@prefix owl: . @prefix dbpedia: . dbpedia:Latent_semantic_analysis owl:sameAs . @prefix foaf: . @prefix ns3: . dbpedia:Latent_semantic_analysis foaf:page ns3:Latent_semantic_analysis . @prefix dbpprop: . dbpedia:Latent_semantic_analysis dbpprop:reference , . @prefix ns5: . dbpedia:Latent_semantic_analysis dbpprop:reference ns5:Latent_semantic_analysis , , , . @prefix rdfs: . dbpedia:Latent_semantic_analysis rdfs:label "\u6F5C\u5728\u8BED\u4E49\u5B66"@zh , "Analyse s\u00E9mantique latente"@fr , "\u041B\u0430\u0442\u0435\u043D\u0442\u043D\u043E-\u0441\u0435\u043C\u0430\u043D\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u0430\u043D\u0430\u043B\u0438\u0437"@ru , "Latent Semantic Indexing"@de , "\u6F5C\u5728\u610F\u5473\u89E3\u6790"@ja , "Latent semantic analysis"@en , "Latent semantisk analys"@sv ; dbpprop:abstract "\u6F5C\u5728\u610F\u5473\u89E3\u6790\uFF08\u82F1: Latent Semantic Analysis, LSA\uFF09\u306F\u3001\u30D9\u30AF\u30C8\u30EB\u7A7A\u9593\u30E2\u30C7\u30EB\u3092\u5229\u7528\u3057\u305F\u81EA\u7136\u8A00\u8A9E\u51E6\u7406\u306E\u6280\u6CD5\u306E1\u3064\u3067\u3001\u6587\u66F8\u7FA4\u3068\u305D\u3053\u306B\u542B\u307E\u308C\u308B\u7528\u8A9E\u7FA4\u306B\u3064\u3044\u3066\u3001\u305D\u308C\u3089\u306B\u95A2\u9023\u3057\u305F\u6982\u5FF5\u306E\u96C6\u5408\u3092\u751F\u6210\u3059\u308B\u3053\u3068\u3067\u3001\u305D\u306E\u95A2\u4FC2\u3092\u5206\u6790\u3059\u308B\u6280\u8853\u3067\u3042\u308B\u3002\u6F5C\u5728\u7684\u610F\u5473\u89E3\u6790\u3068\u3082\u3002 1988\u5E74\u3001\u30A2\u30E1\u30EA\u30AB\u5408\u8846\u56FD\u3067LSA\u306E\u7279\u8A31\u304C\u53D6\u5F97\u3055\u308C\u3066\u3044\u308B\u3002\u60C5\u5831\u691C\u7D22\u306E\u5206\u91CE\u3067\u306F\u3001\u6F5C\u5728\u7684\u610F\u5473\u7D22\u5F15\u307E\u305F\u306F\u6F5C\u5728\u610F\u5473\u30A4\u30F3\u30C7\u30C3\u30AF\u30B9\uFF08\u82F1: Latent Semantic Indexing, LSI\uFF09\u3068\u3082\u547C\u3070\u308C\u3066\u3044\u308B\u3002 \u51FA\u73FE\u884C\u5217 LSA \u3067\u306F\u3001\u5404\u6587\u66F8\u306B\u304A\u3051\u308B\u7528\u8A9E\u306E\u51FA\u73FE\u3092\u8868\u3057\u305F\u6587\u66F8-\u5358\u8A9E\u30DE\u30C8\u30EA\u30AF\u30B9\u304C\u4F7F\u308F\u308C\u308B\u3002\u3053\u308C\u306F\u5217\u304C\u5358\u8A9E\u306B\u5BFE\u5FDC\u3057\u3001\u884C\u304C\u6587\u66F8\u306B\u5BFE\u5FDC\u3057\u305F\u758E\u884C\u5217\u3067\u3042\u308B\u3002\u3053\u306E\u884C\u5217\u306E\u5404\u6210\u5206\u306E\u91CD\u307F\u4ED8\u3051\u306B\u306F tf-idf (term frequency\u2013inverse document frequency) \u304C\u7528\u3044\u3089\u308C\u308B\u3053\u3068\u304C\u591A\u3044\u3002\u3053\u306E\u5834\u5408\u3001\u884C\u5217\u306E\u5404\u6210\u5206\u306F\u305D\u306E\u6587\u66F8\u3067\u305D\u306E\u5358\u8A9E\u304C\u4F7F\u308F\u308C\u305F\u56DE\u6570\u306B\u6BD4\u4F8B\u3057\u305F\u5024\u3067\u3042\u308A\u3001\u5358\u8A9E\u306F\u305D\u306E\u76F8\u5BFE\u7684\u91CD\u8981\u6027\u3092\u53CD\u6620\u3059\u308B\u305F\u3081\u306B\u5F37\u304F\u91CD\u307F\u4ED8\u3051\u3055\u308C\u308B\u3002 \u3053\u306E\u884C\u5217\u306F\u6A19\u6E96\u610F\u5473\u30E2\u30C7\u30EB\u3067\u3082\u4E00\u822C\u7684\u3060\u304C\u3001\u5FC5\u305A\u3057\u3082\u884C\u5217\u3068\u3057\u3066\u660E\u78BA\u306B\u8868\u73FE\u3055\u308C\u308B\u5FC5\u8981\u6027\u306F\u306A\u304F\u3001\u884C\u5217\u3068\u3057\u3066\u6570\u5B66\u7684\u306B\u5229\u7528\u3059\u308B\u3068\u306F\u9650\u3089\u306A\u3044\u3002 LSA \u306F\u3053\u306E\u51FA\u73FE\u884C\u5217\u3092\u7528\u8A9E\u3068\u4F55\u3089\u304B\u306E\u6982\u5FF5\u306E\u95A2\u4FC2\u304A\u3088\u3073\u6982\u5FF5\u3068\u6587\u66F8\u9593\u306E\u95A2\u4FC2\u306B\u5909\u63DB\u3059\u308B\u3002\u3057\u305F\u304C\u3063\u3066\u3001\u7528\u8A9E\u3068\u6587\u66F8\u306F\u6982\u5FF5\u3092\u4ECB\u3057\u3066\u9593\u63A5\u7684\u306B\u95A2\u9023\u4ED8\u3051\u3089\u308C\u308B\u3002 \u5FDC\u7528 \u3053\u306E\u65B0\u305F\u306A\u6982\u5FF5\u7A7A\u9593\u306F\u4EE5\u4E0B\u306E\u3088\u3046\u306A\u5834\u9762\u3067\u5229\u7528\u3055\u308C\u308B\u3002 \u6982\u5FF5\u7A7A\u9593\u3067\u306E\u6587\u66F8\u306E\u6BD4\u8F03\uFF08\u30C7\u30FC\u30BF\u30FB\u30AF\u30E9\u30B9\u30BF\u30EA\u30F3\u30B0\u3001\u6587\u66F8\u5206\u985E\u3001\u306A\u3069\uFF09 \u7FFB\u8A33\u6587\u66F8\u7FA4\u306E\u57FA\u672C\u30BB\u30C3\u30C8\u3092\u5206\u6790\u3057\u305F\u5F8C\u3001\u7570\u306A\u308B\u8A00\u8A9E\u9593\u3067\u985E\u4F3C\u306E\u6587\u66F8\u3092\u63A2\u3059\uFF08\u8A00\u8A9E\u9593\u691C\u7D22\uFF09\u3002 \u7528\u8A9E\u9593\u306E\u95A2\u4FC2\u3092\u63A2\u3059\uFF08\u985E\u7FA9\u6027\u3084\u591A\u7FA9\u6027\uFF09\u3002 \u7528\u8A9E\u7FA4\u306B\u3088\u308B\u30AF\u30A8\u30EA\u3092\u4E0E\u3048\u3089\u308C\u305F\u3068\u304D\u3001\u305D\u308C\u3092\u6982\u5FF5\u7A7A\u9593\u3067\u89E3\u91C8\u3057\u3001\u4E00\u81F4\u3059\u308B\u6587\u66F8\u7FA4\u3092\u63A2\u3059\uFF08\u60C5\u5831\u691C\u7D22\uFF09\u3002 \u81EA\u7136\u8A00\u8A9E\u51E6\u7406\u306B\u304A\u3044\u3066\u3001\u985E\u7FA9\u6027\u3068\u591A\u7FA9\u6027\u306F\u6839\u672C\u7684\u306A\u554F\u984C\u3067\u3042\u308B\u3002 \u985E\u7FA9\u6027\u306F\u3001\u7570\u306A\u308B\u5358\u8A9E\u304C\u540C\u3058\u4E8B\u8C61\u3092\u8868\u3059\u73FE\u8C61\u3067\u3042\u308B\u3002\u3057\u305F\u304C\u3063\u3066\u691C\u7D22\u30A8\u30F3\u30B8\u30F3\u306B\u304A\u3044\u3066\u3001\u30AF\u30A8\u30EA\u306B\u306A\u3044\u985E\u7FA9\u8A9E\u3092\u898B\u843D\u3068\u3057\u3066\u3001\u9069\u5207\u306A\u6587\u66F8\u3092\u691C\u7D22\u3067\u304D\u306A\u3044\u3053\u3068\u304C\u3042\u308B\u3002\u4F8B\u3048\u3070\u3001\"doctors\" \u3092\u691C\u7D22\u3057\u305F\u3068\u304D\u3001\u540C\u7FA9\u3067\u3042\u308B \"physicians\" \u3068\u3044\u3046\u5358\u8A9E\u3092\u542B\u3080\u6587\u66F8\u3092\u691C\u7D22\u3067\u304D\u306A\u3044\u3068\u3044\u3046\u53EF\u80FD\u6027\u304C\u3042\u308B\u3002 \u591A\u7FA9\u6027\u306F\u3001\u540C\u3058\u5358\u8A9E\u304C\u8907\u6570\u306E\u610F\u5473\u3092\u6301\u3064\u73FE\u8C61\u3067\u3042\u308B\u3002\u305D\u306E\u305F\u3081\u3001\u30AF\u30A8\u30EA\u306B\u6307\u5B9A\u3057\u305F\u5358\u8A9E\u304C\u591A\u7FA9\u7684\u3067\u3042\u3063\u305F\u5834\u5408\u3001\u691C\u7D22\u8981\u6C42\u8005\u304C\u610F\u56F3\u3057\u306A\u3044\u610F\u5473\u3067\u4F7F\u3063\u3066\u3044\u308B\u4E0D\u9069\u5207\u306A\u6587\u66F8\u304C\u691C\u7D22\u3055\u308C\u3066\u3057\u307E\u3046\u3053\u3068\u304C\u3042\u308B\u3002\u4F8B\u3048\u3070\u3001\u690D\u7269\u5B66\u8005\u3068\u8A08\u7B97\u6A5F\u79D1\u5B66\u8005\u304C \"tree\" \u3068\u3044\u3046\u5358\u8A9E\u3067\u691C\u7D22\u3057\u305F\u3044\u306E\u306F\u3001\u5168\u304F\u7570\u306A\u308B\u6587\u66F8\u3068\u601D\u308F\u308C\u308B\u3002 \u968E\u6570\u306E\u4F4E\u6E1B \u51FA\u73FE\u884C\u5217\u3092\u69CB\u7BC9\u5F8C\u3001LSA\u3067\u306F\u6587\u66F8-\u5358\u8A9E\u30DE\u30C8\u30EA\u30AF\u30B9\u306E\u884C\u5217\u306E\u968E\u6570\u3092\u4F4E\u6E1B\u3057\u305F\u8FD1\u4F3C\u3092\u884C\u3046\u5FC5\u8981\u304C\u3042\u308B\u5834\u5408\u304C\u3042\u308B\u3002\u305F\u3060\u3057\u3001\u8FD1\u4F3C\u306B\u4F34\u3046\u7CBE\u5EA6\u306E\u4F4E\u4E0B\u3092\u8003\u616E\u306B\u5165\u308C\u306A\u304F\u3066\u306F\u306A\u3089\u306A\u3044\u3002 \u3053\u306E\u8FD1\u4F3C\u306B\u306F\u4EE5\u4E0B\u306E\u3088\u3046\u306A\u7406\u7531\u304C\u3042\u308B\u3002 \u5143\u306E\u6587\u66F8-\u5358\u8A9E\u30DE\u30C8\u30EA\u30AF\u30B9\u304C\u30B3\u30F3\u30D4\u30E5\u30FC\u30BF\u306E\u30E1\u30E2\u30EA\u4E0A\u306B\u683C\u7D0D\u3059\u308B\u306B\u306F\u5927\u304D\u3059\u304E\u308B\u5834\u5408\u3002\u3053\u306E\u5834\u5408\u3001\u968E\u6570\u3092\u4F4E\u6E1B\u3057\u305F\u884C\u5217\u306F\u300C\u8FD1\u4F3C\u300D\u3068\u89E3\u91C8\u3055\u308C\u308B\u3002 \u5143\u306E\u6587\u66F8-\u5358\u8A9E\u30DE\u30C8\u30EA\u30AF\u30B9\u306B\u30CE\u30A4\u30BA\u304C\u591A\u3044\u5834\u5408\u3002\u305D\u306E\u7528\u8A9E\u306E\u9038\u8A71\u7684\u51FA\u73FE\u3092\u9664\u53BB\u3059\u308B\u306A\u3069\u3002\u3053\u306E\u5834\u5408\u306E\u8FD1\u4F3C\u884C\u5217\u306F\u300C\u30CE\u30A4\u30BA\u9664\u53BB\u300D\u884C\u5217\u3068\u89E3\u91C8\u3055\u308C\u308B\u3002 \u5143\u306E\u6587\u66F8-\u5358\u8A9E\u30DE\u30C8\u30EA\u30AF\u30B9\u304C\u7406\u60F3\u7684\u306A\u6587\u66F8-\u5358\u8A9E\u30DE\u30C8\u30EA\u30AF\u30B9\u3088\u308A\u3082\u758E\u3089\u306A\u5834\u5408\u3002\u3059\u306A\u308F\u3061\u3001\u5143\u306E\u884C\u5217\u306B\u306F\u6587\u66F8\u3067\u5B9F\u969B\u306B\u4F7F\u308F\u308C\u3066\u3044\u308B\u5358\u8A9E\u306E\u307F\u30AB\u30A6\u30F3\u30C8\u3055\u308C\u3066\u3044\u308B\u304C\u3001\u5404\u6587\u66F8\u306E\u95A2\u9023\u3059\u308B\u5358\u8A9E\u306B\u8208\u5473\u304C\u3042\u308B\u5834\u5408\u306A\u3069\u3002\u3064\u307E\u308A\u3001\u985E\u7FA9\u6027\u3092\u8003\u616E\u3057\u305F\u884C\u5217\u304C\u307B\u3057\u3044\u5834\u5408\u3002 \u968E\u6570\u306E\u4F4E\u6E1B\u306E\u7D50\u679C\u3001\u3044\u304F\u3064\u304B\u306E\u6B21\u5143\u304C\u7D71\u5408\u3055\u308C\u3001\u8907\u6570\u306E\u5358\u8A9E\u306B\u4F9D\u5B58\u3059\u308B\u3088\u3046\u306B\u306A\u308B\u3002 {(car), (truck), (flower)} --> {(1.3452 * car + 0.2828 * truck), (flower)} \u968E\u6570\u4F4E\u6E1B\u304C\u985E\u4F3C\u306E\u610F\u5473\u3092\u6301\u3064\u7528\u8A9E\u306B\u5BFE\u5FDC\u3059\u308B\u6B21\u5143\u3092\u7D71\u5408\u3059\u308B\u3053\u3068\u3067\u3001\u985E\u7FA9\u6027\u554F\u984C\u304C\u3042\u308B\u7A0B\u5EA6\u89E3\u6D88\u3055\u308C\u308B\u3002\u307E\u305F\u3001\u591A\u7FA9\u8A9E\u306E\u6210\u5206\u304C\u8907\u6570\u306E\u985E\u7FA9\u8A9E\u306B\u5206\u914D\u3055\u308C\u3066\u7D71\u5408\u3055\u308C\u308B\u306A\u3089\u3001\u591A\u7FA9\u6027\u306E\u554F\u984C\u3082\u3042\u308B\u7A0B\u5EA6\u89E3\u6D88\u3055\u308C\u308B\u3002\u9006\u306B\u3001\u4ED6\u306E\u65B9\u5411\u306E\u6210\u5206\u306F\u5358\u306B\u6D88\u53BB\u3055\u308C\u308B\u304B\u3001\u6700\u60AA\u3067\u3082\u610F\u56F3\u3057\u305F\u610F\u5473\u3088\u308A\u3082\u6210\u5206\u3068\u3057\u3066\u5C0F\u3055\u304F\u306A\u308B\u3002 \u5C0E\u51FA \u884C\u5217 <math>X \u306E\u6210\u5206 <math>(i,j) \u306F\u3001\u5358\u8A9E <math>i \u306E\u6587\u66F8 <math>j \u306B\u304A\u3051\u308B\u51FA\u73FE\uFF08\u4F8B\u3048\u3070\u983B\u5EA6\uFF09\u3092\u8868\u3059\u3068\u3059\u308B\u3002<math>X \u306F\u6B21\u306E\u3088\u3046\u306B\u306A\u308B\u3002 \\begin{matrix} \\textbf{d}_j \\downarrow \\textbf{t}_i^T \\rightarrow \\begin{bmatrix} x_{1,1} \\dots x_{1,n} \\vdots \\ddots \\vdots x_{m,1} \\dots x_{m,n} \\end{bmatrix} \\end{matrix} \u3053\u306E\u884C\u5217\u306E\u884C\u306F1\u3064\u306E\u5358\u8A9E\u306B\u5BFE\u5FDC\u3057\u305F\u30D9\u30AF\u30C8\u30EB\u306B\u306A\u3063\u3066\u304A\u308A\u3001\u5404\u6210\u5206\u304C\u5404\u6587\u66F8\u3068\u306E\u95A2\u4FC2\u3092\u793A\u3057\u3066\u3044\u308B\u3002 \\textbf{t}_i^T \\begin{bmatrix} x_{i,1} \\dots x_{i,n} \\end{bmatrix} \u540C\u69D8\u306B\u3001\u3053\u306E\u884C\u5217\u306E\u5217\u306F1\u3064\u306E\u6587\u66F8\u306B\u5BFE\u5FDC\u3057\u305F\u30D9\u30AF\u30C8\u30EB\u306B\u306A\u3063\u3066\u304A\u308A\u3001\u5404\u6210\u5206\u304C\u5404\u5358\u8A9E\u3068\u306E\u95A2\u4FC2\u3092\u793A\u3057\u3066\u3044\u308B\u3002 \\textbf{d}_j \\begin{bmatrix} x_{1,j} \\vdots x_{m,j} \\end{bmatrix} 2\u3064\u306E\u5358\u8A9E\u30D9\u30AF\u30C8\u30EB\u306E\u30C9\u30C3\u30C8\u7A4D <math>\\textbf{t}_i^T \\textbf{t}_p \u306F\u3001\u305D\u306E\u6587\u66F8\u7FA4\u306B\u304A\u3051\u308B\u5358\u8A9E\u9593\u306E\u76F8\u95A2\u3092\u793A\u3059\u3002\u884C\u5217\u7A4D <math>X X^T \u306B\u306F\u305D\u306E\u3088\u3046\u306A\u30C9\u30C3\u30C8\u7A4D\u304C\u5168\u3066\u542B\u307E\u308C\u3066\u3044\u308B\u3002\u305D\u306E\u6210\u5206 <math>(i,p)\uFF08\u6210\u5206 <math>(p,i) \u3068\u7B49\u3057\u3044\uFF09\u306F\u3001\u30C9\u30C3\u30C8\u7A4D <math>\\textbf{t}_i^T \\textbf{t}_p\uFF08<math> \\textbf{t}_p^T \\textbf{t}_i\uFF09\u306B\u306A\u3063\u3066\u3044\u308B\u3002\u540C\u69D8\u306B\u884C\u5217 <math>X^T X \u306F\u5168\u3066\u306E\u6587\u66F8\u30D9\u30AF\u30C8\u30EB\u9593\u306E\u30C9\u30C3\u30C8\u7A4D\u304C\u542B\u307E\u308C\u3066\u3044\u3066\u3001\u305D\u306E\u5358\u8A9E\u7FA4\u306B\u304A\u3051\u308B\u6587\u66F8\u9593\u306E\u76F8\u95A2\u3092\u793A\u3059\u3002\u3059\u306A\u308F\u3061\u3001<math>\\textbf{d}_j^T \\textbf{d}_q \\textbf{d}_q^T \\textbf{d}_j \u3067\u3042\u308B\u3002 <math>X \u306E\u5206\u89E3\u3068\u3057\u3066\u3001\u76F4\u4EA4\u884C\u5217 <math>U \u3068 <math>V\u3001\u5BFE\u89D2\u884C\u5217 <math>\\Sigma \u304C\u5B58\u5728\u3059\u308B\u3068\u4EEE\u5B9A\u3059\u308B\u3002\u3053\u306E\u3088\u3046\u306A\u5206\u89E3\u3092\u7279\u7570\u5024\u5206\u89E3 (SVD) \u3068\u547C\u3076\u3002 X U \\Sigma V^T \u5358\u8A9E\u306E\u76F8\u95A2\u3068\u6587\u66F8\u306E\u76F8\u95A2\u3092\u4E0E\u3048\u308B\u884C\u5217\u7A4D\u306F\u3001\u6B21\u306E\u3088\u3046\u306B\u5C55\u958B\u3055\u308C\u308B\u3002 \\begin{matrix} X X^T (U \\Sigma V^T) (U \\Sigma V^T)^T (U \\Sigma V^T) (V^{T^T} \\Sigma^T U^T) U \\Sigma V^T V \\Sigma^T U^T U \\Sigma \\Sigma^T U^T X^T X (U \\Sigma V^T)^T (U \\Sigma V^T) (V^{T^T} \\Sigma^T U^T) (U \\Sigma V^T) V \\Sigma U^T U \\Sigma V^T V \\Sigma^T \\Sigma V^T \\end{matrix} <math>\\Sigma \\Sigma^T \u3068 <math>\\Sigma^T \\Sigma \u306F\u5BFE\u89D2\u884C\u5217\u306A\u306E\u3067\u3001<math>U \u306B\u306F <math>X X^T \u306E\u56FA\u6709\u30D9\u30AF\u30C8\u30EB\u304C\u542B\u307E\u308C\u308B\u306F\u305A\u3067\u3042\u308A\u3001\u4E00\u65B9 <math>V \u306F <math>X^T X \u306E\u56FA\u6709\u30D9\u30AF\u30C8\u30EB\u306E\u306F\u305A\u3067\u3042\u308B\u3002\u3069\u3061\u3089\u306E\u884C\u5217\u7A4D\u306B\u3082 <math>\\Sigma \\Sigma^T \u306E\u30BC\u30ED\u3067\u306A\u3044\u6210\u5206\u306B\u7531\u6765\u3059\u308B\u3001\u307E\u305F\u306F\u7B49\u4FA1\u7684\u306B <math>\\Sigma^T\\Sigma \u306E\u30BC\u30ED\u3067\u306A\u3044\u6210\u5206\u306B\u7531\u6765\u3059\u308B\u3001\u540C\u3058\u30BC\u30ED\u3067\u306A\u3044\u56FA\u6709\u5024\u304C\u3042\u308B\u3002\u4EE5\u4E0A\u304B\u3089\u5206\u89E3\u306F\u6B21\u306E\u3088\u3046\u306B\u306A\u308B\u3002 \\begin{matrix} X U \\Sigma V^T (\\textbf{d}_j) (\\hat \\textbf{d}_j) \\downarrow \\downarrow (\\textbf{t}_i^T) \\rightarrow \\begin{bmatrix} x_{1,1} \\dots x_{1,n} \\vdots \\ddots \\vdots x_{m,1} \\dots x_{m,n} \\end{bmatrix} (\\hat \\textbf{t}_i^T) \\rightarrow \\begin{bmatrix} \\begin{bmatrix} \\, \\, \\textbf{u}_1 \\, \\,\\end{bmatrix} \\dots \\begin{bmatrix} \\, \\, \\textbf{u}_l \\, \\, \\end{bmatrix} \\end{bmatrix} \\cdot \\begin{bmatrix} \\sigma_1 \\dots 0 \\vdots \\ddots \\vdots 0 \\dots \\sigma_l \\end{bmatrix} \\cdot \\begin{bmatrix} \\begin{bmatrix} \\textbf{v}_1 \\end{bmatrix} \\vdots \\begin{bmatrix} \\textbf{v}_l \\end{bmatrix} \\end{bmatrix} \\end{matrix} <math>\\sigma_1, \\dots, \\sigma_l \u3068\u3044\u3046\u5024\u306F\u7279\u7570\u5024\u3068\u547C\u3070\u308C\u3001<math>u_1, \\dots, u_l \u306F\u5DE6\u7279\u7570\u30D9\u30AF\u30C8\u30EB\u3001<math>v_1, \\dots, v_l \u306F\u53F3\u7279\u7570\u30D9\u30AF\u30C8\u30EB\u3068\u547C\u3070\u308C\u308B\u3002<math>U \u306E\u3046\u3061 <math>\\textbf{t}_i \u306B\u95A2\u4E0E\u3059\u308B\u306E\u306F <math>i \\textrm{'th}\\quad \u884C\u3060\u3051\u3067\u3042\u308B\u3002\u305D\u306E\u884C\u30D9\u30AF\u30C8\u30EB\u3092 <math>\\hat{\\textrm{t}_i} \u3068\u547C\u3076\u3002\u540C\u69D8\u306B\u3001<math>V^T \u306E\u3046\u3061 <math>\\textbf{d}_j \u306B\u95A2\u4E0E\u3059\u308B\u306E\u306F <math>j \\textrm{'th}\\quad \u5217\u3060\u3051\u3067\u3042\u308A\u3001\u3053\u308C\u3092 <math>\\hat{\\textrm{d}_j} \u3068\u547C\u3076\u3002\u3053\u308C\u3089\u306F\u56FA\u6709\u30D9\u30AF\u30C8\u30EB\u3067\u306F\u306A\u3044\u304C\u3001\u5168\u3066\u306E\u56FA\u6709\u30D9\u30AF\u30C8\u30EB\u306B\u4F9D\u5B58\u3057\u3066\u3044\u308B\u3002 <math>k \u500B\u306E\u6700\u5927\u306E\u7279\u7570\u5024\u3068 <math>U \u3068 <math>V \u304B\u3089\u305D\u308C\u306B\u5BFE\u5FDC\u3059\u308B\u7279\u7570\u30D9\u30AF\u30C8\u30EB\u3092\u9078\u3093\u3060\u3068\u304D\u3001\u968E\u6570 <math>k \u306E X \u3078\u306E\u8FD1\u4F3C\u3092\u6700\u5C0F\u8AA4\u5DEE\u3067\u5F97\u308B\u3053\u3068\u304C\u3067\u304D\u308B\uFF08\u30D5\u30ED\u30D9\u30CB\u30A6\u30B9\u30FB\u30CE\u30EB\u30E0\uFF09\u3002\u3053\u306E\u8FD1\u4F3C\u306E\u9A5A\u304F\u3079\u304D\u70B9\u306F\u3001\u5358\u306B\u6700\u5C0F\u8AA4\u5DEE\u3067\u3042\u308B\u3068\u3044\u3046\u70B9\u3060\u3051\u3067\u306A\u304F\u3001\u5358\u8A9E\u30D9\u30AF\u30C8\u30EB\u3068\u6587\u66F8\u30D9\u30AF\u30C8\u30EB\u3092\u6982\u5FF5\u7A7A\u9593\u306B\u5909\u63DB\u3059\u308B\u3068\u3044\u3046\u70B9\u3067\u3042\u308B\u3002\u30D9\u30AF\u30C8\u30EB <math>\\hat{\\textbf{t}_i} \u306B\u306F <math>k \u500B\u306E\u6210\u5206\u304C\u3042\u308A\u3001\u305D\u308C\u305E\u308C\u304C\u5358\u8A9E <math>i \u306E <math>k \u500B\u306E\u6982\u5FF5\u306E1\u3064\u306B\u5BFE\u5FDC\u3057\u305F\u51FA\u73FE\u3092\u8868\u3057\u3066\u3044\u308B\u3002\u540C\u69D8\u306B\u30D9\u30AF\u30C8\u30EB <math>\\hat{\\textbf{d}_j} \u306F\u3001\u6587\u66F8 <math>j \u3068\u5404\u6982\u5FF5\u3068\u306E\u95A2\u4FC2\u3092\u8868\u3057\u3066\u3044\u308B\u3002\u3053\u306E\u8FD1\u4F3C\u3092\u6B21\u306E\u3088\u3046\u306B\u8A18\u8FF0\u3059\u308B\u3002 X_k U_k \\Sigma_k V_k^T \u3053\u3053\u3067\u3001\u4EE5\u4E0B\u306E\u3088\u3046\u306A\u3053\u3068\u304C\u53EF\u80FD\u3068\u306A\u308B\u3002 \u30D9\u30AF\u30C8\u30EB <math>\\hat{\\textbf{d}_j} \u3068 <math>\\hat{\\textbf{d}_q} \u3092\uFF08\u901A\u5E38\u30B3\u30B5\u30A4\u30F3\u76F8\u95A2\u91CF\u306B\u3088\u3063\u3066\uFF09\u6BD4\u8F03\u3059\u308B\u3053\u3068\u3067\u3001\u6587\u66F8 <math>j \u3068 <math>q \u306E\u76F8\u95A2\u306E\u5EA6\u5408\u3044\u304C\u308F\u304B\u308B\u3002\u3053\u308C\u306B\u3088\u3063\u3066\u3001\u6587\u66F8\u7FA4\u306E\u30AF\u30E9\u30B9\u30BF\u30EA\u30F3\u30B0\u304C\u5F97\u3089\u308C\u308B\u3002 \u30D9\u30AF\u30C8\u30EB <math>\\hat{\\textbf{t}_i} \u3068 <math>\\hat{\\textbf{t}_p} \u3092\u6BD4\u8F03\u3059\u308B\u3053\u3068\u3067\u3001\u5358\u8A9E <math>i \u3068 <math>p \u6BD4\u8F03\u3067\u304D\u3001\u6982\u5FF5\u7A7A\u9593\u306B\u304A\u3051\u308B\u5358\u8A9E\u7FA4\u306E\u30AF\u30E9\u30B9\u30BF\u30EA\u30F3\u30B0\u304C\u5F97\u3089\u308C\u308B\u3002 \u30AF\u30A8\u30EA\u304C\u4E0E\u3048\u3089\u308C\u305F\u3068\u304D\u3001\u3053\u308C\u3092\u77ED\u3044\u6587\u66F8\u3068\u8003\u3048\u3001\u6982\u5FF5\u7A7A\u9593\u5185\u3067\u6587\u66F8\u7FA4\u3068\u6BD4\u8F03\u3067\u304D\u308B\u3002 \u6700\u5F8C\u306E\u9805\u76EE\u3092\u884C\u3046\u306B\u306F\u3001\u6700\u521D\u306B\u30AF\u30A8\u30EA\u3092\u6982\u5FF5\u7A7A\u9593\u306B\u5909\u63DB\u3057\u3066\u3084\u308B\u5FC5\u8981\u304C\u3042\u308B\u3002\u3057\u305F\u304C\u3063\u3066\u76F4\u89B3\u7684\u306B\u3001\u6B21\u306E\u3088\u3046\u306B\u6587\u66F8\u7FA4\u306B\u5BFE\u3057\u3066\u884C\u3063\u305F\u306E\u3068\u540C\u3058\u3088\u3046\u306B\u5909\u63DB\u3092\u3059\u308B\u5FC5\u8981\u304C\u3042\u308B\u3002 \\textbf{d}_j U_k \\Sigma_k \\hat \\textbf{d}_j \\hat \\textbf{d}_j \\Sigma_k^{-1} U_k^T \\textbf{d}_j \u3053\u306E\u3053\u3068\u304C\u610F\u5473\u3059\u308B\u306E\u306F\u3001\u30AF\u30A8\u30EA\u30D9\u30AF\u30C8\u30EB <math>q \u304C\u4E0E\u3048\u3089\u308C\u305F\u3068\u304D\u3001\u6982\u5FF5\u7A7A\u9593\u306B\u304A\u3051\u308B\u6587\u66F8\u30D9\u30AF\u30C8\u30EB\u3068\u6BD4\u8F03\u3059\u308B\u524D\u306B <math>\\hat{\\textbf{q}} \\Sigma_k^{-1} U_k^T \\textbf{q} \u3068\u3044\u3046\u5909\u63DB\u3092\u3059\u308B\u5FC5\u8981\u304C\u3042\u308B\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308B\u3002\u540C\u3058\u3053\u3068\u306F\u64EC\u4F3C\u5358\u8A9E\u30D9\u30AF\u30C8\u30EB\u306B\u3082\u884C\u3048\u308B\u3002 \\textbf{t}_i^T \\hat \\textbf{t}_i^T \\Sigma_k V_k^T \\hat \\textbf{t}_i^T \\textbf{t}_i^T V_k^{-T} \\Sigma_k^{-1} \\textbf{t}_i^T V_k \\Sigma_k^{-1} \\hat \\textbf{t}_i \\Sigma_k^{-1} V_k^T \\textbf{t}_i \u5B9F\u88C5 \u7279\u7570\u5024\u5206\u89E3 (SVD) \u306F\u4E00\u822C\u306B\u5927\u898F\u6A21\u884C\u5217\u624B\u6CD5\uFF08\u4F8B\u3048\u3070\u30E9\u30F3\u30BE\u30B9\u6CD5\uFF09\u3092\u4F7F\u3063\u3066\u8A08\u7B97\u3055\u308C\u308B\u304C\u3001\u30CB\u30E5\u30FC\u30E9\u30EB\u30CD\u30C3\u30C8\u30EF\u30FC\u30AF\u7684\u306A\u624B\u6CD5\u3092\u4F7F\u3063\u3066\u8A08\u7B97\u8CC7\u6E90\u3092\u7BC0\u7D04\u3059\u308B\u3053\u3068\u3082\u3067\u304D\u308B\u3002\u5F8C\u8005\u306E\u5834\u5408\u3001\u884C\u5217\u5168\u4F53\u3092\u30E1\u30E2\u30EA\u306B\u4FDD\u6301\u3059\u308B\u5FC5\u8981\u304C\u306A\u3044\u3002 \u9AD8\u901F\u3067\u9010\u6B21\u7684\u306A\u30E1\u30E2\u30EA\u4F7F\u7528\u91CF\u306E\u5C11\u306A\u3044\u5927\u898F\u6A21\u884C\u5217SVD\u30A2\u30EB\u30B4\u30EA\u30BA\u30E0\u304C\u6700\u8FD1\u958B\u767A\u3055\u308C\u3066\u3044\u308B \u9650\u754C LSA \u306B\u306F\u4EE5\u4E0B\u306E2\u3064\u306E\u6B20\u70B9\u304C\u3042\u308B\u3002 \u7D50\u679C\u3068\u3057\u3066\u5F97\u3089\u308C\u308B\u6B21\u5143\u304C\u89E3\u91C8\u304C\u56F0\u96E3\u306A\u5834\u5408\u304C\u3042\u308B\u3002\u4F8B\u3048\u3070\u3001 {(car), (truck), (flower)} --> {(1.3452 * car + 0.2828 * truck), (flower)} \u3068\u306A\u3063\u305F\u5834\u5408\u3001(1.3452 * car + 0.2828 * truck) \u306F\u300C\u8ECA\u300D\u3068\u89E3\u91C8\u3067\u304D\u308B\u3002\u3057\u304B\u3057\u3001\u4EE5\u4E0B\u306E\u3088\u3046\u306A\u5834\u5408 {(car), (bottle), (flower)} --> {(1.3452 * car + 0.2828 * bottle), (flower)} \u6570\u5B66\u7684\u30EC\u30D9\u30EB\u3067\u306F\u554F\u984C\u306A\u3044\u306E\u3060\u304C\u3001\u81EA\u7136\u8A00\u8A9E\u30EC\u30D9\u30EB\u3067\u306F\u89E3\u91C8\u306E\u3057\u3088\u3046\u304C\u306A\u3044\u3002 LSA\u306E\u78BA\u7387\u30E2\u30C7\u30EB\u306F\u6E2C\u5B9A\u30C7\u30FC\u30BF\u3068\u4E00\u81F4\u3057\u306A\u3044\u3002LSA\u3067\u306F\u3001\u30DD\u30A2\u30BD\u30F3\u5206\u5E03\u304C\u89B3\u6E2C\u3055\u308C\u305F\u3068\u3057\u3066\u3082\u3001\u5358\u8A9E\u3068\u6587\u66F8\u306F\u540C\u6642\u6B63\u898F\u5206\u5E03\u30E2\u30C7\u30EB\u3092\u5F62\u6210\u3059\u308B\u3068\u4EEE\u5B9A\u3055\u308C\u308B\uFF08\u30A8\u30EB\u30B4\u30FC\u30C9\u4EEE\u8AAC\uFF09\u3002\u6700\u8FD1\u3067\u306F\u591A\u9805\u5206\u5E03\u30E2\u30C7\u30EB\u306B\u57FA\u3065\u3044\u305F\u78BA\u7387\u7684\u6F5C\u5728\u610F\u5473\u89E3\u6790\u304C\u8003\u6848\u3055\u308C\u3001\u6A19\u6E96\u306E\u6F5C\u5728\u610F\u5473\u89E3\u6790\u3088\u308A\u3082\u3088\u3044\u7D50\u679C\u304C\u5F97\u3089\u308C\u305F\u3068\u306E\u5831\u544A\u304C\u3042\u308B\u3002 \u95A2\u9023\u9805\u76EE \u30D9\u30AF\u30C8\u30EB\u7A7A\u9593\u30E2\u30C7\u30EB \u30B9\u30D1\u30E0\u30C7\u30AD\u30B7\u30F3\u30B0 \u4E3B\u6210\u5206\u5206\u6790 \u811A\u6CE8 \u53C2\u8003\u6587\u732E \"\". . -- Brand \u306E\u30A2\u30EB\u30B4\u30EA\u30BA\u30E0\u306E MATLAB \u3067\u306E\u5B9F\u88C5\u304C\u3042\u308B\u3002 . . \u30E2\u30C7\u30EB\u3092\u63D0\u6848\u3057\u305F\u6700\u521D\u306E\u8AD6\u6587 . PDF. \u6587\u66F8\u691C\u7D22\u3078\u306E\u5FDC\u7528\u306E\u89E3\u8AAC \"\". \"{{{title}}}\".. \"{{{title}}}\".. \"\". \"\". \"\". \u5916\u90E8\u30EA\u30F3\u30AF Latent Semantic Analysis - \u81EA\u7136\u8A00\u8A9E\u51E6\u7406\u3078\u306E\u5FDC\u7528\u4F8B Latent Semantic Indexing - \u6F5C\u5728\u7684\u610F\u5473\u30A4\u30F3\u30C7\u30AF\u30B7\u30F3\u30B0\u306E\u6570\u5B66\u7684\u3067\u306A\u3044\u89E3\u8AAC The Semantic Indexing Project - \u6F5C\u5728\u7684\u610F\u5473\u30A4\u30F3\u30C7\u30AF\u30B7\u30F3\u30B0\u306E\u30AA\u30FC\u30D7\u30F3\u30BD\u30FC\u30B9\u30D7\u30ED\u30B0\u30E9\u30E0 SenseClusters - \u6F5C\u5728\u610F\u5473\u89E3\u6790\u306A\u3069\u306E\u30AA\u30FC\u30D7\u30F3\u30BD\u30FC\u30B9\u30D1\u30C3\u30B1\u30FC\u30B8"@ja , "Latent semantisk analys (eng. Latent Semantic Analysis, LSA) \u00E4r en indexeringsmetod inom spr\u00E5kteknologi som beskriver relationen mellan termer (ord) och dokument i ett korpus. Metoden placerar alla dokument i ett h\u00F6gdimensionellt vektorrum s\u00E5 att konceptuellt besl\u00E4ktade dokument \u00E4ven \u00E4r n\u00E4rliggande i vektorrummet. Ett av metodens fr\u00E4msta m\u00E5l \u00E4r att kunna h\u00E4mta ut alla relevanta dokument vid en s\u00F6kning, \u00E4ven de som inte inneh\u00E5ller just de termer som anv\u00E4ndes i s\u00F6kfrasen."@sv , "L\u2019analyse s\u00E9mantique latente ou indexation s\u00E9mantique latente est un proc\u00E9d\u00E9 de traitement des langues naturelles, dans le cadre de la s\u00E9mantique vectorielle. La LSA fut brevet\u00E9e en 1988 et publi\u00E9e en 1990. Elle permet d'\u00E9tablir des relations entre un ensemble de documents et les termes qu'ils contiennent, en construisant des \u00AB concepts \u00BB li\u00E9s aux documents et aux termes. Matrice des occurrences La LSA utilise une matrice qui d\u00E9crit l'occurrence de certains termes dans les documents. C'est une matrice creuse dont les lignes correspondent aux \u00AB termes \u00BB et dont les colonnes correspondent aux \u00AB documents \u00BB. Les \u00AB termes \u00BB sont g\u00E9n\u00E9ralement des mots tronqu\u00E9s ou ramen\u00E9s \u00E0 leur radical, issus de l'ensemble du corpus. On a donc le nombre d'apparition d'un mot dans chaque document, et pour tous les mots. Ce nombre est normalis\u00E9 en utilisant la pond\u00E9ration tf-idf, combinaison de deux techniques : un coefficient de la matrice est d'autant plus grand qu'il appara\u00EEt beaucoup dans un document, et qu'il est rare \u2014 pour les mettre en avant. Cette matrice est courante dans les mod\u00E8les s\u00E9mantiques standards, comme le mod\u00E8le vectoriel, quoique sa forme matricielle ne soit pas syst\u00E9matique, \u00E9tant donn\u00E9 qu'on ne se sert que rarement des propri\u00E9t\u00E9s math\u00E9matiques des matrices. La LSA transforme la matrice des occurrences en une \u00AB relation \u00BB entre les termes et des \u00AB concepts \u00BB, et une relation entre ces concepts et les documents. On peut donc relier des documents entre eux. Applications Cette organisation entre termes et concepts est g\u00E9n\u00E9ralement employ\u00E9e pour : la comparaison de documents dans l'espace des concepts; la recherche de documents similaires entre diff\u00E9rentes langues, en ayant acc\u00E8s \u00E0 un dictionnaire de documents multilingues; la recherche de relations entre les termes; \u00E9tant donn\u00E9 une requ\u00EAte, traduire les termes de la requ\u00EAte dans l'espace des concepts, pour retrouver des documents li\u00E9s s\u00E9mantiquement. La r\u00E9solution de la synonymie et de la polys\u00E9mie est un enjeu majeur en traitement automatique des langues : deux synonymes d\u00E9crivent une m\u00EAme id\u00E9e, un moteur de recherche pourrait ainsi trouver des documents pertinents mais ne contenant pas le terme exact de la recherche; la polys\u00E9mie d'un mot fait qu'il a plusieurs sens selon le contexte \u2014 on pourrait de m\u00EAme \u00E9viter des documents contenant le mot recherch\u00E9, mais dans une acception qui ne correspond pas \u00E0 ce que l'on d\u00E9sire ou au domaine consid\u00E9r\u00E9. R\u00E9duction du rang Apr\u00E8s avoir construit la matrice des occurrences, la LSA permet de trouver une matrice de rang plus faible, qui donne une approximation de cette matrice des occurrences. On peut justifier cette approximation par plusieurs aspects : la matrice d'origine pourrait \u00EAtre trop grande pour les capacit\u00E9s de calcul de la machine \u2014 on rend ainsi le proc\u00E9d\u00E9 r\u00E9alisable, et c'est un \u00AB mal n\u00E9cessaire \u00BB; la matrice d'origine peut \u00EAtre \u00AB bruit\u00E9e \u00BB : des termes n'apparaissant que de mani\u00E8re anecdotique \u2014 on \u00AB nettoie \u00BB ainsi la matrice, c'est une op\u00E9ration qui am\u00E9liore les r\u00E9sultats; la matrice d'origine peut \u00EAtre