8\u7269\u65e0\u5173\u7684\u8bcd\u8bed\u3002\u7136\u540e\u5206\u522b\u8ba1\u7b97\u8fd9\u4e24\u7ec4\u8bcd\u8bed\u5728\u4e0a\u8ff0\u65b9\u5411<code>avg_vector<\/code>\u7684\u6295\u5f71\u503c\u3002\u89c2\u5bdf\u6295\u5f71\u503c\uff0c\u662f\u5426\u7b26\u5408\u9884\u671f\u3002<\/p>\n\n\n\n<p>\u8fd9\u91cc\u9009\u62e9\u7684\u4e24\u7ec4\u8bcd\u8bed\u5206\u522b\u662f\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e0e\u52a8\u7269\u975e\u5e38\u76f8\u5173\u7684\uff1a&#8221;Camel&#8221;, &#8220;Gorilla&#8221;, &#8220;Cheetah&#8221;<\/li>\n\n\n\n<li>\u4e0e\u52a8\u7269\u65e0\u5173\u7684\uff1a&#8221;Dream&#8221;, &#8220;Chair&#8221;, &#8220;Mathematics&#8221;<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\u8ba1\u7b97\u6295\u5f71\u5e76\u53ef\u89c6\u5316<\/h4>\n\n\n\n<p>\u5177\u4f53\u7684\u7a0b\u5e8f\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"python\" class=\"language-python\">animals_words    = [\"Camel\", \"Gorilla\", \"Cheetah\"]\nun_animals_words = [\"Dream\", \"Chair\", \"Mathematics\"]\n\nfor word_list in (animals_words,un_animals_words):\n    projection_scores = np.dot(model.encode(word_list),\n                              avg_animals_embeddings)\n    results.update({word: score for word,\n                    score in zip(word_list, projection_scores)})\n\nfor word, score in results.items():\n    print(f\"'{word}': {score:.4f}\")\nprint(np.round(avg_animals_embeddings[:10], 4))<\/code><\/pre>\n\n\n\n<p>\u6295\u5f71\u7ed3\u679c\u4e3a\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code class=\"\">'Camel': 0.3887\n'Gorilla': 0.4186\n'Cheetah': 0.3797\n'Dream': 0.2450\n'Chair': 0.2823\n'Mathematics': 0.1972<\/code><\/pre>\n\n\n\n<p>\u5728\u5b9e\u6570\u8f74\u4e0a\u7ed8\u5236\u4e0a\u8ff0\u4e24\u7ec4\u8bcd\u8bed\u7684\u6295\u5f71\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"257\" src=\"https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-11-1024x257.png\" alt=\"\" class=\"wp-image-19516\" style=\"width:796px;height:auto\" srcset=\"https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-11-1024x257.png 1024w, https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-11-300x75.png 300w, https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-11-768x193.png 768w, https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-11.png 1218w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u975e\u5e38\u660e\u663e\u7684\u53ef\u4ee5\u770b\u5230\uff0c\u4e0a\u8ff0\u7684<code>avg_vector<\/code>\u65b9\u5411\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u4ee3\u8868\u4e86\u4e00\u4e2a\u8bcd\u8bed\u7684\u201c\u52a8\u7269\u201d\u5c5e\u6027\uff1a\u5373\u4e0e\u52a8\u7269\u5c5e\u6027\u76f8\u5173\u7684\u8bcd\u8bed\u5728\u8be5\u65b9\u5411\u7684\u6295\u5f71\u5927\uff0c\u65e0\u5173\u7684\u8bcd\u8bed\u5728\u8be5\u65b9\u5411\u7684\u6295\u5f71\u5c0f\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u539f\u7406\u89e3\u91ca<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u6982\u8ff0<\/h4>\n\n\n\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u4e00\u7ec4\u8bcd\u8bedEmbedding\u7684\u201c\u5e73\u5747\u5411\u91cf\u201d\uff08centroids