{"id":7195,"date":"2025-09-30T15:32:25","date_gmt":"2025-09-30T06:32:25","guid":{"rendered":"https:\/\/blog.since2020.jp\/?p=7195"},"modified":"2026-09-29T14:41:37","modified_gmt":"2026-09-29T05:41:37","slug":"manhattan-distance_glossary","status":"publish","type":"post","link":"https:\/\/since2020.jp\/media\/manhattan-distance_glossary\/","title":{"rendered":"\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\uff08L1\uff09\u3092\u672c\u97f3\u3067\u4f7f\u3044\u3053\u306a\u3059\uff1a\u5b9a\u7fa9\u30fb\u5b9f\u88c5\u30fb\u5b9f\u52d9\u3067\u306e\u9078\u3073\u65b9\u30ac\u30a4\u30c9"},"content":{"rendered":"\n

\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\uff08\u30bf\u30af\u30b7\u30fc\u8ddd\u96e2\u30fbL1\u30ce\u30eb\u30e0\uff09\u306e\u5b9a\u7fa9\u304b\u3089\u5b9f\u88c5\u3001k-NN\u3084LASSO\u3068\u306e\u95a2\u4fc2\u3001\u30b9\u30d1\u30fc\u30b9\u30c7\u30fc\u30bf\u3084\u9ad8\u6b21\u5143\u30c7\u30fc\u30bf\u306b\u304a\u3051\u308b\u7279\u5fb4\u3001L2\u3068\u306e\u9055\u3044\u3001\u3055\u3089\u306b\u8fd1\u4f3c\u6700\u8fd1\u508d\u63a2\u7d22\u3084\u30e1\u30c8\u30ea\u30c3\u30af\u5b66\u7fd2\u307e\u3067\u3001\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\u3092\u5b9f\u52d9\u3067\u300c\u3044\u3064\u4f7f\u3046\u3079\u304d\u304b\u300d\u300c\u3044\u3064\u907f\u3051\u308b\u3079\u304d\u304b\u300d\u3092\u5206\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n

\u306f\u3058\u3081\u306b\uff1a\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\u3092\u4eca\u3042\u3089\u305f\u3081\u3066\u8003\u3048\u308b\u7406\u7531<\/h2>\n

\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\uff08Manhattan distance\uff09\u306f\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306b\u3064\u3044\u3066\u5404\u5ea7\u6a19\u306e\u5dee\u306e\u7d76\u5bfe\u5024\u3092\u5408\u8a08\u3059\u308b\u8ddd\u96e2\u5c3a\u5ea6\u3067\u3059\u3002\u300c\u30bf\u30af\u30b7\u30fc\u8ddd\u96e2\u300d\u3084\u300cL1\u8ddd\u96e2\u300d\u3068\u547c\u3070\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u540d\u524d\u306e\u7531\u6765\u306f\u3001\u9053\u8def\u304c\u7881\u76e4\u76ee\u72b6\u306b\u914d\u7f6e\u3055\u308c\u305f\u90fd\u5e02\u3067\u306f\u3001\u5efa\u7269\u540c\u58eb\u3092\u76f4\u7dda\u3067\u7d50\u3076\u8ddd\u96e2\u3067\u306f\u306a\u304f\u3001\u9053\u8def\u306b\u6cbf\u3063\u3066\u7e26\u6a2a\u306b\u79fb\u52d5\u3057\u305f\u8ddd\u96e2\u304c\u5b9f\u969b\u306e\u79fb\u52d5\u91cf\u306b\u8fd1\u304f\u306a\u308b\u3053\u3068\u3067\u3059\u3002<\/p>\n

2\u70b9 x,y\u2208Rdx,y\\in\\mathbb{R}^d \u306e\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\u306f\u3001<\/p>\n

dL1(x,y)=\u2211i=1d\u2223xi\u2212yi\u2223d_{L1}(x,y)=\\sum_{i=1}^{d}|x_i-y_i|<\/p>\n

