{"id":737,"date":"2012-02-12T23:34:38","date_gmt":"2012-02-12T14:34:38","guid":{"rendered":"http:\/\/daily.belltail.jp\/?p=737"},"modified":"2012-02-12T23:43:40","modified_gmt":"2012-02-12T14:43:40","slug":"%e9%ad%9a%e3%81%a7%e3%82%82%e3%82%8f%e3%81%8b%e3%82%8brandom-projection","status":"publish","type":"post","link":"https:\/\/daily.belltail.jp\/?p=737","title":{"rendered":"\u9b5a\u3067\u3082\u308f\u304b\u308bRandom Projection"},"content":{"rendered":"

\u3044\u304d\u306a\u308a\u59cb\u307e\u3063\u305f\u300c\u9b5a\u3067\u3082\u308f\u304b\u308b\u300d\u30b7\u30ea\u30fc\u30ba\uff0e<\/p>\n

\u4eca\u56de\u306f\u60c5\u5831\u79d1\u5b66\u7cfb\u306e\u65b9\u5411\u3051\uff0e
\n\u6b21\u5143\u524a\u6e1b\u306e\u3044\u3061\u624b\u6cd5\u3067\u3042\u308b\u300cRandom Projection\u300d\u3092\u7c21\u5358\u306b\u7d39\u4ecb\u3057\u307e\u3059\uff0e<\/p>\n

\u5177\u4f53\u7684\u306b\u3084\u3063\u3066\u308b\u3053\u3068\uff0c\u3067\u304d\u308b\u3053\u3068\u306f\u3082\u306e\u3063\u305d\u7c21\u5358\u3067\uff0c\u3053\u306a\u3044\u3060Boost\u30a2\u30c9\u30d9\u8a18\u4e8b\u3092\u66f8\u304d\u4e0a\u3052\u3066\u304b\u3089\u5bdd\u4ed8\u3051\u306a\u304b\u3063\u305f\u306e\u3067\u3075\u3068\u601d\u3044\u7acb\u3063\u3066\u53d6\u308a\u7d44\u3093\u3067\u307f\u305f\u3089\u4e00\u767a\u3067\u3059\u3054\u3044\u3061\u3083\u3093\u3068\u3067\u304d\u305f\u306e\u3067\u30d6\u30ed\u30b0\u306b\u307e\u3068\u3081\u308b\u306b\u81f3\u3063\u305f\u6b21\u7b2c(\u305d\u3057\u3066\u305d\u306e\u65e5\u306f\u305d\u306e\u307e\u307e\u5bdd\u4ed8\u3051\u305a\u306b\u663c\u9593\u6b7b\u306c\u304b\u3068\u601d\u3063\u305f\u3068\u3044\u3046)\uff0e
\n\u6700\u521d\u306b\u77e5\u3063\u305f\u306e\u306fMIRU2011\u3068\u3044\u3046\uff0c\u590f\u306b\u3042\u3063\u305f\u5b66\u4f1a\u3067\u3068\u3042\u308b\u8ad6\u6587\u3092\u8aad\u3093\u3060\u6642\uff0e<\/p>\n

\u3082\u3061\u308d\u3093\u308f\u304b\u3063\u3066\u308b\u3068\u601d\u3044\u307e\u3059\u304c\uff0c\u30c4\u30c3\u30b3\u30df\u5f85\u3061\u3067\u3059\uff01\uff01<\/span><\/p>\n

[:contents]<\/p>\n

<\/p>\n

*\u6b21\u5143\u524a\u6e1b\u3068\u306f
\n\u6a5f\u68b0\u5b66\u7fd2\u3084\u30c7\u30fc\u30bf\u51e6\u7406\u3042\u305f\u308a\u306e\u7528\u8a9e\u3067\uff0c\u9ad8\u6b21\u5143\u30c7\u30fc\u30bf\u3092\u305d\u306e\u60c5\u5831\u3092\u306a\u308b\u3079\u304f\u4fdd\u3063\u305f\u307e\u307e\u4f4e\u6b21\u5143\u306b\u5909\u63db\u3059\u308b\u30bf\u30b9\u30af\u3084\u305d\u306e\u6280\u8853\u3092\u6307\u3057\u307e\u3059\uff0e
\n\u5177\u4f53\u7684\u306a\u624b\u6cd5\u3068\u3057\u3066\u4e3b\u6210\u5206\u5206\u6790(PCA)\u3084\u7279\u7570\u5024\u5206\u89e3(SVD)\u3042\u305f\u308a\u306f\u3053\u306e\u5206\u91ce\u306e\u9662\u751f\u30af\u30e9\u30b9\u306a\u3089\u5fc5\u9808\u6559\u990a\u30ec\u30d9\u30eb\u3063\u3066\u8a00\u3063\u3066\u3082\u3044\u3044\u3093\u3058\u3083\u306a\u304b\u308d\u304b\uff0e<\/p>\n

*Random Projection
\n**Random Projection\u3067\u3067\u304d\u308b\u3053\u3068
\n\u4e00\u8a00\u3067\u8a00\u3046\u3068\uff0c\u300c\u8d85\u9ad8\u6b21\u5143\u7a7a\u9593\u306b\u5206\u5e03\u3059\u308b\u70b9\u7fa4\u3092\uff0c\u4e92\u3044\u306e\u8ddd\u96e2\u95a2\u4fc2\u3092\u9ad8\u3044\u78ba\u7387\u3067\u4fdd\u3063\u305f\u307e\u307e<\/strong>\u4f4e\u6b21\u5143\u7a7a\u9593\u306b\u5199\u50cf\u3059\u308b\u300d<\/span>\u3053\u3068\u304c\u3067\u304d\u308b\u624b\u6cd5\uff0e<\/p>\n

\u8ddd\u96e2\u95a2\u4fc2\u3092\u4fdd\u3064\u3068\u8a00\u3046\u306e\u306f\uff0c\u4f8b\u3048\u3070M\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3092N\u6b21\u5143\u306b\u5199\u50cf\u3059\u308b\u5909\u63db{\\bf R}(\u3064\u307e\u308aM \\times N\u884c\u5217)\u304c\u3042\u308b\u3068\u304d\uff0cM\u6b21\u5143\u70b9\u7fa4{\\bf a,b,c}\u306b\u3064\u3044\u3066{\\bf a}\u306b\u6700\u3082\u8fd1\u3044\u70b9\u304c{\\bf b}\uff0c\u9060\u3044\u70b9\u304c{\\bf c}\u3060\u3063\u305f\u306a\u3089\uff0c\u5199\u50cf\u5f8c\u306e\u70b9\u7fa4\u3092\u898b\u3066\u3082{\\bf Ra}\u306b\u6700\u3082\u8fd1\u3044\u70b9\u306f{\\bf Rb}\u3060\u3057\u9060\u3044\u70b9\u306f{\\bf Rc}\u306b\u306a\u308b\uff0c\u3068\u3044\u3046\u3053\u3068\u3067\u3059\uff0e\u3053\u306e\u3053\u3068\u3092\u8a00\u3044\u63db\u3048\u308b\u3068\uff0c\u300c\u7a7a\u9593\u306e\u69cb\u9020\u3092\u4fdd\u3063\u305f\u307e\u307e\u4f4e\u6b21\u5143\u5316\u3059\u308b\u300d<\/strong>\u3053\u3068\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n