pr\u00E9sum\u00E9e \u00AB trop creuse \u00BB : elle contient plut\u00F4t les mots propres \u00E0 chaque documents que les termes li\u00E9s \u00E0 plusieurs documents \u2014 c'est \u00E9galement un probl\u00E8me de synonymie. Cependant, la r\u00E9duction du rang de la matrice des occurrences a pour effet la combinaison de certaines dimensions qui peuvent ne pas \u00EAtre pertinentes. On s'arrange en g\u00E9n\u00E9ral pour \u2014 tant que c'est possible \u2014 fusionner les termes de sens proches. Ainsi, on pourra effectuer la transformation : {(Voiture), (Camion), (Fleur)} \u2192 {(1,3452 \u00D7 Voiture + 0,2828 \u00D7 Camion), (Fleur)} La synonymie est r\u00E9solue de cette mani\u00E8re. Mais quelques fois cela n'est pas possible. Dans ces cas, la LSA peut effectuer la transformation suivante : {(Voiture), (Bouteille), (Fleur)} -\u2192 {(1,3452 \u00D7 Voiture + 0,2828 \u00D7 Bouteille), (Fleur)} Ce regroupement est beaucoup plus difficile \u00E0 interpr\u00E9ter \u2014 il est justifi\u00E9 d'un point de vue math\u00E9matique, mais n'est pas pertinent pour un locuteur humain. Description Construction de la matrice des occurrences Soit X la matrice o\u00F9 l'\u00E9l\u00E9ment (i, j) d\u00E9crit les occurrences du terme i dans le document j \u2014 par exemple la fr\u00E9quence. Alors X aura cette allure : \\begin{matrix} \\textbf{d}_j \\downarrow \\textbf{t}_i^T \\rightarrow \\begin{pmatrix} x_{1,1} \\dots x_{1,n} \\vdots \\ddots \\vdots x_{m,1} \\dots x_{m,n} \\end{pmatrix} \\end{matrix} Une ligne de cette matrice est ainsi un vecteur qui correspond \u00E0 un terme, et dont les composantes donnent sa pr\u00E9sence (ou plut\u00F4t, son importance) dans chaque document : \\textbf{t}_i^T \\begin{pmatrix} x_{i,1} \\dots x_{i,n} \\end{pmatrix} De m\u00EAme, une colonne de cette matrice est un vecteur qui correspond \u00E0 un document, et dont les composantes sont l'importance dans son propre contenu de chaque terme. \\textbf{d}_j \\begin{pmatrix} x_{1,j} \\vdots x_{m,j} \\end{pmatrix} Corr\u00E9lations Le produit scalaire : \\textbf{t}_i^T \\textbf{t}_p entre deux vecteurs \u00AB termes \u00BB donne la corr\u00E9lation entre deux termes sur l'ensemble du corpus. Le produit matriciel <math>X X^T contient tous les produits scalaires de cette forme : l'\u00E9l\u00E9ment (i, p) \u2014 qui est le m\u00EAme que l'\u00E9l\u00E9ment (p, i) car la matrice est sym\u00E9trique \u2014 est ainsi le produit scalaire : \\textbf{t}_i^T \\textbf{t}_p (<math> \\textbf{t}_p^T \\textbf{t}_i). De m\u00EAme, le produit <math>X^T X contient tous les produits scalaires entre les vecteurs \u00AB documents \u00BB, qui donnent leurs corr\u00E9lations sur l'ensemble du lexique : \\textbf{d}_j^T \\textbf{d}_q \\textbf{d}_q^T \\textbf{d}_j. D\u00E9composition en valeurs singuli\u00E8res On effectue alors une d\u00E9composition en valeurs singuli\u00E8res sur X, qui donne deux matrices orthonormales U et V et une matrice diagonale \u03A3. On a alors : X U \\Sigma V^T Les produits de matrice qui donnent les corr\u00E9lations entre les termes d'une part et entre les documents d'autre part s'\u00E9crivent alors : \\begin{matrix} X X^T (U \\Sigma V^T) (U \\Sigma V^T)^T (U \\Sigma V^T) (V^{T^T} \\Sigma^T U^T) U \\Sigma V^T V \\Sigma^T U^T U \\Sigma \\Sigma^T U^T X^T X (U \\Sigma V^T)^T (U \\Sigma V^T) (V^{T^T} \\Sigma^T U^T) (U \\Sigma V^T) V \\Sigma^T U^T U \\Sigma V^T V \\Sigma^T \\Sigma V^T \\end{matrix} Puisque les matrices : \\Sigma \\Sigma^T et <math>\\Sigma^T \\Sigma sont diagonales, U est faite des vecteurs propres de <math>X X^T, et V est faite des vecteurs propres de <math>X^T X. Les deux produits ont alors les m\u00EAmes valeurs propres non-nulles \u2014 qui correspondent aux coefficients diagonaux non-nuls de <math>\\Sigma \\Sigma^T. La d\u00E9composition s'\u00E9crit alors : \\begin{matrix} X U \\Sigma V^T (\\textbf{d}_j) (\\hat \\textbf{d}_j) \\downarrow \\downarrow (\\textbf{t}_i^T) \\rightarrow \\begin{pmatrix} x_{1,1} \\dots x_{1,n} \\vdots \\ddots \\vdots x_{m,1} \\dots x_{m,n} \\end{pmatrix} (\\hat \\textbf{t}_i^T) \\rightarrow \\begin{pmatrix} \\begin{pmatrix} \\, \\, \\textbf{u}_1 \\, \\,\\end{pmatrix} \\dots \\begin{pmatrix} \\, \\, \\textbf{u}_l \\, \\, \\end{pmatrix} \\end{pmatrix} \\cdot \\begin{pmatrix} \\sigma_1 \\dots 0 \\vdots \\ddots \\vdots 0 \\dots \\sigma_l \\end{pmatrix} \\cdot \\begin{pmatrix} \\begin{pmatrix} \\textbf{v}_1 \\end{pmatrix} \\vdots \\begin{pmatrix} \\textbf{v}_l \\end{pmatrix} \\end{pmatrix} \\end{matrix} Les valeurs <math>\\sigma_1, \\dots, \\sigma_l sont les valeurs singuli\u00E8res de X. D'autre part, les vecteurs <math>u_1, \\dots, u_l et <math>v_1, \\dots, v_l sont respectivement singuliers \u00E0 gauches et \u00E0 droite. On remarque \u00E9galement que la seule partie de U qui contribue \u00E0 <math>\\textbf{t}_i est la i ligne. On note d\u00E9sormais ce vecteur <math>\\hat \\textrm{t}_i. De m\u00EAme la seule partie de <math>V^T qui contribue \u00E0 <math>\\textbf{d}_j est la j colonne, que l'on note <math>\\hat \\textrm{d}_j. Espace des concepts Lorsqu'on s\u00E9lectionne les k plus grandes valeurs singuli\u00E8res, ainsi que les vecteurs singuliers correspondants dans U et V, on obtient une approximation de rang k de la matrice des occurrences. Le point important, c'est qu'en faisant cette approximation, les vecteurs \u00AB termes \u00BB et \u00AB documents \u00BB sont traduits dans l'espace