\u3068\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n

\u4e00\u898b\u3059\u308b\u3068\u975e\u5e38\u306b\u5358\u7d14\u3067\u3059\u304c\u3001\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\u306f\u6a5f\u68b0\u5b66\u7fd2\u3001\u30c7\u30fc\u30bf\u30de\u30a4\u30cb\u30f3\u30b0\u3001\u753b\u50cf\u51e6\u7406\u3001\u63a8\u85a6\u30b7\u30b9\u30c6\u30e0\u3001\u81ea\u7136\u8a00\u8a9e\u51e6\u7406\u3001\u30b0\u30ea\u30c3\u30c9\u578b\u306e\u7d4c\u8def\u63a2\u7d22\u306a\u3069\u3001\u5e45\u5e83\u3044\u9818\u57df\u3067\u5229\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u7279\u306b\u3001\u7279\u5fb4\u91cf\u306e\u300c\u5dee\u3092\u4e00\u3064\u305a\u3064\u8db3\u3057\u5408\u308f\u305b\u308b\u300d\u3068\u3044\u3046\u6027\u8cea\u306f\u3001\u30b9\u30d1\u30fc\u30b9\u306a\u30c7\u30fc\u30bf\u3084\u5916\u308c\u5024\u306e\u5f71\u97ff\u3092\u6291\u3048\u305f\u3044\u30b1\u30fc\u30b9\u3067\u91cd\u8981\u3067\u3059\u3002<\/p>\n

\u305f\u3060\u3057\u3001\u300cL1\u3060\u304b\u3089\u5916\u308c\u5024\u306b\u5f37\u3044\u300d\u300c\u9ad8\u6b21\u5143\u306a\u3089L1\u304c\u5fc5\u305a\u6709\u5229\u300d\u3068\u5358\u7d14\u5316\u3059\u308b\u306e\u306f\u5371\u967a\u3067\u3059\u3002\u8ddd\u96e2\u5c3a\u5ea6\u306f\u30c7\u30fc\u30bf\u306e\u5206\u5e03\u3001\u7279\u5fb4\u91cf\u306e\u610f\u5473\u3001\u524d\u51e6\u7406\u3001\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u30bb\u30c3\u30c8\u3067\u8003\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n

<\/p>\n

\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\u306e\u6700\u5927\u306e\u7279\u5fb4\u306f\u3001\u5404\u6b21\u5143\u306e\u8aa4\u5dee\u3092\u7d76\u5bfe\u5024\u3068\u3057\u3066\u8a08\u7b97\u3057\u3001\u305d\u308c\u3089\u3092\u7dda\u5f62\u306b\u5408\u8a08\u3059\u308b\u3053\u3068\u3067\u3059\u3002<\/p>\n

\u4f8b\u3048\u30702\u6b21\u5143\u3067\u3001\u70b9A\u304c\uff081,2\uff09\u3001\u70b9B\u304c\uff084,6\uff09\u306a\u3089\u3001\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\u306f\u3001<\/p>\n

\u22231\u22124\u2223+\u22232\u22126\u2223=3+4=7|1-4|+|2-6|=3+4=7<\/p>\n

\u3068\u306a\u308a\u307e\u3059\u3002\u4e00\u65b9\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\uff08L2\uff09\u306a\u3089\u3001<\/p>\n

(1\u22124)2+(2\u22126)2=5\\sqrt{(1-4)^2+(2-6)^2}=5<\/p>\n

\u3067\u3059\u3002<\/p>\n

L2\u3067\u306f\u5927\u304d\u306a\u5dee\u3092\u4e8c\u4e57\u3059\u308b\u305f\u3081\u3001\u4e00\u90e8\u306e\u6b21\u5143\u3067\u6975\u7aef\u306a\u5dee\u304c\u751f\u3058\u308b\u3068\u3001\u305d\u306e\u5dee\u304c\u8ddd\u96e2\u306b\u5f37\u304f\u53cd\u6620\u3055\u308c\u307e\u3059\u3002L1\u3067\u306f\u5dee\u3092\u4e8c\u4e57\u3057\u306a\u3044\u305f\u3081\u3001\u540c\u3058\u6761\u4ef6\u3067\u306fL2\u307b\u3069\u6975\u7aef\u306a\u5dee\u3092\u5897\u5e45\u3057\u307e\u305b\u3093\u3002\u3053\u306e\u6027\u8cea\u304b\u3089\u3001L1\u306fL2\u3088\u308a\u5916\u308c\u5024\u306e\u5f71\u97ff\u3092\u53d7\u3051\u306b\u304f\u3044\u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n

