"

\u5f15\u8a00

\n\n

\u5728\u4eba\u5de5\u667a\u80fd\u4ece\u5b9e\u9a8c\u5ba4\u8d70\u5411\u5de5\u4e1a\u843d\u5730\u7684\u8fc7\u7a0b\u4e2d\uff0c\u5411\u91cf\u6570\u636e\u5e93\uff08Vector Database\uff09\u5df2\u6210\u4e3a\u4e0d\u53ef\u6216\u7f3a\u7684\u5e95\u5c42\u57fa\u7840\u8bbe\u65bd\u3002\u4ece\u5927\u8bed\u8a00\u6a21\u578b\u7684\u68c0\u7d22\u589e\u5f3a\u751f\u6210\uff08RAG\uff09\u5230\u56fe\u50cf\u641c\u7d22\u3001\u63a8\u8350\u7cfb\u7edf\u548c\u5f02\u5e38\u68c0\u6d4b\uff0c\u5411\u91cf\u6570\u636e\u5e93\u627f\u8f7d\u7740\u5c06\u975e\u7ed3\u6784\u5316\u6570\u636e\u6620\u5c04\u5230\u9ad8\u7ef4\u8bed\u4e49\u7a7a\u95f4\u540e\u7684\u5b58\u50a8\u4e0e\u68c0\u7d22\u4efb\u52a1\u3002\u4e0e\u4f20\u7edf\u5173\u7cfb\u578b\u6570\u636e\u5e93\u7684\u7cbe\u786e\u5339\u914d\u4e0d\u540c\uff0c\u5411\u91cf\u6570\u636e\u5e93\u7684\u6838\u5fc3\u80fd\u529b\u662f\u8fd1\u4f3c\u6700\u8fd1\u90bb\u641c\u7d22\uff08Approximate Nearest Neighbor, ANN\uff09\u2014\u2014\u5728\u6570\u767e\u4e07\u751a\u81f3\u6570\u5341\u4ebf\u4e2a\u9ad8\u7ef4\u5411\u91cf\u4e2d\uff0c\u5728\u6beb\u79d2\u7ea7\u65f6\u95f4\u5185\u627e\u5230\u4e0e\u67e5\u8be2\u5411\u91cf\u6700\u76f8\u4f3c\u7684 Top-K \u4e2a\u7ed3\u679c\u3002

\n\n

\u672c\u6587\u5c06\u4ece\u5411\u91cf\u5d4c\u5165\u7684\u6570\u5b66\u672c\u8d28\u51fa\u53d1\uff0c\u7cfb\u7edf\u68b3\u7406 ANN \u7b97\u6cd5\u7684\u6f14\u8fdb\u8def\u5f84\uff08\u4ece\u66b4\u529b\u641c\u7d22\u5230\u57fa\u4e8e\u56fe\u7684\u65b9\u6cd5\uff09\uff0c\u6df1\u5165\u5206\u6790\u5de5\u4e1a\u7ea7\u5411\u91cf\u6570\u636e\u5e93\u7684\u67b6\u6784\u8bbe\u8ba1\u8981\u70b9\uff0c\u5e76\u901a\u8fc7\u5b9e\u9645\u4ee3\u7801\u793a\u4f8b\u5c55\u793a\u5982\u4f55\u6784\u5efa\u4e00\u4e2a\u751f\u4ea7\u53ef\u7528\u7684\u5411\u91cf\u68c0\u7d22\u7cfb\u7edf\u3002

\n\n

\u4e00\u3001\u5411\u91cf\u5d4c\u5165\u7684\u6570\u5b66\u57fa\u7840

\n\n

1.1 \u4ece\u9ad8\u7ef4\u7a7a\u95f4\u5230\u8bed\u4e49\u7a7a\u95f4

\n\n

\u5411\u91cf\u5d4c\u5165\uff08Embedding\uff09\u7684\u6838\u5fc3\u601d\u60f3\u662f\uff1a\u5c06\u6587\u672c\u3001\u56fe\u50cf\u3001\u97f3\u9891\u7b49\u975e\u7ed3\u6784\u5316\u7684\u5bf9\u8c61\u901a\u8fc7\u4e00\u4e2a\u6620\u5c04\u51fd\u6570 f: X \u2192 \u211d\u1d48 \u8f6c\u6362\u5230 d \u7ef4\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u4e2d\uff0c\u4f7f\u5f97\u8bed\u4e49\u76f8\u4f3c\u7684\u5bf9\u8c61\u5728\u7a7a\u95f4\u4e2d\u7684\u8ddd\u79bb\u66f4\u8fd1\u3002\u5e38\u7528\u7684\u8ddd\u79bb\u5ea6\u91cf\u5305\u62ec\uff1a

\n\n
    \n
  • \u6b27\u51e0\u91cc\u5f97\u8ddd\u79bb\uff08L2\uff09\uff1ad(x,y) = \u221a(\u03a3(x\u1d62 - y\u1d62)\u00b2)
  • \n
  • \u4f59\u5f26\u76f8\u4f3c\u5ea6\uff1acos(x,y) = (x\u00b7y) / (||x|| \u00b7 ||y||)
  • \n
  • \u5185\u79ef\u8ddd\u79bb\uff1aip(x,y) = x\u00b7y\uff08\u9002\u5408\u5f52\u4e00\u5316\u5411\u91cf\uff09
  • \n
  • \u66fc\u54c8\u987f\u8ddd\u79bb\uff08L1\uff09\uff1ad(x,y) = \u03a3|x\u1d62 - y\u1d62|
  • \n
\n\n

1.2 \u7ef4\u5ea6\u8bc5\u5492\u4e0e\u7ef4\u5ea6\u7ea6\u51cf

\n\n

\u5f53\u7ef4\u5ea6 d \u8d85\u8fc7\u51e0\u5341\u7ef4\u65f6\uff0c\u4f20\u7edf\u7684\u7a7a\u95f4\u7d22\u5f15\u7ed3\u6784\uff08\u5982 KD-Tree\u3001R-Tree\uff09\u4f1a\u906d\u9047\"\u7ef4\u5ea6\u8bc5\u5492\"\uff08Curse of Dimensionality\uff09\u2014\u2014\u5728\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u6240\u6709\u70b9\u5bf9\u4e4b\u95f4\u7684\u8ddd\u79bb\u8d8b\u4e8e\u76f8\u540c\uff0c\u57fa\u4e8e\u6811\u5f62\u7ed3\u6784\u7684\u526a\u679d\u7b56\u7565\u51e0\u4e4e\u5931\u6548\u3002\u5b9e\u9a8c\u8868\u660e\uff0c\u5f53 d

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