\u8ddd\u96e2\u95a2\u4fc2\u3059\u306a\u308f\u3061\u7a7a\u9593\u306e\u69cb\u9020\u3092\u4fdd\u3063\u305f\u307e\u307e\u4f4e\u6b21\u5143\u5316\u3067\u304d\u308b\u3068\uff0c\u4f8b\u3048\u3070\u90e8\u5206\u7a7a\u9593\u306b\u57fa\u3065\u304f\u5206\u985e\u554f\u984c\u306e\u89e3\u6cd5\u3068\u3057\u3066\u6709\u540d\u306ak-NN\u306a\u3069\u3092\u5199\u50cf\u5f8c\u306e\u70b9\u7fa4\u306b\u9069\u7528\u3057\u3066\u3082\u7b49\u4fa1\u3067\u3042\u308b\u3068\u307f\u306a\u3057\u3066\u3088\u3044\u3053\u3068\u306b\u306a\u308a\uff0c\u8a08\u7b97\u30b3\u30b9\u30c8\u304c\u4f4e\u6e1b\u3067\u304d\u305f\u308a\u3059\u308b\u308f\u3051\u3067\u3059\uff0e<\/p>\n

**\u3067\u5b9f\u969b\u3069\u3046\u3059\u308b\u304b
\n\u539f\u7406\u3068\u3057\u3066\u306f\u9b5a\u304c\u6b7b\u306c\u3050\u3089\u3044\u30b7\u30f3\u30d7\u30eb\u3067\uff0c\u305d\u306eM\u6b21\u5143\u304b\u3089N\u6b21\u5143\u306b\u5199\u50cf\u3059\u308b\u884c\u5217{\\bf R}\u306e\u8981\u7d20\u3092\u4e71\u6570\u3067\u8a2d\u5b9a\u3059\u308b\uff0c\u3068\u3044\u3046\u3060\u3051\uff0e\u3073\u3063\u304f\u308a\uff0e<\/p>\n

\u8a2d\u5b9a\u3059\u308b\u5024\u3068\u3057\u3066\u306f\uff0c\u3055\u3055\u3063\u3068\u63a2\u3057\u305f\u7bc4\u56f2\u3067\u306f\u4ee5\u4e0b\u306e3\u901a\u308a\u304c\u3042\u308b\u307f\u305f\u3044\uff0e
\n-[][-1,1][]\u306e\u4e00\u69d8\u4e71\u6570
\n-N(0,1)\u306e\u6b63\u898f\u4e71\u6570
\n-1\/6\u306e\u78ba\u7387\u3067\\sqrt{3}\uff0c1\/6\u306e\u78ba\u7387\u3067-\\sqrt{3}\uff0c\u6b8b\u308a\u306f0(\u4ee5\u4e0b\u30d8\u30eb\u30b7\u30f3\u30ad\u3068\u547c\u3073\u307e\u3059\uff57)<\/p>\n

**\u30a4\u30a4\u3068\u3053\u308d<\/p>\n

\u306a\u3093\u3068\u8a00\u3063\u3066\u3082\u540c\u3058\u3088\u3046\u306a\u76ee\u7684\u306b\u4f7f\u3046\u4ed6\u306e\u624b\u6cd5\u306b\u6bd4\u3079\u3066\u8a08\u7b97\u91cf\u304c\u5727\u5012\u7684\u306b\u5c11\u306a\u3044\u3053\u3068\uff0e
\n\u7279\u306b\uff0c\u5f8c\u306e\u5b9f\u9a13\u3067\u3082\u793a\u305b\u3066\u3044\u307e\u3059\u304c\uff0c\u5909\u63db\u884c\u5217\u306f\u304b\u306a\u308a\u758e\u306a\u884c\u5217\u3067\u3082\u3088\u304f\u3066\uff0c\u3053\u306e\u3053\u3068\u306f\u3055\u3089\u306b\u52b9\u7387\u5316\u3067\u304d\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059(\u758e\u884c\u5217\u306b\u7279\u5316\u3057\u305f\u30c7\u30fc\u30bf\u69cb\u9020\u30fb\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u5b58\u5728\u3057\u307e\u3059)\uff0e<\/p>\n

*\u5b9f\u9a131:\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3
\n**\u5b9f\u9a13\u306e\u8003\u3048\u65b9
\n\u300c\u8ddd\u96e2\u95a2\u4fc2\u3092\u4fdd\u3063\u3066\u3044\u308b\u300d\u3053\u3068\u3092\u3069\u3046\u78ba\u8a8d\u3059\u308b\u304b\uff0c\u3067\u3059\uff0e
\n–M\u6b21\u5143\u7a7a\u9593\u306b\u30e9\u30f3\u30c0\u30e0\u306ak\u500b\u306e\u70b9\u7fa4\u3092plot\u3059\u308b
\n-\u3053\u306e\u70b9\u7fa4\u9593\u306e\u76f8\u4e92\u306e\u8ddd\u96e2\u3092\u8a18\u8ff0\u3057\u305f\u5bfe\u79f0\u884c\u5217{\\bf D}_{M}\u3092\u6c42\u3081\u308b
\n-\u5168\u3066\u306e\u70b9\u3092{\\bf R}\u306b\u3088\u3063\u3066N\u6b21\u5143\u3078\u524a\u6e1b\u3057\u305f\u70b9\u7fa4\u3092plot\u3059\u308b
\n-\u3053\u306e\u70b9\u7fa4\u306b\u3064\u3044\u3066\u3082\u8ddd\u96e2\u884c\u5217{\\bf D}_{N}\u3092\u6c42\u3081\u308b
\n–{\\bf D}_{N}\u306e\u5404\u8981\u7d20\u3092{\\bf D}_{M}\u306e\u5bfe\u5fdc\u3059\u308b\u8981\u7d20\u3067\u5272\u308b\uff0e\u3059\u306a\u308f\u3061\uff0c\u8ddd\u96e2\u884c\u5217\u3092\u8ddd\u96e2\u5909\u5316\u7387\u884c\u5217\u306b\u5909\u63db\u3059\u308b<\/p>\n

\u3053\u306e\u3068\u304d\uff0c\u8ddd\u96e2\u95a2\u4fc2\u3092\u5b8c\u5168\u306b\u4fdd\u3063\u305f\u5199\u50cf\u304c\u306a\u3055\u308c\u3066\u3044\u308c\u3070\uff0c\u8ddd\u96e2\u5909\u5316\u7387\u884c\u5217\u306e\u975e\u5bfe\u89d2\u8981\u7d20\u306b\u306f\u5168\u3066\u540c\u4e00\u306e\u5024\u304c\u5165\u3063\u3066\u3044\u308b\u306f\u305a\u3067\u3059\uff0e
\n\u3053\u306e\u3070\u3089\u3064\u304d(\\sigma)\u304c\u5c0f\u3055\u3044\u307b\u3069\uff0c\u8ddd\u96e2\u7a7a\u9593\u3092\u4fdd\u3066\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\uff0e
\n\u3053\u306e\\sigma\u3092\u5e73\u5747\\mu\u3067\u5272\u308b\u3053\u3068\u3067\u6b63\u898f\u5316\u3057\uff0c\u3053\u306e\u5024\\frac{\\sigma}{\\mu}\u3092\u8a55\u4fa1\u306b\u7528\u3044\u307e\u3059\uff0e<\/p>\n

\u4f8b\u3048\u3070\\frac{\\sigma}{\\mu}\u304c0.04\u3060\u3063\u305f\u3089\uff0c\u8ddd\u96e2\u306e\u5909\u5316\u7387\u306f\u3060\u3044\u305f\u304468%\u304c\u00b14%\u4ee5\u5185\u306b\u53ce\u307e\u3063\u3066\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059(1\\sigma\u533a\u9593)\uff0e<\/p>\n