\u305f\u3060\u3057\u3001\u300cL1\u306f\u5916\u308c\u5024\u306b\u5f37\u3044\u300d\u3068\u3044\u3046\u8868\u73fe\u306b\u306f\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\u3002L1\u3082\u5927\u304d\u306a\u5024\u306e\u5f71\u97ff\u3092\u53d7\u3051\u308b\u305f\u3081\u3001\u5916\u308c\u5024\u3092\u7121\u8996\u3059\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3088\u308a\u6b63\u78ba\u306b\u306f\u3001\u300c\u5927\u304d\u306a\u5dee\u3092\u4e8c\u4e57\u306b\u3088\u3063\u3066\u3055\u3089\u306b\u5897\u5e45\u3057\u306a\u3044\u300d\u3068\u3044\u3046\u7279\u5fb4\u3092\u6301\u3064\u3068\u7406\u89e3\u3059\u308b\u306e\u304c\u9069\u5207\u3067\u3059\u3002<\/p>\n

\u307e\u305f\u3001L1\u306f\u30ce\u30eb\u30e0\u3068\u3057\u3066\u975e\u8ca0\u6027\u3001\u540c\u4e00\u6027\u3001\u5bfe\u79f0\u6027\u3001\u4e09\u89d2\u4e0d\u7b49\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u5358\u306a\u308b\u985e\u4f3c\u5ea6\u3067\u306f\u306a\u304f\u3001\u6570\u5b66\u7684\u306b\u6271\u3044\u3084\u3059\u3044\u8ddd\u96e2\u3068\u3057\u3066\u591a\u304f\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u5229\u7528\u3067\u304d\u307e\u3059\u3002<\/p>\n

NumPy\u3067\u5b9f\u88c5\u3059\u308b\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2<\/h2>\n

\u5b9f\u52d9\u3067\u306f\u30012\u70b9\u9593\u306e\u8ddd\u96e2\u3060\u3051\u3067\u306a\u304f\u3001\u8907\u6570\u306e\u70b9\u96c6\u5408\u9593\u306b\u3042\u308b\u5168\u8ddd\u96e2\u3092\u307e\u3068\u3081\u3066\u8a08\u7b97\u3059\u308b\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002NumPy\u306a\u3089\u30d6\u30ed\u30fc\u30c9\u30ad\u30e3\u30b9\u30c8\u3092\u5229\u7528\u3057\u3066\u30d9\u30af\u30c8\u30eb\u5316\u3067\u304d\u307e\u3059\u3002<\/p>\n

