\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u306e\u6570\u5b66\u7684\u5b9a\u7fa9\u304b\u3089GIS\u3084\u6a5f\u68b0\u5b66\u7fd2\u3067\u306e\u5b9f\u52d9\u7684\u306a\u4f7f\u3044\u65b9\u3001\u9ad8\u6b21\u5143\u30c7\u30fc\u30bf\u3067\u306e\u843d\u3068\u3057\u7a74\uff08\u8ddd\u96e2\u96c6\u4e2d\uff09\u306e\u6700\u65b0\u7814\u7a76\u3001\u8fd1\u4f3c\u6700\u8fd1\u508d\uff08ANN\uff09\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u73fe\u72b6\u307e\u3067\u3001\u5b9f\u52d9\u8005\u3068\u7814\u7a76\u8005\u306e\u4e21\u65b9\u304c\u300c\u3053\u3053\u3067\u3057\u304b\u5f97\u3089\u308c\u306a\u3044\u300d\u6d1e\u5bdf\u3092\u5f97\u3089\u308c\u308b\u3088\u3046\u306b\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n
\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u306f\u300c2\u70b9\u9593\u306e\u76f4\u7dda\u8ddd\u96e2\u300d\u3068\u3044\u3046\u76f4\u611f\u7684\u306a\u5b9a\u7fa9\u306e\u305f\u3081\u3001\u30c7\u30fc\u30bf\u89e3\u6790\u3084\u5730\u7406\u60c5\u5831\u51e6\u7406\u3001\u6a5f\u68b0\u5b66\u7fd2\u306e\u51fa\u767a\u70b9\u3068\u3057\u3066\u5e83\u304f\u4f7f\u308f\u308c\u3066\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u4e00\u65b9\u3067\u3001\u5b9f\u52d9\u3067\u30cf\u30de\u308a\u3084\u3059\u3044\u843d\u3068\u3057\u7a74\uff08\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u30fb\u6295\u5f71\u8aa4\u5dee\u30fb\u6b21\u5143\u306e\u546a\u3044\uff09\u3084\u3001\u30b9\u30b1\u30fc\u30eb\u306e\u5927\u304d\u306a\u8fd1\u4f3c\u691c\u7d22\u6280\u8853\u306e\u767b\u5834\u306b\u3088\u308a\u300c\u4f7f\u3044\u3069\u3053\u308d\u300d\u3092\u6b63\u3057\u304f\u898b\u6975\u3081\u308b\u3053\u3068\u304c\u91cd\u8981\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u672c\u7a3f\u3067\u306f\u6570\u5b66\u7684\u57fa\u790e\u304b\u3089\u6700\u65b0\u306e\u5b9f\u88c5\u30fb\u7814\u7a76\u52d5\u5411\u307e\u3067\u3001\u5b9f\u52d9\u3067\u5f79\u7acb\u3064\u89b3\u70b9\u3092\u91cd\u70b9\u7684\u306b\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n
x,y\u2208Rn\\mathbf{x},\\mathbf{y}\\in\\mathbb{R}^nx,y\u2208Rn \u306b\u5bfe\u3057\u3066\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u306f<\/p>\r\n
d(x,y)=\u2211i=1n(xi\u2212yi)2d(\\mathbf{x},\\mathbf{y})=\\sqrt{\\sum_{i=1}^n (x_i-y_i)^2}<\/p>\r\n
d(x,y)=i=1\u2211n(xi\u2212yi)2<\/p>\r\n
\u3067\u3059\u3002\u3053\u308c\u306f L2L^2L2 \u30ce\u30eb\u30e0\u306b\u5bfe\u5fdc\u3057\u3001\u4e09\u89d2\u4e0d\u7b49\u5f0f\u30fb\u5bfe\u79f0\u6027\u30fb\u6b63\u5b9a\u6027\u3092\u6e80\u305f\u3059\u300c\u30e1\u30c8\u30ea\u30c3\u30af\uff08\u8ddd\u96e2\u95a2\u6570\uff09\u300d\u3067\u3059\u3002\u6570\u5b66\u7684\u80cc\u666f\u3084\u8ddd\u96e2\u7a7a\u9593\u3068\u3057\u3066\u306e\u6027\u8cea\u306b\u3064\u3044\u3066\u306f\u5165\u9580\u7cfb\u306e\u89e3\u8aac\u304c\u307e\u3068\u307e\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\r\n
<\/p>\n\n
<\/p>\n\n
