{"id":643,"date":"2019-01-29T13:30:30","date_gmt":"2019-01-29T04:30:30","guid":{"rendered":"https:\/\/mieruca-ai.com\/ai\/?p=643"},"modified":"2019-09-18T10:57:35","modified_gmt":"2019-09-18T01:57:35","slug":"lsa-lsi-svd","status":"publish","type":"post","link":"https:\/\/mieruca-ai.com\/ai\/lsa-lsi-svd\/","title":{"rendered":"\u3010\u6280\u8853\u89e3\u8aac\u3011\u6f5c\u5728\u610f\u5473\u89e3\u6790(LSA) \uff5e\u7279\u7570\u5024\u5206\u89e3(SVD)\u304b\u3089\u6587\u66f8\u691c\u7d22\u307e\u3067\uff5e"},"content":{"rendered":"

<\/p>\n

\n\u4eca\u56de\u306f\u6f5c\u5728\u610f\u5473\u89e3\u6790(Latent Semantic Analysis: LSA)<\/strong>\u3068\u7279\u7570\u5024\u5206\u89e3(Singular Value Decomposition: SVD)<\/strong>\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\uff0e
\nLSA\u306f\u6587\u66f8\u306e\u5206\u985e\u3084\uff0c\u60c5\u5831\u691c\u7d22\u306e\u5206\u91ce(\u3053\u306e\u5206\u91ce\u3067\u306fLSI<\/strong>\u3068\u3057\u3066\u77e5\u3089\u308c\u308b)\u306a\u3069\u306b\u4f7f\u308f\u308c\u308b\u30c8\u30d4\u30c3\u30af\u30e2\u30c7\u30eb<\/strong>\u306e\u4ee3\u8868\u4f8b\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\uff0e
\n\u3053\u306e\u30e2\u30c7\u30eb\u3092\u4f7f\u3046\u3068\uff0c\u5358\u8a9e\u3068\u6587\u66f8\u306e\u305d\u308c\u305e\u308c\u306e\u7d44\u307f\u5408\u308f\u305b\u306b\u3064\u3044\u3066\uff0c\u985e\u4f3c\u5ea6\u3092\u6e2c\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff0e\n<\/p>\n

<\/p>\n

\u76ee\u6b21<\/h3>\n

\n\u6f5c\u5728\u610f\u5473\u89e3\u6790(LSA, LSI)\u3068\u306f<\/a>
\n\u7279\u7570\u5024\u5206\u89e3(SVD)<\/a>
\nLSA\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/a>
\nLSA\u306e\u5fdc\u7528<\/a>
\nLSA\u306e\u554f\u984c\u70b9<\/a>
\n\u53c2\u8003\u6587\u732e<\/a>\n<\/p>\n