of word embeddings\uff09\uff0c\u5219\u67d0\u79cd\u7a0b\u5ea6\u7684\u4ee3\u8868\u8fd9\u7ec4\u8bcd\u8bed\u7684\u201c\u8bed\u4e49\u4e2d\u5fc3\u201d\u3002\u5982\u679c\u8fd9\u7ec4\u8bcd\u6709\u67d0\u4e9b\u5171\u6027\uff0c\u90a3\u4e48\u8fd9\u4e2a\u5e73\u5747\u5411\u91cf\uff0c\u5219\u53ef\u80fd\u5c31\u662f\u8fd9\u4e2a\u5171\u6027\u7684\u4ee3\u8868\u3002<\/p>\n\n\n\n<p>\u5728\u4e0a\u8ff0\u7684\u4f8b\u5b50\u4e2d\uff0c\u523b\u610f\u5730\u7ed9\u51fa\u7684\u4e00\u7ec4\u8bcd\u8bed\u90fd\u662f\u201c\u52a8\u7269\u201d\u540d\u79f0\u3002\u90a3\u4e48\uff0c\u8fd9\u4e2a\u201c\u5e73\u5747\u5411\u91cf\u201d\u5219\u6bd4\u8f83\u6709\u53ef\u80fd\u4ee3\u8868\u4e86\u8fd9\u4e2a\u5411\u91cf\u7a7a\u95f4\u4e2d\u7684\u201c\u52a8\u7269\u201d\u5c5e\u6027\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u6570\u5b66\u63a8\u5bfc<\/h4>\n\n\n\n<p>\u8fd9\u6837\u8003\u8651\u8fd9\u4e2a\u95ee\u9898\uff1a\u73b0\u5728\u7ed9\u51fa\u7684 \\( n \\)  \u4e2a\u5411\u91cf \\( \\alpha_1, \\dots , \\alpha_n  \\)\uff0c\u627e\u51fa\u4e00\u4e2a\u5355\u4f4d\u5411\u91cf \\( \\xi \\) \u4f7f\u5f97 \\( n \\)  \u4e2a\u5411\u91cf\u5728 \\( \\xi \\) \u5411\u91cf\u65b9\u5411\u4e0a\u7684\u6295\u5f71\u503c\u7684\u548c\u6700\u5927\u3002<\/p>\n\n\n\n<p>\u8fd9\u91cc\u53d6 \\( \\bar{\\alpha} = \\frac{\\sum\\limits_{i=1}^{n}\\alpha_i}{n} \\) <\/p>\n\n\n\n<p>\u76ee\u6807\u51fd\u6570 \\( S =  \\sum\\limits_{i=1}^{n}(\\alpha_i \\cdot  \\xi ) = \\sum\\limits_{i=1}^{n}(\\alpha_i) \\cdot  \\xi = n \\bar{\\alpha} \\cdot \\xi = n \\| \\bar{\\alpha}\\| \\| \\xi \\| \\cos\\theta \\)  <\/p>\n\n\n\n<p>\u8fd9\u91cc \\( n \\)\u3001\\( \\bar{\\alpha} \\)\u90fd\u662f\u7ed9\u5b9a\u503c\uff0c\u800c \\( \\| \\xi \\| = 1 \\)\uff0c\u6240\u4ee5\u8fd9\u91cc \\( \\cos\\theta \\)  \u53d6\u6700\u5927\u503c\u65f6\uff0c\u4e0a\u8ff0\u7684\u76ee\u6807\u51fd\u6570 \\( S \\) \u53d6\u6700\u5927\u503c\u3002<\/p>\n\n\n\n<p>\u5373\uff1a\\( \\theta = 0 \\) \u65f6\uff0c \\( S \\) \u53d6\u6700\u5927\u503c\u3002\u5373\u5f53 \\( \\xi \\) \u4e0e \\( \\bar{\\alpha} \\) \u65b9\u5411\u76f8\u540c\u65f6\uff0c\u5373 \\( \\xi = \\frac{\\bar{\\alpha}}{\\|\\bar{\\alpha}\\|} \\) \uff0c\u6240\u6709\u5411\u91cf\u7684\u6295\u5f71\u503c\u7684\u548c\u6700\u5927\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u6295\u5f71\u8ba1\u7b97<\/h4>\n\n\n\n<p>\u592a\u4e45\u4e0d\u78b0\u7ebf\u6027\u4ee3\u6570\u4e86\uff0c\u5bf9\u4e8e\u57fa\u672c\u8fd0\u7b97\u90fd\u4e0d\u662f\u5f88\u719f\u6089\u4e86\u3002\u5411\u91cf \\( \\alpha \\) \u5728 \\( \\beta \\) \u65b9\u5411\u4e0a\u7684\u6295\u5f71\u957f\u5ea6\uff0c\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n<p>$$ proj = \\frac{\\alpha \\cdot \\beta}{\\|\\beta\\|} $$<\/p>\n\n\n\n<p>\u8bc1\u660e\u6bd4\u8f83\u7b80\u5355\uff0c\u8fd9\u91cc\u4e0d\u518d\u8d58\u8ff0\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u5411\u91cf\u7684\u5e73\u5747\u65b9\u5411\u4e0e\u4e3b\u6210\u5206\u65b9\u5411<\/h4>\n\n\n\n<p>\u5f53\u7ed9\u51fa\u4e00\u7ec4\u5411\u91cf\uff0c\u9762\u5bf9\u4e0a\u8ff0\u95ee\u9898\uff0c\u6bd4\u8f83\u5bb9\u6613\u8054\u60f3\u5230\u8fd9\u7ec4\u5411\u91cf\u7684\u201c\u4e3b\u6210\u5206\u5206\u6790\u201d\u7684\u7b2c\u4e00\u4e2a\u7ef4\u5ea6\u3002\u90a3\u4e48\uff0c\u4e0a\u8ff0\u7684\u5e73\u5747\u5411\u91cf\u548c\u4e3b\u6210\u5206\u5206\u6790\u7684\u7b2c\u4e00\u4e2a\u7ef4\u5ea6\u6709\u4ec0\u4e48\u5173\u7cfb\u5462\uff1f\u56de\u7b54\u662f\uff1a\u6ca1\u6709\u592a\u5927\u7684\u5173\u7cfb\u3002<\/p>\n\n\n\n<p>\u53ef\u4ee5\u770b\u4e0b\u9762\u4e09\u4e2a\u56fe\uff1a<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"686\" height=\"701\" src=\"https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-12.png\" alt=\"\" class=\"wp-image-19537\" srcset=\"https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-12.png 686w, https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-12-294x300.png 294w\" sizes=\"auto, (max-width: 686px) 100vw, 686px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"678\" height=\"701\" src=\"https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-13.png\" alt=\"\" class=\"wp-image-19538\" srcset=\"https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-13.png 678w, https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-13-290x300.png 290w\" sizes=\"auto, (max-width: 678px) 100vw, 678px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"689\" height=\"701\" src=\"https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-14.png\" alt=\"\" class=\"wp-image-19539\" srcset=\"https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-14.png 689w, https:\/\/www.orczhou.com\/wp-content\/uploads\/2025\/08\/image-14-295x300.png 295w\" sizes=\"auto, (max-width: 689px) 100vw, 689px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p>\u4e0a\u8ff0\u4e09\u4e2a\u4e8c\u7ef4\u5e73\u9762\u4e2d\u7684\u70b9\u7684\u5e73\u5747\u65b9\u5411\u5747\u4e3a\u7ea2\u8272\uff0c\u5373(1,1)\uff1b\u4f46\u662fPCA\u7684\u7b2c\u4e00\u65b9\u5411\u5219\u5404\u6709\u4e0d\u540c\uff0c\u6709\u65f6\u5019\u4e0e\u5e73\u5747\u5411\u91cf\u76f8\u540c\u3001\u6709\u65f6\u5019\u5782\u76f4\uff0c\u6709\u65f6\u5019\u76f8\u4ea4\u3002\u603b\u4e4b\u662f\u6ca1\u4ec0\u4e48\u5173\u7cfb\u3002<\/p>\n\n\n\n<p>\u53ef\u4ee5\u770b\u5230\uff0c\u5e73\u5747\u5411\u91cf\u65f6\u5728\u5f53\u524d\u7684\u201c\u57fa\u201d\u4e0b\u8ba1\u7b97\u83b7\u5f97\u3002\u800c\u4e3b\u65b9\u5411\u5206\u6790\u7684\u65b9\u5411\uff0c\u5219\u9996\u5148\u5c31\u4e0e\u539f\u70b9\u6ca1\u6709\u5173\u7cfb\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