import numpy as np\n\ndef manhattan_distance_matrix(A, B):\n    # A: (n, d), B: (m, d)\n    return np.abs(A[:, None, :] - B[None, :, :]).sum(axis=2)\n\nA = np.array([\n    [1, 2],\n    [3, 4]\n])\n\nB = np.array([\n    [0, 0],\n    [2, 2],\n    [5, 5]\n])\n\nD = manhattan_distance_matrix(A, B)\nprint(D)\n<\/code><\/pre>\n
\u3053\u306e\u65b9\u6cd5\u3067\u306f\u3001A\u306e\u5404\u70b9\u3068B\u306e\u5404\u70b9\u306b\u3064\u3044\u3066L1\u8ddd\u96e2\u3092\u4e00\u62ec\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002Python\u306e\u30eb\u30fc\u30d7\u3092\u4f55\u91cd\u306b\u3082\u56de\u3059\u3088\u308a\u9ad8\u901f\u306b\u306a\u308a\u3084\u3059\u3044\u4e00\u65b9\u3001\u9014\u4e2d\u3067 n\u00d7m\u00d7dn\\times m\\times d \u306e\u914d\u5217\u3092\u751f\u6210\u3059\u308b\u305f\u3081\u3001\u5927\u898f\u6a21\u30c7\u30fc\u30bf\u3067\u306f\u30e1\u30e2\u30ea\u6d88\u8cbb\u304c\u554f\u984c\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n
\u30c7\u30fc\u30bf\u91cf\u304c\u5927\u304d\u3044\u5834\u5408\u306f\u3001\u30d0\u30c3\u30c1\u5358\u4f4d\u3067\u8ddd\u96e2\u3092\u8a08\u7b97\u3057\u305f\u308a\u3001\u5c02\u7528\u306e\u6700\u8fd1\u508d\u63a2\u7d22\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u5229\u7528\u3057\u305f\u308a\u3059\u308b\u65b9\u304c\u73fe\u5b9f\u7684\u3067\u3059\u3002GPU\u3092\u5229\u7528\u3059\u308b\u5834\u5408\u3082\u3001\u5358\u7d14\u306bGPU\u3078\u79fb\u305b\u3070\u901f\u304f\u306a\u308b\u3068\u306f\u9650\u3089\u305a\u3001\u30c7\u30fc\u30bf\u8ee2\u9001\u3084\u4e2d\u9593\u30c6\u30f3\u30bd\u30eb\u306e\u30b5\u30a4\u30ba\u307e\u3067\u542b\u3081\u3066\u8a55\u4fa1\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n
<\/p>\n
L1\u3068L2\u3001\u3069\u3061\u3089\u3092\u9078\u3076\u3079\u304d\u304b<\/h2>\n
\u5b9f\u52d9\u3067\u6700\u3082\u91cd\u8981\u306a\u306e\u306f\u300cL1\u3068L2\u306e\u3069\u3061\u3089\u304c\u512a\u308c\u3066\u3044\u308b\u304b\u300d\u3067\u306f\u306a\u304f\u3001\u300c\u3069\u3061\u3089\u306e\u8ddd\u96e2\u306e\u610f\u5473\u304c\u3001\u5bfe\u8c61\u30c7\u30fc\u30bf\u3068\u76ee\u7684\u306b\u5408\u3063\u3066\u3044\u308b\u304b\u300d\u3067\u3059\u3002<\/p>\n
L1\u306f\u3001\u7279\u5fb4\u91cf\u3054\u3068\u306e\u5dee\u3092\u7a4d\u307f\u4e0a\u3052\u308b\u3053\u3068\u306b\u610f\u5473\u304c\u3042\u308b\u5834\u5408\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30ef\u30f3\u30db\u30c3\u30c8\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3055\u308c\u305f\u7279\u5fb4\u91cf\u3084\u3001\u975e\u5e38\u306b\u591a\u304f\u306e\u8981\u7d20\u304c\u30bc\u30ed\u306b\u306a\u308b\u30b9\u30d1\u30fc\u30b9\u306a\u30c7\u30fc\u30bf\u3067\u306f\u3001L1\u306e\u89e3\u91c8\u304c\u6bd4\u8f03\u7684\u3057\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002\u6587\u66f8\u3092\u5358\u8a9e\u306e\u51fa\u73fe\u60c5\u5831\u3068\u3057\u3066\u8868\u73fe\u3057\u305f\u30c7\u30fc\u30bf\u306a\u3069\u3067\u3082\u3001L1\u306f\u5019\u88dc\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n