\u6f5c\u5728\u610f\u5473\u89e3\u6790(LSA, LSI)\u3068\u306f<\/h2>\n

\n\t\u6f5c\u5728\u610f\u5473\u89e3\u6790(Latent Semantic Analysis: LSA)<\/strong>\u3068\u306f\uff0c1990\u5e74\u306bDeerwester\u3089\u304c\u767a\u8868\u3057\u305f\uff0c\u6587\u7ae0\u306e\u81ea\u52d5\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u5316\uff0c\u691c\u7d22\u306e\u65b9\u6cd5\u3067\u3042\u308b\uff0e\u691c\u7d22\u306e\u5206\u91ce\u3067\u306f\u6f5c\u5728\u610f\u5473\u30a4\u30f3\u30c7\u30c3\u30af\u30b9(Latent Semantic Indexing: LSI)<\/strong>\u3068\u3082\u547c\u3070\u308c\u308b\uff0e\u9ad8\u6b21\u5143\u306e\u6587\u66f8\u7fa4\u304b\u3089\uff0c\u4e0e\u3048\u3089\u308c\u305f\u30af\u30a8\u30ea\u306b\u610f\u5473\u7684\u306b\u95a2\u9023\u3059\u308b\u6587\u66f8\u3092\u898b\u3064\u3051\u3066\u304f\u308b\u305f\u3081\u306b\u4f5c\u3089\u308c\u305f\uff0e\u5358\u8a9e-\u5358\u8a9e\uff0c\u5358\u8a9e-\u6587\u66f8\uff0c\u6587\u66f8-\u6587\u66f8\u306e\u985e\u4f3c\u5ea6\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e<\/font>
\n\u3000\u3053\u306e\u624b\u6cd5\u3067\u306f\u9ad8\u6b21\u5143\u306e\u6587\u66f8\u306e\u884c\u5217\u3092\uff0c\u7279\u7570\u5024\u5206\u89e3(SVD)<\/strong>\u3068\u3044\u3046\u7dda\u5f62\u4ee3\u6570\u7684\u624b\u6bb5\u3067\u4f4e\u6b21\u5143\u306b\u7e2e\u7d04\u3057\u7528\u3044\u3066\u3044\u308b\uff0e\u5727\u7e2e\u3055\u308c\u3066\u3067\u304d\u305f\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u5185\u3067\u306f\uff0c\u8fd1\u3044\u6982\u5ff5\u306f\u8fd1\u304f\u306b\uff0c\u9060\u3044\u6982\u5ff5\u306f\u9060\u304f\u306b\u30d7\u30ed\u30c3\u30c8\u3055\u308c\u308b\uff0e\u4f4e\u6b21\u5143\u306b\u7e2e\u7d04\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\uff0c\u758e\u3089\u306a\u30c7\u30fc\u30bf\u3084\u30ce\u30a4\u30ba\u304c\u591a\u3044\u30c7\u30fc\u30bf\u306b\u5bfe\u5fdc\u3067\u304d\u308b\uff0e\u307e\u305f\uff0c\u30e1\u30e2\u30ea\u306b\u4e57\u3089\u306a\u3044\u5de8\u5927\u306a\u30c7\u30fc\u30bf\u306b\u3082\u5bfe\u5fdc\u3067\u304d\u308b\uff0e\n<\/p>\n

\u6642\u4ee3\u7684\u80cc\u666f<\/h3>\n

\n\u3000LSA\u4ee5\u524d\u306e\u6642\u4ee3\u306b\u4f5c\u3089\u308c\u305f\u60c5\u5831\u691c\u7d22\u306e\u624b\u6cd5\u3067\u306f\uff0c\u8a9e\u306e\u610f\u5473\u305d\u306e\u3082\u306e\u306b\u7740\u76ee\u3057\u3066\u3044\u305f\uff0e\u3057\u304b\u3057\uff0c\u8a9e\u306e\u610f\u5473\u306f\u591a\u7fa9\u8a9e<\/strong>\u3068\u3057\u3066\u77e5\u3089\u308c\u308b\u3088\u3046\u306b\uff0c\u6587\u8108\u306b\u3088\u3063\u3066\u5909\u308f\u308b\u3053\u3068\u3082\u3042\u308a\u4fe1\u7528\u6027\u306b\u6b20\u3051\u308b\uff0e\u307e\u305f\uff0c\u5358\u8a9eA\u3067\u691c\u7d22\u3057\u305f\u6642\u306b\u305d\u306e\u985e\u7fa9\u8a9e<\/strong>\u306e\u5358\u8a9eB\u306e\u7d50\u679c\u3082\u3042\u308b\u7a0b\u5ea6\u8003\u616e\u3057\u306a\u304f\u3066\u306f\u306a\u3089\u306a\u3044\u304c\uff0c\u3053\u308c\u306b\u5bfe\u5fdc\u3059\u308b\u306e\u306b\u56f0\u96e3\u3057\u3066\u3044\u305f\uff0e\u305d\u306e\u305f\u3081\uff0c\u3088\u308a\u4fe1\u983c\u6027\u306e\u9ad8\u3044\u30a8\u30f3\u30c6\u30a3\u30c6\u30a3\u306e\u96c6\u5408\u306b\u7f6e\u304d\u63db\u3048\u308b\u5fc5\u8981\u304c\u3042\u308b\u3068LSA\u306e\u63d0\u6848\u8005\u305f\u3061\u306f\u8003\u3048\u3066\u3044\u305f\uff0e\n<\/p>\n