\u3053\u308c\u3092\uff0c
\n+\u5909\u63db\u884c\u5217\u306e\u751f\u6210\u624b\u6cd5\u3054\u3068\u306b
\n–\u4e00\u69d8\u4e71\u6570\u306b\u3088\u308b\u624b\u6cd5
\n–\u6b63\u898f\u4e71\u6570\u306b\u3088\u308b\u624b\u6cd5
\n–\u30d8\u30eb\u30b7\u30f3\u30ad\u3067\u306e\u624b\u6cd5
\n+\u70b9\u7fa4\u306e\u6570\u3054\u3068\u306b
\n–100\u70b9
\n–500\u70b9
\n–1000\u70b9
\n+\u5909\u63db\u524d\u306e\u70b9\u306e\u5404\u6b21\u5143\u3054\u3068\u306b
\n–100\u6b21\u5143
\n–1000\u6b21\u5143
\n–10000\u6b21\u5143
\n+\u6b21\u5143\u306e\u524a\u6e1b\u5272\u5408\u3054\u3068\u306b
\n–1% (\u305f\u3060\u3057\u5909\u63db\u524d\u304c100\u6b21\u5143\u306e\u3068\u304d\u306f\u9664\u304f)
\n–2% ( \u3003 )
\n–5%
\n–10%
\n–20%
\n\u3067\u8a66\u3057\u3066\u307f\u307e\u3059\uff0e<\/p>\n

**\u5b9f\u9a13\u624b\u6cd5
\nC++\u3067eigen\u3068boost\u3092\u4f7f\u3044\u5012\u3057\u3066\u3084\u308a\u307e\u3059\uff0e\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u5f8c\u306e\u65b9\u306b\u63b2\u8f09\u3057\u307e\u3059\u304c\uff0c\u304b\u306a\u308a\u30b7\u30f3\u30d7\u30eb\uff0e
\n\u3067\u3082\u3053\u3046\u3044\u3046\u3068\u304dMATLAB\u3084Octave\u3084R\u3092\uff73\uff9e\uff67\uff98\uff73\uff9e\uff67\uff98\u4f7f\u3044\u3053\u306a\u305b\u308b\u3068\u5f37\u3044\u3088\u306a\u3041\u2026<\/p>\n

\u9ad8\u3044\u65b9\u306e\u6b21\u5143\u6570M\u3068\u4f4e\u3044\u65b9\u306e\u6b21\u5143\u6570N\uff0c\u70b9\u7fa4\u306e\u6570k\uff0cProjection\u884c\u5217\u306e\u4e71\u6570\u306b\u8a2d\u5b9a\u3059\u308b\u5024\u3092\u4e0a\u8a18\u306e3\u901a\u308a\u304b\u3089\u9078\u3073\uff0c\u305d\u308c\u305e\u308c\u5909\u66f4\u3067\u304d\u307e\u3059\uff0e
\n\u30c7\u30fc\u30bf\u70b9\u7fa4\u306f\uff0c\u57fa\u5e95\u3054\u3068\u306b\u4e00\u69d8\u4e71\u6570\u3067\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u3067\u751f\u6210\uff0e\u3053\u308c\u304c\u5f8c\u3067\u5c11\u3057\u554f\u984c\u306b\u306a\u308b\u306e\u3067\u3059\u304c\uff0e<\/p>\n

**\u5b9f\u9a13\u7d50\u679c\u4f8b<\/p>\n

\u4ee5\u4e0b\u3060\u3089\u3060\u3089\u3068\u9577\u3044\u7d50\u679c\u304c\u7d9a\u304d\u307e\u3059\u306e\u3067\uff0c\u7d50\u8ad6\u304b\u3089\uff0e<\/p>\n

-\u6b21\u5143\u306e\u843d\u3068\u3057\u65b9\u304c\u3042\u307e\u308a\u306b\u6975\u7aef\u3067\u306a\u3051\u308c\u3070\uff0c\\frac{\\sigma}{\\mu}\u306f\u5341\u5206\u5c0f\u3055\u3044
\n–\u3086\u3048\u306b\uff0cRandom Projection\u306b\u3088\u3063\u3066\u8ddd\u96e2\u95a2\u4fc2\u3092\u304b\u306a\u308a\u3088\u304f\u4fdd\u3063\u305f\u307e\u307e\u6b21\u5143\u3092\u843d\u3068\u305b\u3066\u3044\u308b
\n–{\\bf R}\u306e\u8a2d\u5b9a\u306e\u624b\u6cd5\u306b\u3088\u308b\u9055\u3044\u306f\u307b\u3068\u3093\u3069\u306a\u3055\u305d\u3046
\n-\u3055\u3089\u306b\uff0c{\\bf R}\u3092\uff0c\u5bc6\u5ea610%\u3067\u8981\u7d20\u306f[-1:1]\u306e\u758e\u884c\u5217\u3068\u3057\u305f\u5834\u5408\u3082\u6027\u80fd\u306f\u5168\u304f\u304a\u3061\u3066\u3044\u306a\u3044
\n–\u884c\u5217\u30d9\u30af\u30c8\u30eb\u7a4d\u306e\u6642\u9593\u306fNNZ\u306b\u6bd4\u4f8b\u3059\u308b\u305f\u3081\u5bc6\u5ea610%\u306a\u308910\u500d\u3092\u4e0a\u9650\u306b\u9ad8\u901f\u5316\u3067\u304d\u308b
\n—\u3055\u3089\u306b\u5bc6\u5ea6\u3092\u843d\u3068\u3057\u3066\u3082\u304b\u306a\u308a\u3044\u3051\u305f\u3051\u3069\uff0c\u82e5\u5e72\u4e0d\u5b89\u5b9a\u307f\u305f\u3044
\n-\u307e\u305f\uff0c\u3053\u3053\u306b\u306f\u8f09\u305b\u3066\u306a\u3044\u3051\u3069\uff0c\u70b9\u7fa4\u306e\u6570\u306f\u7121\u95a2\u4fc2
\n–\u5f53\u305f\u308a\u524d\u304b<\/p>\n

***{\\bf R}\u3092[-1:1]\u306e\u4e00\u69d8\u4e71\u6570\u3067\u8a2d\u5b9a\u3057\u305f\u5834\u5408
\n–\u524a\u6e1b\u73871%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|1000|10|0.256491|
\n|10000|100|0.0723984|<\/p>\n

–\u524a\u6e1b\u73872%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|1000|20|0.166879|
\n|10000|200|0.0500503|<\/p>\n

–\u524a\u6e1b\u73875%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|100|5|0.418443|
\n|1000|50|0.104068|
\n|10000|500|0.0317905|<\/p>\n

–\u524a\u6e1b\u738710%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|100|10|0.252291|
\n|1000|100|0.0699945|
\n|10000|1000|0.0224399|<\/p>\n

–\u524a\u6e1b\u738720%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|100|20|0.168808|
\n|1000|200|0.0508375|
\n|10000|2000|0.0159634|<\/p>\n

***{\\bf R}\u3092\\mathrm{N}(0,1)\u306e\u6b63\u898f\u4e71\u6570\u3067\u8a2d\u5b9a\u3057\u305f\u5834\u5408
\n–\u524a\u6e1b\u73871%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|1000|10|0.252391|
\n|10000|100|0.0714362|<\/p>\n

–\u524a\u6e1b\u73872%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|1000|20|0.167512|
\n|10000|200|0.051086|<\/p>\n

–\u524a\u6e1b\u73875%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|100|5|0.423773|
\n|1000|50|0.101857|
\n|10000|500|0.0315046|<\/p>\n

–\u524a\u6e1b\u738710%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|100|10|0.246678|
\n|1000|100|0.0714717|
\n|10000|1000|0.0224643|<\/p>\n

–\u524a\u6e1b\u738720%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|100|20|0.164085|
\n|1000|200|0.0507155|
\n|10000|2000|0.0156286|<\/p>\n

***{\\bf R}\u30921\/6\u306e\u78ba\u7387\u3067\\sqrt{3}\uff0c1\/6\u306e\u78ba\u7387\u3067-\\sqrt{3}\uff0c\u6b8b\u308a\u306f0\u3068\u306a\u308b\u3088\u3046\u8a2d\u5b9a\u3057\u305f\u5834\u5408
\n–\u524a\u6e1b\u73871%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|1000|10|0.248877|
\n|10000|100|0.0720375|<\/p>\n

–\u524a\u6e1b\u73872%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|1000|20|0.166422|
\n|10000|200|0.0504729|<\/p>\n