des \u00AB concepts \u00BB. Le vecteur <math>\\hat \\textbf{t}_i poss\u00E8de alors k composantes, qui chacune donne l'importance du terme i dans chacun des k diff\u00E9rents \u00AB concepts \u00BB. De m\u00EAme, le vecteur <math>\\hat \\textbf{d}_j donne l'intensit\u00E9 des relations entre le document j et chaque concept. On \u00E9crit cette approximation sous la forme suivante : X_k U_k \\Sigma_k V_k^T On peut alors effectuer les op\u00E9rations suivantes : voir dans quelle mesure les documents j et q sont li\u00E9s, dans l'espace des concepts, en comparant les vecteurs <math>\\hat \\textbf{d}_j et <math>\\hat \\textbf{d}_q. On peut faire cela en \u00E9valuant la similarit\u00E9 cosinus, qui peut se calculer ainsi : \\cos{\\theta} \\frac{{\\hat \\textbf{d}_j} \\cdot {\\hat \\textbf{d}_q}}{\\left\\| {\\hat \\textbf{d}_j} \\right\\| \\left \\| {\\hat \\textbf{d}_q} \\right\\|}; comparer les termes i et p en comparant les vecteurs <math>\\hat \\textbf{t}_i et <math>\\hat \\textbf{t}_p par la m\u00EAme m\u00E9thode; une requ\u00EAte \u00E9tant donn\u00E9e, on peut la traiter comme un \u00AB mini-document \u00BB et la comparer dans l'espace des concepts \u00E0 un corpus pour construire une liste des documents les plus pertinents. Pour faire cela, il faut d\u00E9j\u00E0 traduire la requ\u00EAte dans l'espace des concepts, en la transformant de la m\u00EAme mani\u00E8re que les documents. Si la requ\u00EAte est q, il faut calculer : \\hat \\textbf{q} \\Sigma_k^{-1} U_k^T \\textbf{q} avant de comparer ce vecteur au corpus. Impl\u00E9mentations La d\u00E9composition en valeurs singuli\u00E8res est g\u00E9n\u00E9ralement calcul\u00E9e par des m\u00E9thodes optimis\u00E9es pour les matrices larges \u2014 par exemple l'algorithme de Lanczos \u2014 par des programmes it\u00E9ratifs, ou encore par des r\u00E9seaux de neurones, cette derni\u00E8re approche ne n\u00E9cessitant pas que l'int\u00E9gralit\u00E9 de la matrice soit gard\u00E9e en m\u00E9moire . Analyse s\u00E9mantique latente probabiliste (PLSA) Le mod\u00E8le statistique de l'analyse s\u00E9mantique latente ne correspond pas aux donn\u00E9es observ\u00E9es : elle suppose que les mots et documents forment ensemble un mod\u00E8le gaussien, alors qu'on observe une distribution de Poisson. Ainsi, une approche plus r\u00E9cente est l'analyse s\u00E9mantique latente probabiliste, ou PLSA, bas\u00E9e sur un mod\u00E8le multinomial. Annexes Bibliographie The Latent Semantic Indexing home page, Universit\u00E9 du Colorado; PDF. Erreur de param\u00E9trage de {{Lien web}} : les param\u00E8tres url et titre sont obligatoires. T. Hofmann, Probabilistic Latent Semantic Analysis, Uncertainty in Artificial Intelligence, 1999. G. Gorell et B. Webb, \u00AB Generalized Hebbian Algorithm for Latent Semantic Analysis \u00BB, Interspeech, 2005. Erreur de param\u00E9trage de {{Lien web}} : les param\u00E8tres url et titre sont obligatoires. Erreur de param\u00E9trage de {{Lien web}} : les param\u00E8tres url et titre sont obligatoires. Notes et r\u00E9f\u00E9rences Source Voir aussi Articles connexes S\u00E9mantique vectorielle D\u00E9composition en valeurs singuli\u00E8res Liens externes The Semantic Indexing Project, un projet Open Source d'indexation s\u00E9mantique latente."@fr , "\u041B\u0430\u0442\u0435\u043D\u0442\u043D\u043E-\u0441\u0435\u043C\u0430\u043D\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u0430\u043D\u0430\u043B\u0438\u0437 (\u041B\u0421\u0410) - \u044D\u0442\u043E \u043C\u0435\u0442\u043E\u0434 \u043E\u0431\u0440\u0430\u0431\u043E\u0442\u043A\u0438 \u0438\u043D\u0444\u043E\u0440\u043C\u0430\u0446\u0438\u0438 \u043D\u0430 \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u043E\u043C \u044F\u0437\u044B\u043A\u0435, \u0430\u043D\u0430\u043B\u0438\u0437\u0438\u0440\u0443\u044E\u0449\u0438\u0439 \u0432\u0437\u0430\u0438\u043C\u043E\u0441\u0432\u044F\u0437\u044C \u043C\u0435\u0436\u0434\u0443 \u043A\u043E\u043B\u043B\u0435\u043A\u0446\u0438\u0435\u0439 \u0434\u043E\u043A\u0443\u043C\u0435\u043D\u0442\u043E\u0432 \u0438 \u0442\u0435\u0440\u043C\u0438\u043D\u0430\u043C\u0438 \u0432 \u043D\u0438\u0445 \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044E\u0449\u0438\u043C\u0438\u0441\u044F, \u0441\u043E\u043F\u043E\u0441\u0442\u0430\u0432\u043B\u044F\u0449\u0438\u0439 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0435 \u0444\u0430\u043A\u0442\u043E\u0440\u044B (\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438) \u0432\u0441\u0435\u043C \u0434\u043E\u043A\u0443\u043C\u0435\u043D\u0442\u0430\u043C \u0438 \u0442\u0435\u0440\u043C\u0430\u043C. \u041B\u0421\u0410 \u0431\u044B\u043B \u0437\u0430\u043F\u0430\u0442\u0435\u043D\u0442\u043E\u0432\u0430\u043D \u0432 1988 \u0433\u043E\u0434\u0443 Scott Deerwester, Susan Dumais, George Furnas, Richard Harshman, Thomas Landauer, Karen Lochbaum \u0438 Lynn Streeter. \u0412 \u043E\u0431\u043B\u0430\u0441\u0442\u0438 \u0438\u043D\u0444\u043E\u0440\u043C\u0430\u0446\u0438\u043E\u043D\u043D\u043E\u0433\u043E \u043F\u043E\u0438\u0441\u043A\u0430 \u0434\u0430\u043D\u043D\u044B\u0439 \u043F\u043E\u0434\u0445\u043E\u0434 \u043D\u0430\u0437\u044B\u0432\u0430\u044E\u0442 \u043B\u0430\u0442\u0435\u043D\u0442\u043D\u043E-\u0441\u0435\u043C\u0430\u043D\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u043C \u0438\u043D\u0434\u0435\u043A\u0441\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u0435\u043C."