\u4e00\u65b9\u3001\u9023\u7d9a\u5024\u306e\u7279\u5fb4\u91cf\u306b\u3064\u3044\u3066\u300c\u7a7a\u9593\u4e0a\u306e\u76f4\u7dda\u8ddd\u96e2\u300d\u3092\u8868\u73fe\u3057\u305f\u3044\u5834\u5408\u306f\u3001L2\u304c\u81ea\u7136\u306a\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u753b\u50cf\u3084\u9023\u7d9a\u7684\u306a\u7279\u5fb4\u30d9\u30af\u30c8\u30eb\u3067\u3082\u3001L2\u304c\u9069\u5207\u306a\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u753b\u50cf\u30fb\u57cb\u3081\u8fbc\u307f\u30fb\u7279\u5fb4\u8868\u73fe\u3067\u306f\u30c7\u30fc\u30bf\u306e\u5b66\u7fd2\u65b9\u6cd5\u3084\u6b63\u898f\u5316\u306b\u3088\u3063\u3066\u9069\u5207\u306a\u8ddd\u96e2\u304c\u5909\u308f\u308b\u305f\u3081\u3001L2\u3092\u81ea\u52d5\u7684\u306b\u9078\u3076\u3079\u304d\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n
\u3055\u3089\u306b\u91cd\u8981\u306a\u306e\u304c\u3001\u7279\u5fb4\u91cf\u306e\u30b9\u30b1\u30fc\u30eb\u3067\u3059\u3002\u4f8b\u3048\u3070\u300c\u5e74\u9f62\u300d\u304c0\u301c100\u3001\u300c\u5e74\u53ce\u300d\u304c0\u301c2,000\u4e07\u5186\u3001\u300c\u8cfc\u5165\u56de\u6570\u300d\u304c0\u301c50\u3068\u3044\u3046\u30c7\u30fc\u30bf\u3092\u305d\u306e\u307e\u307eL1\u3067\u6bd4\u8f03\u3059\u308b\u3068\u3001\u5358\u4f4d\u3084\u6570\u5024\u30ec\u30f3\u30b8\u306e\u5927\u304d\u3044\u7279\u5fb4\u91cf\u304c\u8ddd\u96e2\u3092\u652f\u914d\u3057\u307e\u3059\u3002\u3053\u308c\u306fL2\u3067\u3082\u540c\u69d8\u3067\u3059\u304c\u3001\u8ddd\u96e2\u30d9\u30fc\u30b9\u306e\u30e2\u30c7\u30eb\u3067\u306f\u7279\u306b\u6df1\u523b\u3067\u3059\u3002<\/p>\n
\u3057\u305f\u304c\u3063\u3066\u3001k-NN\u306a\u3069\u3092\u5229\u7528\u3059\u308b\u5834\u5408\u306f\u3001\u6a19\u6e96\u5316\u3084\u6b63\u898f\u5316\u3092\u542b\u3081\u305f\u524d\u51e6\u7406\u3092\u30d1\u30a4\u30d7\u30e9\u30a4\u30f3\u5316\u3057\u3001\u4ea4\u5dee\u691c\u8a3c\u306b\u3088\u3063\u3066\u8ddd\u96e2\u5c3a\u5ea6\u3068\u524d\u51e6\u7406\u3092\u307e\u3068\u3081\u3066\u8a55\u4fa1\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002<\/p>\n
k-NN\u3067\u306f\u8ddd\u96e2\u306e\u9078\u629e\u304c\u305d\u306e\u307e\u307e\u4e88\u6e2c\u306b\u5f71\u97ff\u3059\u308b<\/h2>\n
k-NN\uff08k\u8fd1\u508d\u6cd5\uff09\u306f\u3001\u672a\u77e5\u30c7\u30fc\u30bf\u306b\u8fd1\u3044\u5b66\u7fd2\u30c7\u30fc\u30bf\u3092\u63a2\u3057\u3001\u305d\u306e\u8fd1\u508d\u306e\u30e9\u30d9\u30eb\u306a\u3069\u3092\u5229\u7528\u3057\u3066\u4e88\u6e2c\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u8ddd\u96e2\u306e\u5b9a\u7fa9\u305d\u306e\u3082\u306e\u304c\u30e2\u30c7\u30eb\u306e\u6319\u52d5\u3092\u6c7a\u3081\u307e\u3059\u3002<\/p>\n