–\u524a\u6e1b\u73875%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|100|5|0.418621|
\n|1000|50|0.104153|
\n|10000|500|0.0318519|<\/p>\n

–\u524a\u6e1b\u738710%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|100|10|0.252088|
\n|1000|100|0.071656|
\n|10000|1000|0.0221902|<\/p>\n

–\u524a\u6e1b\u738720%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|100|20|0.170909|
\n|1000|200|0.050107|
\n|10000|2000|0.0158383|<\/p>\n

***{\\bf R}\u3092\u5bc6\u5ea610%\u306e\u758e\u884c\u5217\uff0c\u975e\u96f6\u8981\u7d20\u306f[-1:1]\u3068\u306a\u308b\u3088\u3046\u8a2d\u5b9a\u3057\u305f\u5834\u5408
\n–\u524a\u6e1b\u73871%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|1000|10|0.25434|
\n|10000|100|0.070818|<\/p>\n

–\u524a\u6e1b\u73872%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|1000|20|0.170246|
\n|10000|200|0.0502912|<\/p>\n

–\u524a\u6e1b\u73875%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|100|5|0.430903|
\n|1000|50|0.102259|
\n|10000|500|0.0314751|<\/p>\n

–\u524a\u6e1b\u738710%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|100|10|0.26406|
\n|1000|100|0.0704771|
\n|10000|1000|0.0220059|<\/p>\n

–\u524a\u6e1b\u738720%
\n|*M|*N(=M*\u524a\u6e1b\u7387)|*\\frac{\\sigma}{\\mu}|
\n|100|20|0.175899|
\n|1000|200|0.0511966|
\n|10000|2000|0.0161958|<\/p>\n

**\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u306e\u5165\u529b\u70b9\u7fa4\uff0c\u305d\u308c\u307e\u305a\u304f\u306f\u306a\u3044\u304b\u3044\uff1f<\/p>\n

\u4e0a\u3067\u89e6\u308c\u305f\u3088\u3046\u306b\uff0c\u30c7\u30fc\u30bf\u70b9\u7fa4\u306f\uff0c\u57fa\u5e95\u3054\u3068\u306b\u4e00\u69d8\u4e71\u6570\u3067\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u3067\u751f\u6210\u3057\u3066\u308b\u308f\u3051\u3067\u3059\u304c\uff0c\u3053\u308c\u5c11\u3057\u307e\u305a\u3044\u6c17\u304c\u3059\u308b\u3093\u3067\u3059\u306d\uff0e
\n\u306a\u3093\u3067\u3067\u3057\u3087\u3046\uff0e<\/p>\n

10\u6b21\u5143\uff0c100\u6b21\u5143\uff0c1000\u6b21\u5143\u3054\u3068\u306b\uff0c\u5404\u57fa\u5e95\u304c[-1:1]\u306e\u4e00\u69d8\u306a\u5024\u3092\u3068\u308b10000\u70b9\u304b\u3089\u306a\u308b\u70b9\u7fa4\u3092\u7528\u610f\u3057\uff0c\u5404\u30d9\u30af\u30c8\u30eb\u306e\u8868\u3059\u70b9\u306e\u539f\u70b9\u304b\u3089\u306e\u8ddd\u96e2<\/strong>\u3067\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u53d6\u3063\u3066\u307f\u308b\u3068\uff0c\u6b21\u306e\u3088\u3046\u306a\u5206\u5e03\u306b\u306a\u308a\u307e\u3059\uff0e
\nxrange\u306f\u5404\u6b21\u5143\u3067\u306e\u8ddd\u96e2\u306e\u5024\u57df\u3067\u3059\uff0e<\/p>\n

\"\"<\/a><\/p>\n

\"\"<\/a><\/p>\n

\"\"<\/a><\/p>\n

\u9ad8\u6b21\u5143\u306b\u306a\u308b\u307b\u3069\u5206\u5e03\u304c\u6975\u7aef\u306b\u306a\u3063\u3066\u304d\u307e\u3059\uff0e
\n\u300c\u307b\u3068\u3093\u3069\u5168\u3066\u306e\u70b9\u304c\uff0c\u539f\u70b9\u304b\u3089\u306e\u8ddd\u96e2\u304c\u3042\u308b\u4e00\u5b9a\u5024\u300d\u2026\u7403\u9762\u3067\u3059\u306d\uff0e
\n\u30e9\u30f3\u30c0\u30e0\u306b\u8a2d\u5b9a\u3057\u305f\u306f\u305a\u306e\u70b9\u304c\uff0c\u7403\u9762\u4ed8\u8fd1\u306b\u96c6\u4e2d\u3057\u3066\u3057\u307e\u3046\u3093\u3067\u3059\uff0e<\/p>\n

\u3053\u306e\u7406\u7531\u3068\u3044\u3046\u306e\u306f\u5927\u5b66\u3084\u9ad8\u5c02\u30ec\u30d9\u30eb\u306e\u78ba\u7387\u8ad6\u306e\u304a\u8a71\u3067\uff0c\u8981\u306f\uff0c\u72ec\u7acb\u306a\u4e00\u69d8\u4e71\u6570\u306e\u548c\u306f\u6b63\u898f\u4e71\u6570\u306b\u306a\u3063\u3066\uff0c\u8db3\u3059\u6570\u304c\u5897\u3048\u308b\u307b\u3069\u305d\u306e\\sigma\u306f\u5c0f\u3055\u304f\u306a\u308b\u3088\u3068\u3044\u3046\u8a71\u3067\u3059\uff0e
\n\u70b9\u306e\u5404\u8981\u7d20\u306f\u72ec\u7acb\u306a\u4e00\u69d8\u4e71\u6570\u306a\u306e\u3067\uff0c\u539f\u70b9\u304b\u3089\u306e\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u3082\u304a\u3088\u305d\u4e00\u69d8\u4e71\u6570\u306e\u548c\u3068\u306a\u3063\u3061\u3083\u3046\u304b\u3089(\u3053\u3053\u5c11\u3057\u3060\u3051\u30a6\u30bd\u3064\u3044\u3066\u307e\u3059\u304c)\uff0c\u8ddd\u96e2\u304c\u6b63\u898f\u4e71\u6570\u3068\u306a\u308b\u308f\u3051\u3067\u3059\uff0e<\/p>\n

2\u6b21\u5143\u4ee5\u4e0a\u306e\u7a7a\u9593\u3067\u306a\u3089\u5fc5\u305a\u751f\u3058\u307e\u3059\u304c\uff0c\u4f4e\u6b21\u5143\u3067\u306f\\sigma\u304c\u5927\u304d\u3044\u306e\u3067\u6c17\u3065\u304d\u307e\u305b\u3093\uff0e
\n\u3057\u304b\u3057\u9ad8\u6b21\u5143\u306b\u306a\u308b\u3068\uff0c\u5747\u7b49\u5206\u5e03\u3057\u306a\u3044\u306e\u3067\u3059\uff0e\u305d\u3057\u3066\u305d\u308c\u304c\u898b\u3048\u306a\u3044\u304b\u3089\u30bf\u30c1\u304c\u60aa\u3044\uff0e<\/p>\n

\u3067\uff0c\u3053\u308c\u3092\u3069\u3046\u3057\u305f\u3089\u3044\u3044\u304b\u306f\u3088\u304f\u308f\u304b\u3089\u306a\u3044\uff0e<\/p>\n

\u5e83\u5cf6\u5927\u5b66\u306e\u7389\u6728\u5148\u751f\u304b\u3089\u52a9\u3051\u821f\u3092\u3044\u305f\u3060\u3044\u305f\u308a\u3082\u3057\u3066\u3044\u308b\u306e\u3067\u3059\u304c\u2026\uff0e<\/p>\n

[blackbirdpie url=”https:\/\/twitter.com\/#!\/ttttamaki\/status\/147035480817545216″]<\/p>\n