\u7279\u7570\u5024\u5206\u89e3(SVD)<\/h2>\n

\n\u3000LSA\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u3046\u3061\u5927\u5207\u306a\u90e8\u5206\u304c\u3053\u306e\u7279\u7570\u5024\u5206\u89e3(SVD)\u3067\u3042\u308b\uff0e\u307e\u305a\u306f\uff0c\u3053\u306e\u6280\u8853\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3066\u3044\u304f\uff0e\n<\/p>\n

\u7279\u7570\u5024\u5206\u89e3(SVD)\u3068\u306f<\/h3>\n

\"SVD\"<\/p>\n

\n \u7279\u7570\u5024\u5206\u89e3(Singular Value Decompositon: SVD)<\/strong>\u3068\u306f\u4e00\u8a00\u3067\u3044\u3046\u3068\u4e0a\u306e\u56f3\u306e\u3088\u3046\u306b\uff0c\u4efb\u610f\u306e\u5b9f\u884c\u5217\u304c\u4e8c\u3064\u306e\u76f4\u4ea4\u884c\u5217\u3068\u7279\u7570\u5024\u304b\u3089\u306a\u308b\u5bfe\u89d2\u884c\u5217\u306e\u5185\u7a4d\u306b\u5206\u89e3\u3067\u304d\u308b<\/strong>\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\uff0e\n<\/p>\n

\n\t$$
\n\t\\displaystyle
\n\tA = U\u03a3V^T
\n\t$$\n<\/div>\n

\n\t\u53f3\u8fba\u306e\uff0c\u5de6\u53f3\u306e\u884c\u5217($U$\u3068$V^T$)\u306e\u5404\u5217\u3092\u305d\u308c\u305e\u308c\uff0c\u53f3\u7279\u7570\u30d9\u30af\u30c8\u30eb\uff0c\u5de6\u7279\u7570\u30d9\u30af\u30c8\u30eb\u3068\u547c\u3076\uff0e\u307e\u305f\uff0c\u305d\u308c\u305e\u308c\u5165\u529b\u306e\u884c\uff0c\u5217\u30d9\u30af\u30c8\u30eb\u306e\u5f35\u308b\u7a7a\u9593\u306e\u6b63\u898f\u76f4\u4ea4\u57fa\u5e95\u3092\u8868\u3059\uff0e\u3053\u3053\u3067\uff0c\u884c\u5217$A$\u306e\u7279\u7570\u5024<\/strong>\u3068\u306f\uff0c$A$\u3068\u305d\u306e\u968f\u4f34\u884c\u5217$A^{*}$\uff08\u8907\u7d20\u5171\u5f79\u304b\u3064\u8ee2\u7f6e\u884c\u5217\uff09\u3067\u3042\u308b\u3068\u306e\u7a4d\u306e\u305d\u308c\u305e\u308c\u306e\u56fa\u6709\u5024\u306b\u304a\u3051\u308b\uff0c\u975e\u8ca0\u306e\u5e73\u65b9\u6839\u306e\u3053\u3068\u3067\u3042\u308b\uff0e\u3064\u307e\u308a\uff0c\u771f\u3093\u4e2d\u306e\u884c\u5217$\u03a3$\u306e\u5bfe\u89d2\u6210\u5206\u306e\u4e8c\u4e57\u306f\u56fa\u6709\u5024\u3067\u3042\u308b\uff0e\u7279\u7570\u5024\u306f\u5404\u57fa\u5e95\u306e\u91cd\u8981\u5ea6\u3092\u8868\u3057\u3066\u3044\u308b\uff0e
\n\t\uff08LSA\u306e\u8ad6\u6587\u4e2d\u3067\u306f\uff0c$X = T_{0}S_{0}D_{0}^{*}$\u3068\u8a18\u3055\u308c\u3066\u3044\u308b\uff0eT:term, S:semantic space, D:document\u3092\u8868\u3057\u3066\u3044\u308b\u3068\u601d\u308f\u308c\u308b\uff0e\uff09\n<\/p>\n