L1\u3092\u4f7f\u3046\u3068\u300c\u5404\u7279\u5fb4\u91cf\u3067\u3069\u308c\u3060\u3051\u9055\u3046\u304b\u300d\u3092\u7a4d\u307f\u4e0a\u3052\u305f\u8fd1\u508d\u304c\u9078\u3070\u308c\u307e\u3059\u3002L2\u306a\u3089\u300c\u5168\u4f53\u3068\u3057\u3066\u3069\u308c\u3060\u3051\u76f4\u7dda\u7684\u306b\u96e2\u308c\u3066\u3044\u308b\u304b\u300d\u3092\u91cd\u8996\u3059\u308b\u8fd1\u508d\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n
\u3053\u306e\u9055\u3044\u306f\u3001\u30c7\u30fc\u30bf\u306b\u3088\u3063\u3066\u7d50\u679c\u304c\u5909\u308f\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u300c\u30ef\u30f3\u30db\u30c3\u30c8\u306a\u3089L1\u300d\u300c\u9023\u7d9a\u5024\u306a\u3089L2\u300d\u3068\u3044\u3046\u30eb\u30fc\u30eb\u3060\u3051\u3067\u6c7a\u3081\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u540c\u4e00\u306e\u5b66\u7fd2\u30fb\u691c\u8a3c\u6761\u4ef6\u3067\u8907\u6570\u306e\u8ddd\u96e2\u3092\u6bd4\u8f03\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002<\/p>\n
\u7279\u306b\u9ad8\u6b21\u5143\u30c7\u30fc\u30bf\u3067\u306f\u3001\u8ddd\u96e2\u305d\u306e\u3082\u306e\u306e\u8b58\u5225\u529b\u304c\u4f4e\u4e0b\u3059\u308b\u300c\u6b21\u5143\u306e\u546a\u3044\u300d\u306b\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\u3002\u6b21\u5143\u304c\u5897\u3048\u308b\u307b\u3069\u3001\u6700\u3082\u8fd1\u3044\u70b9\u3068\u9060\u3044\u70b9\u306e\u8ddd\u96e2\u306e\u5dee\u304c\u76f8\u5bfe\u7684\u306b\u5c0f\u3055\u304f\u306a\u308a\u3001\u8fd1\u508d\u63a2\u7d22\u304c\u96e3\u3057\u304f\u306a\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u5358\u306bL1\u3078\u5909\u66f4\u3059\u308b\u3060\u3051\u3067\u306f\u3001\u3053\u306e\u554f\u984c\u3092\u6839\u672c\u7684\u306b\u89e3\u6c7a\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n
L1\u6b63\u5247\u5316\u3068\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\u306f\u5225\u7269\u3060\u304c\u3001\u5171\u901a\u3059\u308b\u6570\u5b66\u7684\u6027\u8cea\u304c\u3042\u308b<\/h2>\n
\u300cL1\u8ddd\u96e2\u300d\u3068\u300cL1\u6b63\u5247\u5316\u300d\u306f\u95a2\u9023\u3059\u308b\u8003\u3048\u65b9\u3067\u3059\u304c\u3001\u540c\u3058\u3082\u306e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n
L1\u6b63\u5247\u5316\u3067\u306f\u3001\u30e2\u30c7\u30eb\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u7d76\u5bfe\u5024\u306e\u5408\u8a08\u3092\u30da\u30ca\u30eb\u30c6\u30a3\u3068\u3057\u3066\u52a0\u3048\u307e\u3059\u3002\u4ee3\u8868\u4f8b\u304cLASSO\u3067\u3059\u3002L1\u30da\u30ca\u30eb\u30c6\u30a3\u306b\u306f\u3001\u4e00\u90e8\u306e\u4fc2\u6570\u3092\u3061\u3087\u3046\u30690\u306b\u3059\u308b\u65b9\u5411\u3078\u50cd\u304d\u3084\u3059\u3044\u3068\u3044\u3046\u7279\u5fb4\u304c\u3042\u308a\u3001\u7279\u5fb4\u9078\u629e\u3084\u30e2\u30c7\u30eb\u306e\u30b9\u30d1\u30fc\u30b9\u5316\u306b\u5229\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n