(\u7389\u6728\u5148\u751f\u306b\u306f\u307b\u3093\u3068\u3044\u3064\u3082\u304a\u4e16\u8a71\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u2026\uff57)<\/p>\n

**\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u5b9f\u9a13\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u4f8b<\/p>\n

170\u884c\u3068\u82e5\u5e72\u9577\u3044\u306e\u3067\u6298\u308a\u305f\u305f\u3093\u3067\u307e\u3059\uff0e
\n\u3080\u3057\u308d170\u884c\u3067\u3059\u3093\u3067\u308b\u306e\u306f\u3059\u3054\u3044\u304b\u3082\u3057\u3089\u3093\u306d\uff0e<\/p>\n

\r\n#include <iostream>\r\n#include <vector>\r\n#include <array>\r\n#include <boost\/random.hpp>\r\n#include <boost\/accumulators\/accumulators.hpp>\r\n#include <boost\/accumulators\/statistics.hpp>\r\n#include <boost\/lexical_cast.hpp>\r\n#include <eigen3\/Eigen\/Core>\r\n\r\nusing Eigen::MatrixXd;\r\nusing Eigen::VectorXd;\r\n\r\ntemplate<class T>\r\nMatrixXd gen_projection_matrix(int N, int D, T& rand)\r\n{\r\n\tMatrixXd mat(D, N);\r\n\tfor(int i = 0; i < N; i++)\r\n\t\tfor(int j = 0; j < D; j++)\r\n\t\t\tmat(j, i) = rand();\r\n\treturn mat;\r\n}\r\n\r\nstd::vector<Eigen::VectorXd> gen_random_points(int N, int num, boost::mt19937& gen)\r\n{\r\n\tboost::uniform_real<> dst(-100, 100);\r\n\tboost::variate_generator< boost::mt19937&, boost::uniform_real<> > rand(gen, dst);\r\n\r\n\tstd::vector<Eigen::VectorXd> results(num);\r\n\tstd::generate(results.begin(), results.end(), [N, &rand]()\r\n\t{\r\n\t\tEigen::VectorXd vec(N);\r\n\t\tfor(int j = 0; j < N; ++j) vec[j] = rand();\r\n\t\treturn vec; \r\n\t});\r\n\treturn results;\r\n}\r\n\r\nstd::vector<Eigen::VectorXd> projection_points(int N, int D, const MatrixXd& projection, const std::vector<Eigen::VectorXd>& srcs)\r\n{\r\n\tstd::vector<Eigen::VectorXd> result(srcs.size());\r\n\tstd::transform(srcs.begin(), srcs.end(), result.begin(),\r\n\t\t\t[projection](const Eigen::VectorXd& vec) { return projection * vec; });\r\n\treturn result;\r\n}\r\n\r\nMatrixXd gen_distance_vector(const std::vector<Eigen::VectorXd>& points)\r\n{\r\n\tconst int n = points.size();\r\n\tMatrixXd dist(n, n);\r\n\r\n\tfor(int i = 0; i < n; i++)\r\n\t\tfor(int j = i; j < n; j++)\r\n\t\t\tdist(i, j) = dist(j, i) = (points[i] - points[j]).norm();\r\n\r\n\treturn dist;\r\n}\r\n\r\nMatrixXd calc_relative_error(const MatrixXd& mat1, const MatrixXd& mat2)\r\n{\r\n\tassert(mat1.rows() == mat2.rows() && mat1.cols() == mat2.cols());\r\n\r\n\tconst int rows = mat1.rows();\r\n\tconst int cols = mat1.cols();\r\n\tMatrixXd result(rows, cols);\r\n\r\n\tfor(int i = 0; i < rows; i++)\r\n\t\tfor(int j = 0; j < cols; j++)\r\n\t\t\tresult(i, j) = i - j ? (mat1(i, j) \/ mat2(i, j)) : 0;\r\n\r\n\treturn result;\r\n}\r\n\r\ntemplate<class T, class Iter>\r\nvoid calc_statistics(Iter begin, Iter end, std::ostream& os)\r\n{\r\n\tusing namespace boost::accumulators;\r\n\taccumulator_set<double, features<tag::min, tag::max, tag::mean, tag::variance> > acc;\r\n\tfor(; begin != end; ++begin) acc(*begin);\r\n\t\/\/\u3044\u308d\u3044\u308d\u8868\u793a\u3057\u305f\u3044\u306a\u3089\r\n\t\/\/os << "\u5e73\u5747:" << extract::mean(acc) << std::endl;\r\n\t\/\/os << "\u6a19\u6e96\u504f\u5dee:" << std::sqrt(extract::variance(acc)) << std::endl;\r\n\t\/\/os << "\u6700\u5927:" << extract::max(acc) << std::endl;\r\n\t\/\/os << "\u6700\u5c0f:" << extract::min(acc) << std::endl;\r\n\tos << "sigma\/mu = " << std::sqrt(extract::variance(acc)) \/ extract::mean(acc) << std::endl;\r\n}\r\n\r\nvoid calc_statistics_of_points(const std::vector<Eigen::VectorXd>& points, std::ostream& os = std::cout)\r\n{\r\n\tstd::vector<double> t(points.size());\r\n\tstd::transform(points.begin(), points.end(), t.begin(), [](const Eigen::VectorXd& p){ return p.norm(); });\r\n\tcalc_statistics<double>(t.begin(), t.end(), os);\r\n}\r\n\r\nvoid calc_statistics_of_distance(const MatrixXd& mat, std::ostream& os = std::cout)\r\n{\r\n\tconst int rows = mat.rows();\r\n\tconst int cols = mat.cols();\r\n\tstd::vector<double> t;\r\n\tfor(int i = 0; i < rows; i++)\r\n\t\tfor(int j = i + 1; j < cols; j++)\r\n\t\t\tif(1e-6 < mat(i, j))\r\n\t\t\t\tt.push_back(mat(i, j));\r\n\tcalc_statistics<double>(t.begin(), t.end(), os);\r\n}\r\n\r\n\r\nint main()\r\n{\r\n\tboost::mt19937 gen(static_cast<unsigned long>(time(0)));\r\n\r\n\tboost::uniform_real<> dst_uniform(-1, 1);\r\n\tboost::variate_generator< boost::mt19937&, boost::uniform_real<> > rand_uniform(gen, dst_uniform);\r\n\t\r\n\tboost::normal_distribution<> dst_normal(0, 1);\r\n\tboost::variate_generator< boost::mt19937&, boost::normal_distribution<> > rand_normal(gen, dst_normal);\r\n\t\r\n\tauto rand_helsinki = [&gen](){\r\n\t\tint t(gen() % 6);\r\n\t\tif(t == 0)\t\treturn std::sqrt(3);\r\n\t\telse if(t == 1)\treturn -std::sqrt(3);\r\n\t\telse\t\t\treturn 0.0;\r\n\t};\r\n\r\n\tauto rand_sparse = [&rand_uniform](){\r\n\t\tconstexpr double density = 0.01;\r\n\t\tif(fabs(rand_uniform()) < density)\r\n\t\t\treturn rand_uniform();\r\n\t\telse\r\n\t\t\treturn 0.0;\r\n\t};\r\n\r\n\tconst std::vector<int> ks = {100, 500, 