SVD\u306e\u8a3c\u660e\u6982\u7565<\/h3>\n

\n\u4ee5\u4e0b\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u793a\u3059\uff0e\n<\/p>\n

$$A = U\u03a3V^T$$<\/p>\n

\n\u4efb\u610f\u306e$m\u00d7n(m\\geq n)$\u5b9f\u884c\u5217$A (rank=k)$\u306b\u304a\u3044\u3066\uff0c$A^{T}A$\u306f\u5bfe\u79f0\u884c\u5217\u3067\u3042\u308b\uff0e
\n\u3000\uff08\u2235 $(A^{T}A)^{T}=A^{T}A$\uff09
\n\u305d\u306e\u305f\u3081\uff0c\u6b63\u898f\u76f4\u4ea4\u57fa\u5e95\u3092\u7528\u3044\u3066\u5bfe\u89d2\u5316\u53ef\u80fd\u3067\u3042\u308b\uff0e
\n\u307e\u305f\uff0c\u56fa\u6709\u5024\u306f\u5b9f\u6570\u3067\uff0c\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306f\u4e92\u3044\u306b\u76f4\u4ea4\u3059\u308b\uff0e\n<\/p>\n

\n$A^{T}A$\u3092\u56fa\u6709\u5024\u306e\u5b9a\u7fa9<\/strong>\u306b\u5f93\u3044\u56fa\u6709\u5206\u89e3\u3059\u308b\uff0e
\n$A^{T}AV=\u039bV$
\n\u305f\u3060\u3057\uff0c$\u039b$\u306f$n$\u500b\u306e\u56fa\u6709\u5024
\n\u3000$\u03bb_1>…>\u03bb_r>0, \u03bb_{r+1}=…=\u03bb_k=0$
\n\u304b\u3089\u306a\u308b\u5bfe\u89d2\u884c\u5217$Diag(\u03bb_1,…,\u03bb_k)$\u3067\u3042\u308b\uff0e
\n\u307e\u305f\uff0c$V$\u306f\u3053\u308c\u306b\u5bfe\u3059\u308b\u56fa\u6709\u30d9\u30af\u30c8\u30eb\uff08\u6b63\u898f\u76f4\u4ea4\u57fa\u5e95\uff09<\/strong>\u3092\u5217\u306b\u3082\u3064\u884c\u5217\u3067\u3042\u308b\uff0e
\n\u3000$V=[v_1 v_2 … v_k]$\n<\/p>\n

\n$i\\leq r$\u306e\u6642\uff0c\u56fa\u6709\u5024\u306e\u5b9a\u7fa9\u5f0f\u304b\u3089\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3064\uff0e
\n$A^TAv_i = \u03bb_iv_i$
\n$i\\geq r+1$\u306e\u6642\u306b\u306f\uff0c\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3064\uff0e
\n$A^TAv_i = 0v_i = 0$\n<\/p>\n

\n\u3053\u3053\u3067\uff0c$i\\leq r$\u306e\u6642$u_i=\\frac{Av_i}{\\sqrt{\u03bb_i}}$\u3068\u304a\u304f\uff0e
\n$u_i^Tu_j$
\n$= \\frac{1}{\\sqrt{\u03bb_i}\\sqrt{\u03bb_j}}(Av_i)^T(Av_j)$
\n$= \\frac{1}{\\sqrt{\u03bb_i}\\sqrt{\u03bb_j}}v_i^TA^TAv_j$
\n$= \\frac{1}{\\sqrt{\u03bb_i}\\sqrt{\u03bb_j}}v_i^T\u03bb_iv_j$
\n$= \\frac{\\sqrt{\u03bb_j}}{\\sqrt{\u03bb_i}}v_i^Tv_j$
\n$= \u03b4_{i,j}$
\n\u3068\u306a\u308b\u305f\u3081\uff0c$u$\u3082\u307e\u305f\u6b63\u898f\u76f4\u4ea4\u7cfb<\/strong>\u3092\u306a\u3059\uff0e\n<\/p>\n