u66f4\u6df1\u5c42\u6b21\u7684\u7406\u89e3<\/h3>\n\n\n\n<p>\u73b0\u5728\u7684Embedding\u7b97\u6cd5\uff0c\u90fd\u662f\u57fa\u4e8e\u73b0\u5b9e\u4e16\u754c\u8bed\u6599\u5e93\u8bad\u7ec3\u800c\u6765\uff0c\u53cd\u5e94\u4e86\u4eba\u7c7b\u8ba4\u77e5\u4e2d\u201c\u8bed\u8a00\u201d\u4e0e\u73b0\u5b9e\u4e16\u754c\u7684\u5bf9\u5e94\u5173\u7cfb\u3002\u800c\u5728\u4eba\u7c7b\u7684\u8ba4\u77e5\u4e2d\uff0c\u8fd9\u4e2a\u4e16\u754c\u662f\u6709\u201c\u7ef4\u5ea6\u201d\u7684\uff0c\u6700\u4e3a\u76f4\u767d\u7684\u4f8b\u5b50\u5c31\u662f\uff1a\u6211\u4eec\u4f1a\u5c06\u8bcd\u8bed\u5212\u5206\u201c\u8912\u4e49\u8bcd\u201d\u3001\u201c\u8d2c\u4e49\u8bcd\u201d\u3002\u6b64\u5916\uff0c\u53ef\u80fd\u8fd8\u6709\uff1a\u52a8\u7269\u6027\u3001\u60c5\u611f\u5f3a\u70c8\u5ea6\u3001\u8bcd\u6027\u7b49\u3002\u90a3\u4e48\uff0c\u5728\u4eba\u7c7b\u8ba4\u77e5\u4e2d\u8fd9\u79cd\u201c\u8ba4\u77e5\u201d\u6709\u591a\u5c11\u4e2a\u7ef4\u5ea6\u5462\uff1f\u8fd9\u5176\u5b9e\u662f\u672a\u77e5\u7684\uff0c\u800c\u5404\u79cd<code>Embedding<\/code>\u7b97\u6cd5\u5219\u662f\u5728\u5c1d\u8bd5\u4f7f\u7528\u91cf\u5316\u7684\u65b9\u5f0f\u63cf\u8ff0\u8fd9\u4e9b\u7ef4\u5ea6\u3002<\/p>\n\n\n\n<p>\u4f46\u662f\uff0c\u5728\u5b9e\u9645\u8bad\u7ec3\u51fa\u7684\u5404\u79cdEmbedding\u5b9e\u73b0\uff0c\u4f8b\u5982\u4e00\u4e2a768\u7ef4\u7684Embedding\uff0c\u5176\u5355\u4f4d\u5411\u91cf\u65b9\u5411\uff0c\u4e0d\u592a\u53ef\u80fd\u662f\u4e0a\u8ff0\u7684\u4eba\u7c7b\u201c\u8ba4\u77e5\u201d\u7ef4\u5ea6\u3002\u5982\u679c\u628a\u8bad\u7ec3\u51fa\u6765\u7684Embedding\u7684\u5355\u4f4d\u5411\u91cf\u8bb0\u4e3a\uff1a\\( \\alpha_1, \\dots , \\alpha_n \\)\uff0c\u800c\u628a\u4eba\u7c7b\u8ba4\u77e5\u7684\u7ef4\u5ea6\u8bb0\u4e3a\uff1a \\( \\beta_1, \\dots , \\beta_n \\) \u3002<\/p>\n\n\n\n<p>\u90a3\u4e48\uff0c\u5219\u5b58\u5728\u4e00\u4e2a\u8fc7\u6e21\u77e9\u9635 $T$\uff0c\u53ef\u4ee5\u5b9e\u73b0\u4e0a\u8ff0\u5411\u91cf\u7a7a\u95f4<code>\u57fa<\/code>\u7684\u53d8\u6362\u3002<\/p>\n\n\n\n<p>\u53ef\u662f\uff0c\u73b0\u5b9e\u4e16\u754c\u6ca1\u6709\u90a3\u4e48\u7406\u60f3\u3002Embedding\u7a7a\u95f4\u786e\u5b9e\u7ed9\u51fa\u4e86\u4e00\u7ec4\u6b63\u4ea4\u57fa\uff0c\u4f46\u662f\u4eba\u7c7b\u8ba4\u8bc6\u5374\u5f88\u96be\u5bfb\u627e\u8fd9\u6837\u7684\u6b63\u4ea4\u57fa\uff0c\u4f8b\u5982\u201c\u52a8\u7269\u201d\u5c5e\u6027\u7684\u8bcd\u8bed\uff0c\u53ef\u80fd\u4f1a\u5e26\u6709\u201c\u60c5\u611f\u201d\u5c5e\u6027\uff0c\u4f8b\u5982\uff0c\u201c\u864e\u72fc\u4e4b\u8bcd\u201d\u7b49\uff0c\u90fd\u5e26\u6709\u67d0\u79cd\u60c5\u611f\u5c5e\u6027\u3002<\/p>\n\n\n\n<p>\u867d\u7136\uff0c\u8ba4\u77e5\u5f88\u96be\u627e\u5230\u6b63\u4ea4\u7684\u201c\u57fa\u201d\uff0c\u4f46\u662f\u627e\u5230\u67d0\u4e2a\u5177\u4f53\u7684\u5c5e\u6027\u65b9\u5411\uff0c\u5219\u53ef\u4ee5\u4f7f\u7528\u672c\u4e66\u7684\u65b9\u6cd5\u3002\u8fd9\u6b63\u662f\u672c\u6587\u6240\u63cf\u8ff0\u65b9\u6cd5\u7684\u5c40\u9650\u6027\u548c\u4ef7\u503c\u6240\u5728\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u8865\u5145\u8bf4\u660e<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u672c\u6587\u4e2d\uff0c\u6240\u8bf4\u7684Word