1000};\t\/\/\u70b9\u7fa4\u306e\u6570\r\n\tconst std::vector<int> Ms = {100, 1000, 10000};\t\/\/\u6b21\u5143\r\n\tconst std::vector<double> rs = {0.01, 0.02, 0.05, 0.1, 0.2};\t\/\/\u524a\u6e1b\u7387\r\n\t\r\n\tfor(double r: rs)\r\n\t{\r\n\t\tstd::cerr << "\u524a\u6e1b\u7387:" << (r * 100) << "%" << std::endl;\r\n\t\tfor(int M: Ms)\r\n\t\t{\r\n\t\t\tint N = static_cast<int>(r * M);\r\n\r\n\t\t\tfor(int k: ks)\r\n\t\t\t{\r\n\t\t\t\t\/\/\u3053\u3053\u306b\u6e21\u3059\u306e\u3092\u5207\u308a\u66ff\u3048\u308b\u3053\u3068\u3067\u5909\u63db\u884c\u5217\u751f\u6210\u65b9\u6cd5\u3092\u5909\u3048\u307e\u3059\uff1e\uff1c\r\n\t\t\t\tconst MatrixXd R = gen_projection_matrix(M, N, rand_sparse);\r\n\t\t\t\tconst std::vector<Eigen::VectorXd> srcs = gen_random_points(M, k, gen);\r\n\t\t\t\tconst std::vector<Eigen::VectorXd> dsts = projection_points(M, N, R, srcs);\r\n\t\t\t\tconst MatrixXd src_dist = gen_distance_vector(srcs);\r\n\t\t\t\tconst MatrixXd dst_dist = gen_distance_vector(dsts);\r\n\t\t\t\tconst MatrixXd relative = calc_relative_error(src_dist, dst_dist);\r\n\r\n\t\t\t\t\/*\r\n\t\t\t\t\/\/\u8ddd\u96e2\u884c\u5217\u3068\u8ddd\u96e2\u5909\u5316\u7387\u884c\u5217\u306e\u8868\u793a\r\n\t\t\t\tstd::cerr << src_dist << std::endl << std::endl;\r\n\t\t\t\tstd::cerr << dst_dist << std::endl << std::endl;\r\n\t\t\t\tstd::cerr << relative << std::endl << std::endl;\r\n\t\t\t\t*\/\r\n\r\n\t\t\t\t\/*\r\n\t\t\t\t\/\/\u751f\u6210\u70b9\u7fa4\u304c\u7403\u9762\u4e0a\u306b\u5206\u5e03\u3057\u3066\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\r\n\t\t\t\tstd::cerr << "\u5143\u306e\u70b9\u7fa4\u306e\u539f\u70b9\u304b\u3089\u306e\u8ddd\u96e2\u306e\u5206\u5e03" << std::endl;\r\n\t\t\t\tcalc_statistics_of_points(srcs, std::cerr);\r\n\r\n\t\t\t\t\/\/\u5909\u63db\u5f8c\u306e\u70b9\u7fa4\u306f\u305d\u308c\u307b\u3069\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3084\u306f\u308a\u7403\u9762\u4ed8\u8fd1\u306b\u5206\u5e03\u3057\u3066\u3044\u307e\u3059\r\n\t\t\t\tstd::cerr << "\u5909\u63db\u5f8c\u306e\u70b9\u7fa4\u306e\u539f\u70b9\u304b\u3089\u306e\u8ddd\u96e2\u306e\u5206\u5e03" << std::endl;\r\n\t\t\t\tcalc_statistics_of_points(dsts, std::cerr);\r\n\t\t\t\t*\/\r\n\r\n\t\t\t\tstd::cerr << M << "\u6b21\u5143 -> " << N << "\u6b21\u5143";\r\n\t\t\t\tcalc_statistics_of_distance(relative, std::cerr);\r\n\t\t\t}\r\n\t\t}\r\n\t}\r\n}\r\n<\/pre>\n
*\u5b9f\u9a132:SIFT\u7279\u5fb4\u91cf\u306e\u6b21\u5143\u524a\u6e1b\u306b\u3088\u308b\u753b\u50cf\u9593\u5bfe\u5fdc\u4ed8\u3051<\/p>\n
\u8a73\u7d30\u306f\u8ff0\u3079\u307e\u305b\u3093\u304c\uff0cSIFT\u3068\u3044\u3046\u5c40\u6240\u7279\u5fb4\u91cf\u304c\u3042\u308a\uff0c\u3042\u308b\u70b9\u3092\u4e2d\u5fc3\u3068\u3057\u3066\u6700\u3082\u305d\u306e\u70b9\u306e\u7279\u5fb4\u3092\u3088\u304f\u8868\u3059\u7bc4\u56f2\u306e\u69d8\u5b50\u3092\u56de\u8ee2\u30fb\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u30fb\u7167\u660e\u5909\u52d5\u306b\u9811\u5065\u306a\u5f62\u3067128\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3067\u8a18\u8ff0\u3059\u308b\u624b\u6cd5\u304c\u3042\u308a\u307e\u3059\uff0e
\n1\u679a\u306e\u753b\u50cf\u304b\u3089\u305f\u304f\u3055\u3093\u306eSIFT\u7279\u5fb4\u91cf(\u305f\u3044\u3066\u3044\u6570\u767e\u304b\u3089\u6570\u5343\u70b9)\uff0c\u3059\u306a\u308f\u3061128\u6b21\u5143\u306e\u70b9\u7fa4\u3092\u6c42\u3081\u308b\u3068\uff0c\u5225\u306e\u753b\u50cf\u304b\u3089\u540c\u69d8\u306b\u5f97\u305f\u7279\u5fb4\u91cf\u3068\u306e\u6700\u8fd1\u508d\u63a2\u7d22\u306b\u3088\u3063\u3066\u7570\u306a\u308b\u753b\u50cf\u306e2\u70b9\u304c\u540c\u4e00\u306e\u3082\u306e\u3092\u5199\u3057\u3066\u308b\u3068\u5224\u65ad\u3067\u304d\u308b\u2026\u3068\u3044\u3046\u3088\u3046\u306a\u3082\u306e\u3067\u3059\uff0e<\/p>\n
\u305f\u3076\u3093128\u6b21\u5143\u3068\u3044\u3063\u305f\u3089\u305d\u308c\u307b\u3069\u9ad8\u6b21\u5143\u3058\u3083\u306a\u3044\u306e\u3067\uff0cRandom Projection\u306e\u5b9f\u9a13\u3068\u3057\u3066\u306f\u305d\u308c\u307b\u3069\u9069\u5207\u3058\u3083\u306a\u3044\u304b\u3082\u3057\u308c\u306a\u3044\uff0e
\n\u8d85\u5287\u7684\u306a\u52b9\u679c\u3063\u3066\u3053\u3068\u306f\u306a\u3044\u3068\u304a\u3082\u3044\u307e\u3059\uff0e<\/p>\n
**\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u6982\u8981<\/p>\n
2\u679a\u306e\u753b\u50cf\u3092\u8aad\u307f\u8fbc\u3093\u3067\uff0c\u305d\u308c\u305e\u308c\u304b\u3089SIFT\u7279\u5fb4\u91cf\u3092\u5f97\u307e\u3059\uff0e
\n\u3053\u306e\u7279\u5fb4\u91cf\u540c\u58eb\u306e\u5bfe\u5fdc\u4ed8\u3051\u3092128\u6b21\u5143\u306e\u307e\u307e\u884c\u3063\u305f\u5834\u5408\u3068\uff0c\u9806\u306b64\u6b21\u5143\uff0c32\u6b21\u5143\uff0c16\u6b21\u5143\uff0c8\u6b21\u5143\u306b\u843d\u3068\u3057\u305f\u5834\u5408\u3067\u6bd4\u3079\u3066\u307f\u307e\u3059\uff0e<\/p>\n
**\u5b9f\u88c5<\/p>\n
OpenCV 2.3.1a\u3092\u4f7f\u3063\u3066\u3044\u307e\u3059\uff0e<\/p>\n