\n\u3053\u308c\u3092\u4e26\u3079\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u7f6e\u304f\uff0e
\n$U=[u_i … u_m]$
\n$u$\u304c\u6b63\u898f\u76f4\u4ea4\u7cfb\u3092\u306a\u3059\u3053\u3068\u304b\u3089\uff0c$U$\u306f\u76f4\u884c\u884c\u5217<\/strong>\u3067\u3042\u308b\uff0e
\n\uff08$UU^{T}=U^{T}U=E$\uff09\n<\/p>\n

\n$U^TAV$
\n$= U^T[Av_1, … , Av_n]$
\n$= U^T[\\sqrt{\u03bb_1}u_1, … , \\sqrt{\u03bb_r}u_r, 0, …, 0]$
\n$= [\\sqrt{\u03bb_1}U^Tu_1, … , \\sqrt{\u03bb_r}U^Tu_r, 0, …, 0]$
\n$= Diag(\\sqrt{\u03bb_1},…, \\sqrt{\u03bb_n})$
\n\u3068\u306a\u308b\uff0e
\n\u3053\u308c\u3092$\u03a3$\u3068\u304a\u304f\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\uff0e
\n$U^TAV=\u03a3$
\n\u3053\u308c\u306b\u5de6\u304b\u3089$U$\u3092\uff0c\u53f3\u304b\u3089$V^T$\u3092\u304b\u3051\u308b\u3053\u3068\u3067\u4ee5\u4e0b\u3092\u5f97\u308b\uff0e
\n$UU^TAVV^T = U\u03a3V^T$
\n$A = U\u03a3V^T$
\n\uff08\u8a3c\u660e\u7d42\u4e86\uff09\n<\/p>\n

LSA\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/h2>\n

\"LSA\"<\/p>\n

\n SVD\u304c\u308f\u304b\u308c\u3070\uff0cLSA\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5927\u65b9\u304c\u308f\u304b\u3063\u305f\u3068\u8a00\u3063\u3066\u3082\u904e\u8a00\u3067\u306f\u306a\u3044\uff0eLSA\u3067\u306fSVD\u3067\u6c42\u307e\u3063\u305f\u7279\u7570\u5024\u3092\u5f71\u97ff\u5ea6\u306e\u5c11\u306a\u3044\u9806\u306b\u524a\u3063\u3066\u3044\u304f<\/strong>\u3053\u3068\u306b\u3088\u3063\u3066\u6b21\u5143\u3092\u524a\u6e1b\u3059\u308b\uff0e\u305d\u306e\u5f8c\uff0c\u6b21\u5143\u524a\u6e1b\u3055\u308c\u305f\u7279\u7570\u5024\u306e\u884c\u5217\u3092\u7528\u3044\u3066\u985e\u4f3c\u5ea6\u3092\u7b97\u51fa\u3059\u308b\uff0e\u3053\u308c\u3092\u4e0a\u56f3\u306b\u3088\u308a\u56f3\u89e3\u3057\u305f\uff0e\u30aa\u30ec\u30f3\u30b8\u8272\u306e\u90e8\u5206\u306f\u6b21\u5143\u524a\u6e1b\u5f8c\u306e\u91cd\u8981\u90e8\u5206\u3092\u8868\u3057\u3066\u3044\u308b\uff0e
\n \u4ee5\u964d\uff0cDeerwester\u3089\u306e\u8ad6\u6587\uff08\u539f\u8457\uff09\u306b\u5408\u308f\u305b\u308b\u305f\u3081\uff0cSVD\u3067\u5358\u8a9e\u3068\u30c9\u30ad\u30e5\u30e1\u30f3\u30c8\u306e\u884c\u5217X\u3092\u5206\u89e3\u3057\u305f\u7d50\u679c\u3092\uff0c\u4ee5\u4e0b\u306e\u8868\u8a18\u3092\u7528\u3044\u3066\u8868\u3059\uff0e
\n $$X = TSD^T$$
\n \u3053\u306e\u884c\u5217\u306e\u5024\u306b\u306f\u5171\u8d77\u56de\u6570\uff08\u5404\u6587\u66f8\u306b\u304a\u3051\u308b\u5358\u8a9e\u306e\u51fa\u73fe\u56de\u6570\uff09\u304c\u5165\u308a\uff0cTF-IDF\u3067\u91cd\u307f\u3065\u3051\u3055\u308c\u308b\u3053\u3068\u304c\u4e00\u822c\u7684\u3067\u3042\u308b\uff0e\n<\/p>\n