ArcGIS \u306e Euclidean Distance \u30c4\u30fc\u30eb\u306f\u3001\u30bd\u30fc\u30b9\u304b\u3089\u5404\u30bb\u30eb\u307e\u3067\u306e\u6700\u8fd1\u63a5\u8ddd\u96e2\u3092\u300c\u30bb\u30eb\u4e2d\u5fc3 \u2192 \u30bb\u30eb\u4e2d\u5fc3\u300d\u3067\u8a08\u7b97\u3057\u3001\u7d50\u679c\u306f\u5165\u529b\u30e9\u30b9\u30bf\u306e\u6295\u5f71\u5358\u4f4d\uff08\u30e1\u30fc\u30c8\u30eb\u30fb\u30d5\u30a3\u30fc\u30c8 \u7b49\uff09\u3067\u8fd4\u3055\u308c\u307e\u3059\u3002\u65b9\u5411\uff08azimuth\uff09\u3084\u5272\u308a\u5f53\u3066\uff08allocation\uff09\u306a\u3069\u51fa\u529b\u30aa\u30d7\u30b7\u30e7\u30f3\u3082\u3042\u308a\u3001\u7a7a\u9593\u89e3\u6790\u3067\u4fbf\u5229\u3067\u3059\u3002\u305f\u3060\u3057\u91cd\u8981\u306a\u6ce8\u610f\u70b9\u306f\u300c\u6295\u5f71\u300d\u3068\u300cNoData\u300d\u306e\u6271\u3044\uff1a\u5730\u7406\u5ea7\u6a19\uff08\u7def\u5ea6\u7d4c\u5ea6\uff09\u306e\u307e\u307e\u5b9f\u884c\u3059\u308b\u3068\u5ea6\u3092\u5358\u4f4d\u3068\u3057\u305f\u201c\u76f4\u7dda\u8ddd\u96e2\u201d\u306b\u306a\u308a\u3001\u5b9f\u8ddd\u96e2\uff08\u30e1\u30fc\u30c8\u30eb\uff09\u3068\u306f\u4e00\u81f4\u3057\u307e\u305b\u3093\u3002\u5b9f\u904b\u7528\u3067\u306f\u9069\u5207\u306a\u6295\u5f71\uff08UTM \u7b49\uff09\u306b\u5909\u63db\u3057\u3066\u304b\u3089\u8ddd\u96e2\u89e3\u6790\u3092\u884c\u3046\u306e\u304c\u6b63\u653b\u6cd5\u3067\u3059\u3002<\/p>\n\n
<\/p>\n\n
\u9ad8\u6b21\u5143\u30c7\u30fc\u30bf\u3067\u306f\u8ddd\u96e2\u304c\u201c\u5e73\u5747\u5024\u306b\u53ce\u675f\u201d\u3057\u3001\u6700\u5c0f\u8ddd\u96e2\u3068\u6700\u5927\u8ddd\u96e2\u306e\u5dee\u304c\u5c0f\u3055\u304f\u306a\u308b\u73fe\u8c61\uff08\u8ddd\u96e2\u306e\u96c6\u4e2d\uff09\u304c\u8d77\u304d\u307e\u3059\u3002Beyer \u3089\uff081999\uff09\u306f\u3053\u306e\u73fe\u8c61\u304c\u8fd1\u508d\u63a2\u7d22\u306e\u6709\u52b9\u6027\u3092\u640d\u306a\u3046\u6761\u4ef6\u3092\u793a\u3057\u3001\u5b9f\u30c7\u30fc\u30bf\u3067\u308210\u301c15\u6b21\u5143\u7a0b\u5ea6\u304b\u3089\u554f\u984c\u304c\u8868\u9762\u5316\u3059\u308b\u30b1\u30fc\u30b9\u304c\u3042\u308b\u3053\u3068\u3092\u5831\u544a\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u300c\u5358\u7d14\u306b\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u3092\u7528\u3048\u3070\u826f\u3044\u300d\u3068\u3044\u3046\u5e38\u8b58\u3092\u7591\u308f\u305b\u308b\u91cd\u8981\u306a\u8b66\u544a\u3067\u3059\u3002\u5bfe\u7b56\u3068\u3057\u3066\u306f**\u6b21\u5143\u524a\u6e1b\uff08PCA\uff0f\u30aa\u30fc\u30c8\u30a8\u30f3\u30b3\u30fc\u30c0\uff09\u3084\u5909\u6570\u9078\u629e\u3001\u7279\u5fb4\u5b66\u7fd2\uff08\u57cb\u3081\u8fbc\u307f\u5b66\u7fd2\uff09**\u304c\u6709\u52b9\u3067\u3059\u3002<\/p>\n\n
import numpy as np\r\n\r\ndef euclidean(a, b):\r\n return np.linalg.norm(a - b)\r\n\r\na = np.array([1.0, 2.0, 3.0])\r\nb = np.array([2.0, 0.0, 4.0])\r\nprint(euclidean(a, b)) # \u51fa\u529b: 2.449...\r\n\r\n<\/code><\/pre>\r\n\uff08\u5b9f\u904b\u7528\u3067\u306f scikit-learn<\/code> \u306e NearestNeighbors<\/code>\u3001faiss<\/code>\u3001scann<\/code> \u306a\u3069\u3092\u4f7f\u3046\u306e\u304c\u52b9\u7387\u7684\uff09<\/p>\r\n<\/p>\n\n