OpenCV\u306eSIFT Descriptor\u3067\u62bd\u51fa\u3055\u308c\u305f128\u6b21\u5143\u306e\u7279\u5fb4\u91cf\u7fa4\u306fcv::Mat\u306b\u3088\u3063\u3066(\u7279\u5fb4\u70b9\u6570)\u884c\u00d7128\u5217\u306e\u884c\u5217\u3068\u3057\u3066\u8a18\u8ff0\u3055\u308c\uff0c\u305d\u306e\u5404\u884c\u304c\u3072\u3068\u3064\u306e\u7279\u5fb4\u91cf\u3092\u8868\u3057\u307e\u3059\uff0e\u3053\u308c\u3092\u5909\u63db\u3057\u3066\uff0c(\u7279\u5fb4\u70b9\u6570)\u884c\u00d7(\u843d\u3068\u3057\u305f\u6b21\u5143\u6570)\u5217\u306e\u884c\u5217\u3092\u3064\u304f\u308a\uff0c\u3042\u3068\u306fOpenCV\u306b\u307e\u304b\u305b\u3066\u6700\u8fd1\u508d\u63a2\u7d22\u306b\u3088\u308b\u5bfe\u5fdc\u4ed8\u3051\u3092\u884c\u3044\u307e\u3059\uff0e<\/p>\n
\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u5b9f\u884c\u3059\u308b\u306b\u306f\uff0c\u753b\u50cf\u30d5\u30a1\u30a4\u30eb\u540d\u3092\u3075\u305f\u3064\uff0c\u843d\u3068\u3059\u6b21\u5143\u6570\u3092\u6307\u5b9a\u3057\u307e\u3059\uff0e
\nSIFT\u306e\u7279\u5fb4\u91cf\u305d\u306e\u307e\u307e\u3067\u306e\u5bfe\u5fdc\u4ed8\u3051\u7d50\u679c\u3092”128.jpg”\u306b\uff0c\u6b21\u5143\u3092\u843d\u3068\u3057\u3066\u5bfe\u5fdc\u4ed8\u3051\u305f\u7d50\u679c\u3092”N.jpg”\u306b\u51fa\u529b\u3057\u3066\u3044\u307e\u3059\uff0e
\n\u306a\u304a\u30a8\u30e9\u30fc\u30c1\u30a7\u30c3\u30af\u306e\u985e\u306f\u4e00\u5207\u884c\u3063\u3066\u3044\u307e\u305b\u3093\uff0e<\/p>\n
\u4ee5\u4e0b\u30b3\u30f3\u30d1\u30a4\u30eb\u304b\u3089\u5b9f\u884c\u307e\u3067\uff0e<\/p>\n
\r\n% g++ prog.cpp -Wall -O2 -std=c++0x -I\/usr\/local\/include\/opencv -I\/usr\/local\/include\/eigen3 -lopencv_features2d -lopencv_core -lopencv_highgui\r\n% .\/a.out img1.jpg img2.jpg 32\r\n% display 128.jpg\r\n% display N.jpg\r\n<\/pre>\n
**\u5b9f\u884c\u4f8b<\/p>\n
\u9762\u5012\u306a\u306e\u3067\u5b9a\u91cf\u7684\u306a\u8a55\u4fa1\u306f\u884c\u3044\u307e\u305b\u3093\uff0e
\n\u6027\u80fd\u8a55\u4fa1\u3082\u884c\u3044\u307e\u305b\u3093\uff0e
\n\u3071\u3063\u3068\u898b\u3061\u3083\u3068\u3067\u304d\u3066\u308b\u306e\u3067\u3088\u3057\u3068\u3057\u307e\u3059\uff0e<\/p>\n
***\u540c\u3058\u753b\u50cf\u3067\u306e\u5bfe\u5fdc\u4ed8\u3051<\/p>\n
\u3053\u308c\u304c\u3061\u3083\u3093\u3068\u3067\u304d\u3066\u308b\u306e\u306f\u5f53\u7136\u3067\u3059\uff57<\/p>\n
\u307e\u305aSIFT\u3067\u306e\u5bfe\u5fdc\u4ed8\u3051\uff0e\u4ee5\u4e0b\u3053\u308c\u3068\u6bd4\u8f03\u3057\u3066\u304f\u3060\u3055\u3044\u306a\uff0e
\n\"\"<\/a><\/p>\n
64\u6b21\u5143\u306b\u843d\u3068\u3057\u3066\u5bfe\u5fdc\u4ed8\u3051\u305f\u7d50\u679c\uff0e
\n\"\"<\/a><\/p>\n
32\u6b21\u5143\u306b\u843d\u3068\u3057\u3066\u5bfe\u5fdc\u4ed8\u3051\u305f\u7d50\u679c\uff0e
\n\"\"<\/a><\/p>\n
16\u6b21\u5143\u306b\u843d\u3068\u3057\u3066\u5bfe\u5fdc\u4ed8\u3051\u305f\u7d50\u679c\uff0e
\n\"\"<\/a><\/p>\n
8\u6b21\u5143\u306b\u843d\u3068\u3057\u3066\u5bfe\u5fdc\u4ed8\u3051\u305f\u7d50\u679c\uff0e
\n\"\"<\/a><\/p>\n
***\u56de\u8ee2\u30fb\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u753b\u50cf\u3067\u306e\u5bfe\u5fdc\u4ed8\u3051<\/p>\n
256×256\u306eLenna\u3092\u3060\u3044\u305f\u304445\u5ea6\u304f\u3089\u3044\u50be\u3051\u3066\u7e2e\u5c0f\u3057\u305f\u3082\u306e\u3067\u3059\uff0e<\/p>\n
\u307e\u305a\u3053\u3061\u3089\u304cSIFT\u305d\u306e\u307e\u307e\u3067\u5bfe\u5fdc\u4ed8\u3051\uff0e
\n\"\"<\/a><\/p>\n
64\u6b21\u5143\uff0e
\n\"\"<\/a><\/p>\n
32\u6b21\u5143\uff0e
\n\"\"<\/a><\/p>\n
16\u6b21\u5143\uff0e
\n\"\"<\/a><\/p>\n
8\u6b21\u5143\uff0e
\n\"\"<\/a><\/p>\n
\u305d\u3053\u305d\u3053\u3044\u3051\u3066\u306a\u3044\u3067\u3059\u304b\uff1f<\/p>\n
**\u30d7\u30ed\u30b0\u30e9\u30e0<\/p>\n
\u30bd\u30fc\u30b9\u305c\u3093\u3076\u8f09\u305b\u307e\u3059\uff0e\u30b3\u30f3\u30d1\u30a4\u30eb\u65b9\u6cd5\u306f\u4e0a\u306b\u3061\u3087\u3063\u3068\u66f8\u3044\u305f\u901a\u308a\uff0e<\/p>\n
\r\n#include <vector>\r\n#include <eigen3\/Eigen\/Core>\r\n#include <opencv2\/opencv.hpp>\r\n#include <opencv2\/core\/core.hpp>\r\n#include <opencv2\/core\/eigen.hpp>\r\n#include <opencv2\/highgui\/highgui.hpp>\r\n\r\n#include <boost\/lexical_cast.hpp>\r\n#include <boost\/random.hpp>\r\n\r\n\r\n\/\/\u203b\u884c\u5217\u751f\u6210\u306f\u307b\u307c\u4e0a\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u5b9f\u9a13\u306e\u3068\u540c\u3058\u3067\u3059\u304c\uff0c\r\n\/\/\u3000MatrixXd\u3058\u3083\u306a\u304f\u3066MatrixXf\u306b\u3057\u3066\u3042\u308a\u307e\u3059\uff0e\r\ntemplate<class T>\r\nEigen::MatrixXf gen_projection_matrix(int N, int D, T& rand)\r\n{\r\n\tEigen::MatrixXf mat(D, N);\r\n\tfor(int i = 0; i < N; i++)\r\n\t\tfor(int j = 0; j < D; j++)\r\n\t\t\tmat(j, i) = rand();\r\n\treturn mat;\r\n}\r\n\r\ncv::Mat random_projection(const cv::Mat& dsc, const Eigen::MatrixXf& R)\r\n{\r\n\tconst int rows = dsc.rows;\r\n\tcv::Mat result(rows, R.rows(), CV_32FC1);\r\n\r\n\tfor(int r = 0; r < rows; r++)\r\n\t{\r\n\t\t\/\/\u884c\u3092\u3068\u3063\u3066\u304d\u3066Eigen\u306e\u30d9\u30af\u30c8\u30eb\u306b\u5909\u63db\r\n\t\tcv::Mat row = dsc.row(r);\r\n\t\tEigen::MatrixXf row_eigen;\r\n\t\tcv::cv2eigen(row, row_eigen);\r\n\r\n\t\t\/\/R\u306b\u3088\u308b\u5c04\u5f71\r\n\t\trow_eigen = (R * row_eigen.transpose()).transpose();\r\n\r\n\t\t\/\/cv::Mat\u306b\u623b\u3059\r\n\t\t\/\/\u203b\u9818\u57df\u7684\u306a\u3054\u3061\u3083\u3054\u3061\u3083\u3067\u624b\u4f5c\u696d\u30b3\u30d4\u30fc\u3057\u3066\u307e\u3059\uff1b\uff1b\r\n\t\tfor(int