\u6b21\u5143\u306e\u5727\u7e2e<\/h3>\n

\n\u3000SVD\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u305f\u5206\u89e3\u306e\u3046\u3061\uff0c\u771f\u3093\u4e2d\u306e\u7279\u7570\u5024\u884c\u5217\u3092\u305d\u306e\u8981\u7d20\u3067\u3042\u308b\u7279\u7570\u5024\u306e\u5c0f\u3055\u3044\u9806\u306b0\u306b\u3057\u3066\u3044\u304f\uff08\u4e0a\u56f3\u53c2\u7167\uff09\uff0e0\u306b\u3059\u308b\u7279\u7570\u5024\u306e\u500b\u6570\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3057\u3066\u8a2d\u5b9a\u3055\u308c\uff0c0\u306b\u3057\u305f\u500b\u6570\u304c\u5c11\u306a\u3044\u307b\u3069\u5143\u306e\u884c\u5217\u306b\u8fd1\u304f\uff0c\u591a\u3044\u307b\u3069\u5727\u7e2e\u5ea6\u306e\u9ad8\u3044\u884c\u5217\u3068\u306a\u308b\uff0e\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u6700\u9069\u306a\u5024\u306e\u6642\u3053\u306e\u884c\u5217\u306f\uff0c\u5143\u306e\u30c7\u30fc\u30bf\u3092\u8868\u3059\u306e\u306b\u306f\u5341\u5206<\/strong>\u3067\u3042\u308a\u3064\u3064\uff0c\u3042\u307e\u308a\u91cd\u8981\u3067\u306f\u306a\u3044\u30c7\u30fc\u30bf\u3084\u30ce\u30a4\u30ba\u3092\u5fa9\u5143\u3059\u308b\u306e\u306b\u306f\u4e0d\u5341\u5206<\/strong>\u3067\u3042\u308b\u3053\u3068\u304c\u671f\u5f85\u3067\u304d\u308b\uff0e
\n \u8a08\u7b97\u306e\u969b\u306b\u306f\uff0c0\u306b\u3057\u305f\u7b87\u6240\u306b\u5bfe\u5fdc\u3059\u308b\u90e8\u5206\u306f\u524a\u3063\u3066\u8a08\u7b97\u3059\u308b\uff0e\u3053\u3046\u3059\u308b\u3053\u3068\u306b\u3088\u308a\uff0c\u8a08\u7b97\u91cf\u3092\u524a\u6e1b\u3067\u304d\u308b\uff0e
\n \u307e\u305f\uff0c\u3053\u3046\u3057\u3066\u5f97\u3089\u308c\u305f\u884c\u5217\u306f\u5404\u6b21\u5143\u306b\u304a\u3044\u3066\uff0c\u5143\u306e\u884c\u5217\u306e\u6700\u5c0f\u4e8c\u4e57(\u30d5\u30ed\u30d9\u30cb\u30a6\u30b9\u30ce\u30eb\u30e0\u304c\u6700\u5c0f)\u306e\u8fd1\u4f3c<\/strong>\u3068\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u308b\uff0e
\n \u5404\u985e\u4f3c\u5ea6\u306f\uff0c\u305d\u308c\u306b\u5bfe\u5fdc\u3059\u308b\u30d9\u30af\u30c8\u30eb\u306e\u30c9\u30c3\u30c8\u7a4d\u3067\u8868\u3059\uff0e\u3053\u308c\u306f\uff0c\u81ea\u7136\u8a00\u8a9e\u51e6\u7406\u306e\u5206\u91ce\u3067\u3088\u304f\u4f7f\u308f\u308c\u3066\u3044\u308b\u30b3\u30b5\u30a4\u30f3\u985e\u4f3c\u5ea6\u306e\u5206\u5b50\u306e\u90e8\u5206\u306b\u3042\u305f\u308b\uff0e\n<\/p>\n