\u3064\u307e\u308a\u3001L1\u3068\u3044\u3046\u6570\u5b66\u7684\u69cb\u9020\u306f\u300c2\u3064\u306e\u30c7\u30fc\u30bf\u304c\u3069\u308c\u3060\u3051\u96e2\u308c\u3066\u3044\u308b\u304b\u300d\u3092\u6e2c\u308b\u5834\u5408\u3060\u3051\u3067\u306a\u304f\u3001\u300c\u30e2\u30c7\u30eb\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u3069\u306e\u3088\u3046\u306b\u5236\u7d04\u3059\u308b\u304b\u300d\u3068\u3044\u3046\u5834\u9762\u306b\u3082\u767b\u5834\u3057\u307e\u3059\u3002<\/p>\n
\u305f\u3060\u3057\u3001L1\u8ddd\u96e2\u3092\u4f7f\u3063\u305f\u304b\u3089\u30e2\u30c7\u30eb\u304c\u81ea\u52d5\u7684\u306b\u30b9\u30d1\u30fc\u30b9\u306b\u306a\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u8ddd\u96e2\u3068\u3057\u3066\u306eL1\u3068\u3001\u6b63\u5247\u5316\u3068\u3057\u3066\u306eL1\u306f\u76ee\u7684\u304c\u7570\u306a\u308b\u305f\u3081\u3001\u6df7\u540c\u3057\u306a\u3044\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002<\/p>\n
\u30ed\u30dc\u30c6\u30a3\u30af\u30b9\u3084\u90fd\u5e02\u89e3\u6790\u3067\u306fL1\u306e\u610f\u5473\u304c\u3055\u3089\u306b\u660e\u78ba\u306b\u306a\u308b<\/h2>\n
\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\u304c\u7279\u306b\u76f4\u611f\u7684\u306a\u306e\u306f\u3001\u79fb\u52d5\u65b9\u5411\u304c\u9650\u5b9a\u3055\u308c\u305f\u30b0\u30ea\u30c3\u30c9\u7a7a\u9593\u3067\u3059\u3002<\/p>\n
\u4f8b\u3048\u3070\u30ed\u30dc\u30c3\u30c8\u304c\u4e0a\u4e0b\u5de6\u53f3\u306b\u3057\u304b\u79fb\u52d5\u3067\u304d\u306a\u3044\u683c\u5b50\u72b6\u30de\u30c3\u30d7\u3067\u306f\u3001\u659c\u3081\u306b\u76f4\u7dda\u79fb\u52d5\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u59cb\u70b9\u3068\u7d42\u70b9\u306eL1\u8ddd\u96e2\u306f\u6700\u5c0f\u79fb\u52d5\u91cf\u3092\u8003\u3048\u308b\u969b\u306e\u81ea\u7136\u306a\u6307\u6a19\u306b\u306a\u308a\u307e\u3059\u3002\u90fd\u5e02\u306e\u9053\u8def\u7db2\u304c\u7881\u76e4\u76ee\u72b6\u3067\u3042\u308b\u5834\u5408\u3082\u3001\u76f4\u7dda\u8ddd\u96e2\u3088\u308aL1\u8ddd\u96e2\u306e\u65b9\u304c\u5b9f\u969b\u306e\u79fb\u52d5\u30b3\u30b9\u30c8\u306b\u8fd1\u3044\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n