i = 0; i < R.rows(); i++)\r\n\t\t\tresult.at<float>(r, i) = row_eigen(i);\r\n\t}\r\n\treturn result;\r\n}\r\n\r\n\r\nint main(int argc, char *argv[])\r\n{\r\n\tif(argc != 4)\r\n\t\treturn -1;\r\n\r\n\t\/\/Random Projection\u306e\u884c\u5217\u751f\u6210\u65b9\u6cd5\u306e\u4e00\u89a7\r\n\tboost::mt19937 gen(static_cast<unsigned long>(time(0)));\r\n\r\n\tboost::uniform_real<> dst_uniform(-1, 1);\r\n\tboost::variate_generator< boost::mt19937&, boost::uniform_real<> > rand_uniform(gen, dst_uniform);\r\n\t\r\n\tboost::normal_distribution<> dst_normal(0, 1);\r\n\tboost::variate_generator< boost::mt19937&, boost::normal_distribution<> > rand_normal(gen, dst_normal);\r\n\t\r\n\tauto rand_helsinki = [&gen](){\r\n\t\tint t(gen() % 6);\r\n\t\tif(t == 0)\t\treturn std::sqrt(3);\r\n\t\telse if(t == 1)\treturn -std::sqrt(3);\r\n\t\telse\t\t\treturn 0.0;\r\n\t};\r\n\r\n\tauto rand_sparse = [&rand_uniform](){\r\n\t\tconstexpr double density = 0.01;\r\n\t\tif(fabs(rand_uniform()) < density)\r\n\t\t\treturn rand_uniform();\r\n\t\telse\r\n\t\t\treturn 0.0;\r\n\t};\r\n\r\n\t\/\/\u5909\u63db\u884c\u5217\u751f\u6210(\u4e0a\u306erand_*\u306e\u3069\u308c\u304b)\r\n\tconst int N = boost::lexical_cast<int>(argv[3]);\r\n\tconst Eigen::MatrixXf R = gen_projection_matrix(128, N, rand_uniform);\r\n\r\n\t\/\/SIFT\u95a2\u4fc2\r\n\tcv::SiftFeatureDetector detector;\r\n\tcv::SiftDescriptorExtractor extractor;\r\n\tcv::BruteForceMatcher<cv::L2<float> > matcher;\r\n\r\n\t\/\/\u753b\u50cf\u8aad\u307f\u8fbc\u307f\r\n\tcv::Mat img1 = cv::imread(argv[1]);\r\n\tcv::Mat img2 = cv::imread(argv[2]);\r\n\r\n\t\/\/\u753b\u50cf1\u304b\u3089\u7279\u5fb4\u91cf\u62bd\u51fa\r\n\tstd::vector<cv::KeyPoint> kps1;\r\n\tcv::Mat dsc1;\r\n\tdetector.detect(img1, kps1);\r\n\textractor.compute(img1, kps1, dsc1);\r\n\r\n\t\/\/\u753b\u50cf2\u304b\u3089\u7279\u5fb4\u91cf\u62bd\u51fa\r\n\tstd::vector<cv::KeyPoint> kps2;\r\n\tcv::Mat dsc2;\r\n\tdetector.detect(img2, kps2);\r\n\textractor.compute(img2, kps2, dsc2);\r\n\r\n\t\/\/128\u6b21\u5143\u3092N\u6b21\u5143\u306b\u843d\u3068\u3059\r\n\tcv::Mat dsc1_N = random_projection(dsc1, R);\r\n\tcv::Mat dsc2_N = random_projection(dsc2, R);\r\n\tstd::vector<cv::DMatch> matches_N;\r\n\tmatcher.match(dsc1_N, dsc2_N, matches_N);\r\n\tcv::Mat result_N;\r\n\tcv::drawMatches(img1, kps1, img2, kps2, matches_N, result_N);\r\n\r\n\t\/\/128\u6b21\u5143\u306eSIFT\u7279\u5fb4\u91cf\u305d\u306e\u307e\u307e\u3067\u6700\u8fd1\u508d\u63a2\u7d22\r\n\tstd::vector<cv::DMatch> matches128;\r\n\tmatcher.match(dsc1, dsc2, matches128);\r\n\tcv::Mat result128;\r\n\tcv::drawMatches(img1, kps1, img2, kps2, matches128, result128);\r\n\r\n\tcv::imwrite("128.jpg", result128);\r\n\tcv::imwrite("N.jpg", result_N);\r\n}\r\n<\/pre>\n
*\u307e\u3068\u3081<\/p>\n
\u3053\u3046\u3044\u3046\u306e\u306f\u307b\u3093\u3068\u304a\u3082\u3057\u308d\u3044\u3067\u3059\u306d\uff0e<\/p>\n
\u3082\u3063\u3068\u7406\u8ad6\u7684\u306b\u8a70\u3081\u3066\u7406\u89e3\u3057\u305f\u3044\u3093\u3067\u3059\u3051\u3069\u3082\uff0e<\/p>\n
\u30c4\u30c3\u30b3\u30df\u3069\u3053\u308d\u306f\u305f\u304f\u3055\u3093\u3042\u308b\u3068\u601d\u3044\u307e\u3059\u306e\u3067\uff0c\u5bb9\u8d66\u306a\u304f\u304a\u9858\u3044\u81f4\u3057\u307e\u3059\uff0e<\/p>\n","protected":false},"excerpt":{"rendered":"
\u3044\u304d\u306a\u308a\u59cb\u307e\u3063\u305f\u300c\u9b5a\u3067\u3082\u308f\u304b\u308b\u300d\u30b7\u30ea\u30fc\u30ba\uff0e \u4eca\u56de\u306f\u60c5\u5831\u79d1\u5b66\u7cfb\u306e\u65b9\u5411\u3051\uff0e \u6b21\u5143\u524a\u6e1b\u306e\u3044\u3061\u624b\u6cd5\u3067\u3042\u308b\u300cRandom Projection\u300d\u3092\u7c21\u5358\u306b\u7d39\u4ecb\u3057\u307e\u3059\uff0e \u5177\u4f53\u7684\u306b\u3084\u3063\u3066\u308b\u3053\u3068\uff0c\u3067\u304d\u308b\u3053\u3068\u306f\u3082\u306e\u3063\u305d\u7c21\u5358\u3067\uff0c\u3053\u306a\u3044\u3060Boo […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[26,27,25],"class_list":["post-737","post","type-post","status-publish","format-standard","hentry","category-1","tag-cvprml","tag-27","tag-25"],"_links":{"self":[{"href":"https:\/\/daily.belltail.jp\/index.php?rest_route=\/wp\/v2\/posts\/737","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/daily.belltail.jp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/daily.belltail.jp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/daily.belltail.jp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/daily.belltail.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=737"}],"version-history":[{"count":0,"href":"https:\/\/daily.belltail.jp\/index.php?rest_route=\/wp\/v2\/posts\/737\/revisions"}],"wp:attachment":[{"href":"https:\/\/daily.belltail.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=737"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daily.belltail.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=737"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daily.belltail.jp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=737"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}