\u30b9\u30b1\u30fc\u30eb\u3055\u305b\u308b\uff1a\u8fd1\u4f3c\u6700\u8fd1\u508d\uff08ANN\uff09\u30e9\u30a4\u30d6\u30e9\u30ea\u3068\u6700\u65b0\u52d5\u5411<\/h2>\n
\u8fd1\u5e74\u3001Billion-scale \u306e\u30d9\u30af\u30c8\u30eb\u691c\u7d22\u304c\u73fe\u5b9f\u7684\u306b\u306a\u308a\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\uff08L2\uff09\u3084\u5185\u7a4d\uff08IP\uff09\u3092\u524d\u63d0\u3068\u3057\u305f\u30e9\u30a4\u30d6\u30e9\u30ea\u304c\u6210\u719f\u3057\u3066\u3044\u307e\u3059\u3002\u4ee3\u8868\u7684\u306a\u3082\u306e\uff1a<\/p>\r\n
\r\n\t- Faiss\uff08Meta\uff09<\/strong>\uff1a\u5927\u898f\u6a21\u30d9\u30af\u30c8\u30eb\u691c\u7d22\u3068 GPU \u30b5\u30dd\u30fc\u30c8\u3067\u5b9f\u904b\u7528\u306b\u5e83\u304f\u4f7f\u308f\u308c\u3066\u3044\u307e\u3059\u3002\u5b9f\u88c5\u3068\u30c1\u30e5\u30fc\u30cb\u30f3\u30b0\u304c\u8c4a\u5bcc\u3002<\/li>\r\n\t
- HNSW\uff08Hierarchical Navigable Small World\uff09<\/strong>\uff1a\u30b0\u30e9\u30d5\u30d9\u30fc\u30b9\u3067\u9ad8\u30ea\u30b3\u30fc\u30eb\u304b\u3064\u9ad8\u901f\u3002\u6700\u8fd1\u306f HNSW \u3092\u30d9\u30fc\u30b9\u306b\u3059\u308b\u30e9\u30a4\u30d6\u30e9\u30ea\uff08hnswlib \u7b49\uff09\u304c\u4eba\u6c17\u3002<\/li>\r\n\t
- ScaNN\uff08Google\uff09<\/strong>\uff1aScaNN \u3068\u305d\u306e\u6539\u826f\uff08SOAR \u306a\u3069\uff09\u306f\u901f\u5ea6\u30fb\u7cbe\u5ea6\u306e\u5b9f\u7528\u7684\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u3067\u6ce8\u76ee\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u30af\u30e9\u30a6\u30c9\u30d9\u30f3\u30c0\u30fc\u306e\u30de\u30cd\u30fc\u30b8\u30c9\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u306b\u3082\u7d44\u307f\u8fbc\u307e\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\r\n<\/ul>\r\n
\u5b9f\u52d9TIPS<\/strong>\uff1aHNSW \u306f\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0\u8ffd\u52a0\uff08\u52d5\u7684\u66f4\u65b0\uff09\u306b\u6bd4\u8f03\u7684\u5f37\u304f\u3001FAISS \u306f\u91cf\u5b50\u5316\uff08PQ\uff09\u3068\u7d44\u307f\u5408\u308f\u305b\u308b\u3068\u30e1\u30e2\u30ea\u52b9\u7387\u304c\u826f\u304f\u306a\u308b\u3002ScaNN \u306f\u5927\u898f\u6a21\u30af\u30e9\u30a6\u30c9\u30b5\u30fc\u30d3\u30b9\u3067\u306e\u5b9f\u7e3e\u304c\u5897\u3048\u3066\u3044\u307e\u3059\u3002\u7528\u9014\u306b\u5fdc\u3058\u3066\u300c\u30ea\u30b3\u30fc\u30eb\u91cd\u8996\u300d\u300c\u30ec\u30a4\u30c6\u30f3\u30b7\u91cd\u8996\u300d\u300c\u30e1\u30e2\u30ea\u5236\u7d04\u300d\u3092\u512a\u5148\u3057\u3066\u9078\u629e\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\r\n<\/p>\n\n
\u5b66\u7fd2\u30d9\u30fc\u30b9\u306e\u8ddd\u96e2\uff08\u30e1\u30c8\u30ea\u30c3\u30af\u5b66\u7fd2\uff09\uff1a\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u3092\u201c\u610f\u5473\u3042\u308b\u201d\u7a7a\u9593\u3067\u4f7f\u3046<\/h2>\n