Embedding\uff0c\u901a\u5e38\u662f\u6307Sentence Embedding\u4e2d\u7684Token Embedding\u3002\u5728\u8fd9\u91cc\uff0c\u65e0\u9700\u533a\u5206\u4e24\u8005\u3002<\/li>\n\n\n\n<li>\u5b9e\u9645\u7684\u60c5\u51b5\u66f4\u52a0\u590d\u6742\uff0c\u4f8b\u5982\u672c\u6587\u4e2d\u7684\u201c\u52a8\u7269\u201d\u5c5e\u6027\uff0c\u53ea\u662f\u8fd9\u4e9b\u8bcd\u6240\u4ee3\u8868\u7684\u201c\u52a8\u7269\u201d\u5c5e\u6027\u3002\u4ec0\u4e48\u662f\u771f\u6b63\u7684\u201c\u52a8\u7269\u201d\u5c5e\u6027\uff0c\u5e76\u4e0d\u5b58\u5728\u8fd9\u6837\u7684\u7cbe\u786e\u6982\u5ff5\u3002\u4eba\u7c7b\u8bed\u8a00\u4e2d\u7684\u201c\u52a8\u7269\u201d\u662f\u4e00\u4e2a\u62bd\u8c61\u7684\uff0c\u5e76\u6ca1\u6709\u6570\u5b57\u5316\u3001\u6570\u5b66\u5316\u7684\u7cbe\u786e\u5b9a\u4e49\u3002<\/li>\n\n\n\n<li>\u5b8c\u6574\u7684\u5b9e\u73b0\u4ee3\u7801\uff0c\u53c2\u8003\uff1a<a href=\"https:\/\/www.orczhou.com\/codes\/embedding_research_01.py.txt\">embedding_research_01.py<\/a>\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Word Embedding\u662f\u6bd4\u8f83\u62bd\u8c61\u7684\uff0c\u4f46\u662f\u8fd9\u4e9b\u62bd\u8c61\u80cc\u540e\u662f\u4e00\u4e9b\u201c\u5177\u8c61\u201d\u7684\u542b\u4e49\u7684\uff0c\u672c\u6587\u901a\u8fc7\u4e00\u4e9b\u7b80\u5355\u7684\u8ba1\u7b97\uff08\u53d8\u6362\uff09\u6765\u5c06Embedding\u7684\u67d0\u4e9b\u7ef4\u5ea6\/\u5c5e\u6027\u5177\u8c61\u5316\u3002\u5177\u4f53\u7684&#8230;<\/p>\n","protected":false},"author":1,"featured_media":21427,"comment_status":"open","ping_status":"closed","sticky":false,"template":"wp-custom-template-a-1440-px-width-template","format":"standard","meta":{"_eb_attr":"","inline_featured_image":false,"_tocer_settings":[],"footnotes":""},"categories":[4,137],"tags":[],"class_list":["post-19505","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-code-detail","category-learning-more"],"_links":{"self":[{"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/posts\/19505","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/comments?post=19505"}],"version-history":[{"count":45,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/posts\/19505\/revisions"}],"predecessor-version":[{"id":21426,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/posts\/19505\/revisions\/21426"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/media\/21427"}],"wp:attachment":[{"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/media?parent=19505"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/categories?post=19505"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.orczhou.com\/index.php\/wp-json\/wp\/v2\/tags?post=19505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}