\u305f\u3060\u3057\u3001\u73fe\u5b9f\u306e\u9053\u8def\u306b\u306f\u4e00\u65b9\u901a\u884c\u3001\u4ea4\u5dee\u70b9\u3001\u6a4b\u3001\u5742\u3001\u901a\u884c\u898f\u5236\u306a\u3069\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u5b9f\u969b\u306e\u7d4c\u8def\u3092\u6c42\u3081\u308b\u7528\u9014\u3067\u306fL1\u8ddd\u96e2\u3092\u305d\u306e\u307e\u307e\u300c\u6700\u77ed\u7d4c\u8def\u300d\u3068\u307f\u306a\u3059\u306e\u3067\u306f\u306a\u304f\u3001\u30b0\u30e9\u30d5\u63a2\u7d22\u3084\u9053\u8def\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u4e0a\u306e\u30b3\u30b9\u30c8\u3068\u7d44\u307f\u5408\u308f\u305b\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n
\u5b9f\u52d9\u3067\u898b\u843d\u3068\u3057\u3084\u3059\u3044\u843d\u3068\u3057\u7a74<\/h2>\n
\u7b2c\u4e00\u306b\u3001\u7279\u5fb4\u91cf\u306e\u30b9\u30b1\u30fc\u30eb\u3067\u3059\u3002\u8ddd\u96e2\u30d9\u30fc\u30b9\u306e\u624b\u6cd5\u3067\u306f\u3001\u5358\u4f4d\u306e\u9055\u3044\u304c\u7d50\u679c\u3092\u5927\u304d\u304f\u5909\u3048\u307e\u3059\u3002\u6a19\u6e96\u5316\u3001\u6b63\u898f\u5316\u3001\u30ed\u30d0\u30b9\u30c8\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u306a\u3069\u3092\u30c7\u30fc\u30bf\u7279\u6027\u306b\u5fdc\u3058\u3066\u691c\u8a0e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n
\u7b2c\u4e8c\u306b\u3001\u7279\u5fb4\u91cf\u306e\u76f8\u95a2\u3067\u3059\u3002L1\u8ddd\u96e2\u306f\u5404\u8ef8\u306e\u5dee\u3092\u5358\u7d14\u306b\u5408\u8a08\u3059\u308b\u305f\u3081\u3001\u5f37\u304f\u76f8\u95a2\u3057\u305f\u7279\u5fb4\u91cf\u3092\u8907\u6570\u5165\u308c\u308b\u3068\u3001\u540c\u3058\u60c5\u5831\u3092\u91cd\u8907\u3057\u3066\u8ddd\u96e2\u306b\u53cd\u6620\u3057\u3066\u3057\u307e\u3046\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n
\u7b2c\u4e09\u306b\u3001\u8ef8\u3078\u306e\u4f9d\u5b58\u6027\u3067\u3059\u3002L1\u8ddd\u96e2\u306f\u5ea7\u6a19\u8ef8\u306b\u4f9d\u5b58\u3059\u308b\u305f\u3081\u3001\u5ea7\u6a19\u7a7a\u9593\u3092\u56de\u8ee2\u3055\u305b\u308b\u3068\u8ddd\u96e2\u306e\u95a2\u4fc2\u304c\u5909\u5316\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u300c\u3069\u306e\u7279\u5fb4\u91cf\u3092\u8ef8\u3068\u3057\u3066\u5b9a\u7fa9\u3059\u308b\u304b\u300d\u304c\u91cd\u8981\u306a\u30c7\u30fc\u30bf\u3067\u306f\u7121\u8996\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n
\u7b2c\u56db\u306b\u3001\u9ad8\u6b21\u5143\u5316\u3067\u3059\u3002\u7279\u5fb4\u91cf\u3092\u5897\u3084\u305b\u3070\u60c5\u5831\u91cf\u304c\u5897\u3048\u308b\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002\u4e0d\u8981\u306a\u7279\u5fb4\u3092\u5927\u91cf\u306b\u8ffd\u52a0\u3059\u308b\u3068\u3001\u8ddd\u96e2\u306e\u610f\u5473\u304c\u8584\u304f\u306a\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u7279\u5fb4\u9078\u629e\u3084\u6b21\u5143\u524a\u6e1b\u3092\u691c\u8a0e\u3059\u308b\u4fa1\u5024\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n
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[d(x,y)=\\sum_i w_i|x_i-y_i|]<\/p>\n
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