\u5358\u8a9e-\u5358\u8a9e\u306e\u95a2\u9023\u6027\u3092\u6c42\u3081\u308b<\/h3>\n

\n\u3000\u305d\u308c\u305e\u308c\u306e\u884c\u5217\u306f\u6b21\u5143\u524a\u6e1b\u3092\u3057\u305f\u5f8c\u306e\u884c\u5217\u3068\u3059\u308b\uff0e
\n\u3000$T$\u304c\u76f4\u884c\u884c\u5217<\/strong>\uff0c$S$\u304c\u5bfe\u89d2\u884c\u5217<\/strong>\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\uff0c$X$\u306e\u305d\u308c\u305e\u308c\u306e\u884c<\/strong>\u306b\u5bfe\u3057\u3066\u30c9\u30c3\u30c8\u7a4d\u3092\u6c42\u3081\u308c\u3070\u3088\u3044\uff0e
\n\u3000$$XX^T = TS^2T^T$$\n<\/p>\n

\u6587\u66f8-\u6587\u66f8\u306e\u95a2\u9023\u6027\u3092\u6c42\u3081\u308b<\/h3>\n

\n\u3000$D$\u304c\u76f4\u884c\u884c\u5217<\/strong>\uff0c$S$\u304c\u5bfe\u89d2\u884c\u5217<\/strong>\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\uff0c$X$\u306e\u305d\u308c\u305e\u308c\u306e\u5217<\/strong>\u306b\u5bfe\u3057\u3066\u30c9\u30c3\u30c8\u7a4d\u3092\u6c42\u3081\u308c\u3070\u3088\u3044\uff0e
\n\u3000$$X^TX = DS^2D^T$$\n<\/p>\n

\u5358\u8a9e-\u6587\u66f8\u306e\u95a2\u9023\u6027\u3092\u6c42\u3081\u308b<\/h3>\n

\n\u3000$X$\u81ea\u4f53\u304c\u3053\u308c\u3089\u306e\u95a2\u9023\u6027\u3092\u8868\u3057\u3066\u3044\u308b\uff0e
\n\u3000$$X = TSD^T$$\n<\/p>\n

LSA\u306e\u5fdc\u7528<\/h2>\n

\n\u3000\u691c\u7d22\u30a8\u30f3\u30b8\u30f3<\/strong>\u3084\u30ec\u30b3\u30e1\u30f3\u30c9\u30a8\u30f3\u30b8\u30f3<\/strong>\u306a\u3069\u306e\u60c5\u5831\u691c\u7d22<\/strong>\u306e\u5206\u91ce\u3084\uff0c\u6982\u5ff5\u306e\u5b66\u7fd2\u904e\u7a0b\u306e\u8a08\u7b97\u30e2\u30c7\u30eb\u3068\u3057\u3066\u5fc3\u7406\u5b66<\/strong>\u306e\u5206\u91ce\u3067\u3082\u7528\u3044\u3089\u308c\u308b\uff0e
\n \u307e\u305f\uff0c\u6587\u7ae0\u306e\u307f\u3067\u306a\u304f\uff0c\u5143\u306e\u884c\u5217\u3092\u30e6\u30fc\u30b6\u30fc\u3068\u305d\u306e\u6027\u8cea\u306a\u3069\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3082\u53ef\u80fd\u3067\u3042\u308b\uff0e\u4f8b\u3048\u3070EC\u30b5\u30a4\u30c8\u306b\u304a\u3051\u308b\u30e6\u30fc\u30b6\u30fc\u306e\u8cfc\u8cb7\u30c7\u30fc\u30bf\u3092\u96c6\u3081\u305f\u3082\u306e\u3092\u884c\u5217\u3068\u3059\u308b\u3053\u3068\u3067\uff0c\u8cfc\u8cb7\u5c65\u6b74\u304b\u3089\u4f3c\u3066\u3044\u308b\u30e6\u30fc\u30b6\u30fc\u304c\u8cb7\u3063\u3066\u3044\u308b\u5546\u54c1\u3092\u30ec\u30b3\u30e1\u30f3\u30c9\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\n<\/p>\n