\u751f\u306e\u7279\u5fb4\u7a7a\u9593\u3067\u306f\u8ddd\u96e2\u304c\u610f\u5473\u3092\u306a\u3055\u306a\u3044\u5834\u5408\u3001\u57cb\u3081\u8fbc\u307f\uff08embedding\uff09\u3092\u5b66\u7fd2\u3057\u3066\u304b\u3089\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u3092\u4f7f\u3046<\/span>\u30a2\u30d7\u30ed\u30fc\u30c1\u304c\u975e\u5e38\u306b\u6709\u52b9\u3067\u3059\u3002Siamese \u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff08one-shot \u5b66\u7fd2\uff09\u3001\u30c8\u30ea\u30d7\u30ec\u30c3\u30c8\u30ed\u30b9\uff08FaceNet \u7b49\uff09\u304c\u4ee3\u8868\u4f8b\u3067\u3001\u300c\u4f3c\u3066\u3044\u308b\u3082\u306e\u540c\u58eb\u304c L2 \u7a7a\u9593\u3067\u8fd1\u304f\u306a\u308b\u300d\u3088\u3046\u306b\u5b66\u7fd2\u3057\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u5f97\u305f\u57cb\u3081\u8fbc\u307f\u7a7a\u9593\u3067\u306f\u3001\u5358\u7d14\u306a\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u304c\u5f37\u529b\u306a\u985e\u4f3c\u6307\u6a19\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\u30b1\u30fc\u30b9\u30b9\u30bf\u30c7\u30a3\uff08\u77ed\u3081\uff09<\/h2>\n\u4e8b\u4f8bA\uff1a\u90fd\u5e02\u5206\u6790\uff08GIS\uff09<\/b>\r\n
\u9053\u8def\u7db2\u3084\u5efa\u7269\u70b9\u7fa4\u306b\u5bfe\u3057\u3066 ArcGIS \u306e Euclidean Distance \u3092\u4f7f\u3044\u300c\u6700\u5bc4\u308a\u65bd\u8a2d\u307e\u3067\u306e\u8ddd\u96e2\u30de\u30c3\u30d7\u300d\u3092\u4f5c\u6210\u3059\u308b\u5834\u5408\u3001\u5165\u529b\u306e\u6295\u5f71\uff08\u5730\u7406\u5ea7\u6a19\u2192\u9069\u5207\u306a\u6295\u5f71\uff09\u3068\u30e9\u30b9\u30bf\u89e3\u50cf\u5ea6\u306e\u9078\u5b9a\u304c\u7d50\u679c\u306e\u7cbe\u5ea6\u3092\u6c7a\u3081\u307e\u3059\u3002\u7279\u306b\u5c71\u5cb3\u5730\u306a\u3069\u3067\u659c\u9762\u8ddd\u96e2\u3084\u9053\u8def\u7db2\u8ddd\u96e2\uff08\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u8ddd\u96e2\uff09\u304c\u5fc5\u8981\u306a\u5834\u5408\u3001\u5358\u7d14\u306a\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u3067\u306f\u8aa4\u3063\u305f\u610f\u601d\u6c7a\u5b9a\u3092\u5c0e\u304f\u306e\u3067\u6ce8\u610f\u3002<\/p>\r\n\u4e8b\u4f8bB\uff1a\u30ec\u30b3\u30e1\u30f3\u30c7\u30fc\u30b7\u30e7\u30f3\uff08\u5927\u898f\u6a21\u57cb\u3081\u8fbc\u307f+FAISS\uff09<\/b>\r\n
\u5546\u54c1\u57cb\u3081\u8fbc\u307f\u3092 FAISS \u306b\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3057\u3066 L2 \u691c\u7d22\u3092\u884c\u3046\u69cb\u6210\u3002\u57cb\u3081\u8fbc\u307f\u306f\u4e8b\u524d\u306b\u6b63\u898f\u5316\u3057\u3066\u30b3\u30b5\u30a4\u30f3\u985e\u4f3c\u5ea6\u306b\u5408\u308f\u305b\u308b\u304b\u3001L2\u305d\u306e\u307e\u307e\u4f7f\u3046\u304b\u3067\u8a2d\u8a08\u304c\u5206\u304b\u308c\u308b\u3002\u91cf\u5b50\u5316\u3092\u4f7f\u3063\u3066\u30e1\u30e2\u30ea\u3092\u5727\u7e2e\u3059\u308b\u3068\u691c\u7d22\u54c1\u8cea\u3068\u901f\u5ea6\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u304c\u767a\u751f\u3059\u308b\u3002<\/p>\r\n
<\/p>\n\n
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