LSA\u306e\u554f\u984c\u70b9<\/h2>\n

\n\u30fb\u5404\u30c8\u30d4\u30c3\u30af\u306f\u4e92\u3044\u306b\u76f4\u4ea4\u3057\u3066\u304a\u308a\uff0c\u305d\u308c\u3089\u306e\u95a2\u9023\u6027\u306f\u307f\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\uff0e
\n\u30fb\u51fa\u73fe\u983b\u5ea6\u3057\u304b\u898b\u3066\u3044\u306a\u3044\u305f\u3081\uff0c\u9006\u8aac\u306e\u63a5\u7d9a\u8a5e\u306a\u3069\u306e\u6587\u8108\u69cb\u9020\u304c\u8003\u616e\u3055\u308c\u3066\u3044\u306a\u3044\uff0e
\n\u30fb\u30c8\u30d4\u30c3\u30af\u306b\u540d\u524d\u304c\u3064\u3044\u3066\u3044\u306a\u304f\uff0c\u305d\u308c\u305e\u308c\u304c\u4f55\u3092\u8868\u3059\u30c8\u30d4\u30c3\u30af\u306a\u306e\u304b\u308f\u304b\u3089\u306a\u3044\uff0e\n<\/p>\n

\u53c2\u8003\u6587\u732e<\/h2>\n

\u3010\u8ad6\u6587\u3011
\nS. Deerwester, S.T. Dumais, G.W. Furnas, T.K. Landauer, and R. Harshman. Indexing by Latent Semantic Analysis, Journal of the American Society for Information Science<\/em>, 41(6):391-407, 1990.<\/p>\n

\u3010Web\u30b5\u30a4\u30c8\u3011
\nECEN 601: Linear Network Analysis<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

\u4eca\u56de\u306f\u6f5c\u5728\u610f\u5473\u89e3\u6790(Latent Semantic Analysis: LSA)\u3068\u7279\u7570\u5024\u5206\u89e3(Singular Value Decomposition: SVD)\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\uff0e LSA\u306f\u6587\u66f8\u306e\u5206\u985e\u3084\uff0c\u60c5\u5831\u691c\u7d22\u306e\u5206\u91ce(\u3053\u306e\u5206\u91ce\u3067\u306fLSI\u3068\u3057\u3066\u77e5\u3089\u308c\u308b)\u306a\u3069\u306b\u4f7f\u308f\u308c\u308b\u30c8\u30d4\u30c3\u30af\u30e2\u30c7\u30eb\u306e\u4ee3\u8868\u4f8b\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\uff0e \u3053\u306e\u30e2\u30c7\u30eb\u3092\u4f7f\u3046\u3068\uff0c\u5358\u8a9e\u3068\u6587\u66f8\u306e\u305d\u308c\u305e\u308c\u306e\u7d44\u307f\u5408\u308f\u305b\u306b\u3064\u3044\u3066\uff0c\u985e\u4f3c\u5ea6\u3092\u6e2c\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n","protected":false},"author":1,"featured_media":772,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4,5],"tags":[],"_links":{"self":[{"href":"https:\/\/mieruca-ai.com\/ai\/wp-json\/wp\/v2\/posts\/643"}],"collection":[{"href":"https:\/\/mieruca-ai.com\/ai\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mieruca-ai.com\/ai\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mieruca-ai.com\/ai\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mieruca-ai.com\/ai\/wp-json\/wp\/v2\/comments?post=643"}],"version-history":[{"count":93,"href":"https:\/\/mieruca-ai.com\/ai\/wp-json\/wp\/v2\/posts\/643\/revisions"}],"predecessor-version":[{"id":1080,"href":"https:\/\/mieruca-ai.com\/ai\/wp-json\/wp\/v2\/posts\/643\/revisions\/1080"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mieruca-ai.com\/ai\/wp-json\/wp\/v2\/media\/772"}],"wp:attachment":[{"href":"https:\/\/mieruca-ai.com\/ai\/wp-json\/wp\/v2\/media?parent=643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mieruca-ai.com\/ai\/wp-json\/wp\/v2\/categories?post=643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mieruca-ai.com\/ai\/wp-json\/wp\/v2\/tags?post=643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}