@ru , "\u6F5C\u5728\u8BED\u4E49\u5B66\uFF08Latent Semantic Analysis\uFF09\uFF0C\u662F\u8BED\u4E49\u5B66\u7684\u4E00\u4E2A\u65B0\u7684\u5206\u652F\u3002\u4F20\u7EDF\u7684\u8BED\u4E49\u5B66\u901A\u5E38\u7814\u7A76\u5B57\u3001\u8BCD\u7684\u542B\u4E49\u4EE5\u53CA\u8BCD\u4E0E\u8BCD\u4E4B\u95F4\u7684\u5173\u7CFB\uFF0C\u5982\u540C\u4E49\uFF0C\u8FD1\u4E49\uFF0C\u53CD\u4E49\u7B49\u7B49\u3002\u6F5C\u5728\u8BED\u4E49\u5B66\u63A2\u8BA8\u7684\u662F\u9690\u85CF\u5728\u5B57\u8BCD\u80CC\u540E\u7684\u67D0\u79CD\u5173\u7CFB\uFF0C\u8FD9\u79CD\u5173\u7CFB\u4E0D\u662F\u4EE5\u8BCD\u5178\u4E0A\u7684\u5B9A\u4E49\u4E3A\u57FA\u7840\uFF0C\u800C\u662F\u4EE5\u5B57\u8BCD\u7684\u4F7F\u7528\u73AF\u5883\u4F5C\u4E3A\u6700\u57FA\u672C\u7684\u53C2\u8003\u3002\u8FD9\u79CD\u601D\u60F3\u6765\u81EA\u4E8E\u5FC3\u7406\u8BED\u8A00\u5B66\u5BB6\u3002\u4ED6\u4EEC\u8BA4\u4E3A\uFF0C\u4E16\u754C\u4E0A\u6570\u4EE5\u767E\u8BA1\u7684\u8BED\u8A00\u90FD\u5E94\u8BE5\u6709\u4E00\u79CD\u5171\u540C\u7684\u7B80\u5355\u7684\u673A\u5236\uFF0C\u4F7F\u5F97\u4EFB\u4F55\u4EBA\u53EA\u8981\u662F\u5728\u67D0\u79CD\u7279\u5B9A\u7684\u8BED\u8A00\u73AF\u5883\u4E0B\u957F\u5927\u90FD\u80FD\u638C\u63E1\u90A3\u79CD\u8BED\u8A00\u3002\u5728\u8FD9\u79CD\u601D\u60F3\u7684\u6307\u5BFC\u4E0B\uFF0C\u4EBA\u4EEC\u627E\u5230\u4E86\u4E00\u79CD\u7B80\u5355\u7684\u6570\u5B66\u6A21\u578B\uFF0C\u8FD9\u79CD\u6A21\u578B\u7684\u8F93\u5165\u662F\u7531\u4EFB\u4F55\u4E00\u79CD\u8BED\u8A00\u4E66\u5199\u7684\u6587\u732E\u6784\u6210\u7684\u6587\u5E93\uFF0C\u8F93\u51FA\u662F\u8BE5\u8BED\u8A00\u7684\u5B57\u3001\u8BCD\u7684\u4E00\u79CD\u6570\u5B66\u8868\u8FBE\uFF08\u5411\u91CF\uFF09\u3002\u5B57\u3001\u8BCD\u4E4B\u95F4\u7684\u5173\u7CFB\u4E43\u81F3\u4EFB\u4F55\u6587\u7AE0\u7247\u65AD\u4E4B\u95F4\u7684\u542B\u4E49\u7684\u6BD4\u8F83\u5C31\u7531\u8FD9\u79CD\u5411\u91CF\u4E4B\u95F4\u7684\u8FD0\u7B97\u4EA7\u751F\u3002 \u6F5B\u5728\u8A9E\u7FA9\u5B78\u7684\u89C0\u5FF5\u4E5F\u88AB\u61C9\u7528\u5728\u8CC7\u8A0A\u6AA2\u7D22\u4E0A\uFF0C\u6240\u4EE5\u6709\u6642\u6F5B\u5728\u8A9E\u7FA9\u5B78\u4E5F\u88AB\u7A31\u70BA\u96B1\u542B\u8A9E\u7FA9\u7D22\u5F15\uFF08Latent Semantic Indexing\uFF0CLSI\uFF09\u3002"@zh , "Latent semantic analysis (LSA) is a technique in natural language processing, in particular in vectorial semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms. LSA was patented in 1988 by Scott Deerwester, Susan Dumais, George Furnas, Richard Harshman, Thomas Landauer, Karen Lochbaum and Lynn Streeter. In the context of its application to information retrieval, it is sometimes called Latent Semantic Indexing (LSI). Occurrence matrix LSA can use a term-document matrix which describes the occurrences of terms in documents; it is a sparse matrix whose rows correspond to terms and whose columns correspond to documents. A typical example of the weighting of the elements of the matrix is tf-idf (term frequency\u2013inverse document frequency): the element of the matrix is proportional to the number of times the terms appear in each document, where rare terms are upweighted to reflect their relative importance. This matrix is also common to standard semantic models, though it is not necessarily explicitly expressed as a matrix, since the mathematical properties of matrices are not always used. LSA transforms the occurrence matrix into a relation between the terms and some concepts, and a relation between those concepts and the documents. Thus the terms and documents are now indirectly related through the concepts. Applications The new concept space typically can be used to: Compare the documents in the concept space. Find similar documents across languages, after analyzing a base set of translated documents. Find relations between terms. Given a query of terms, translate it into the concept space, and find matching documents. Synonymy and polysemy are fundamental problems in natural language processing: Synonymy is the phenomenon where different words describe the same idea. Thus, a query in a search engine may fail to retrieve a relevant document that does not contain the words which appeared in the query. For example, a search for \"doctors\" may not return a document containing the word \"physicians\", even though the words have the same meaning. Polysemy is the phenomenon where the same word has multiple meanings. So a search may retrieve irrelevant documents containing the desired words in the wrong meaning. For example, a botanist and a computer scientist looking for the word \"tree\" probably desire different sets of documents. Rank lowering After the construction of the occurrence matrix, LSA finds a low-rank approximation to the term-document matrix. There could be various reasons for these approximations: The original term-document matrix is presumed too large for the computing resources; in this case, the approximated low rank matrix is interpreted as an approximation (a \"least and necessary evil\"). The original term-document matrix is presumed noisy: for example, anecdotal instances of terms are to be eliminated. From this point of view, the approximated matrix is interpreted as a de-noisified matrix (a better matrix than the original). The original term-document matrix is presumed overly sparse relative to the \"true\" term-document matrix. That is, the original matrix lists only the words actually in each document, whereas we might be interested in all words related to each document--generally a much larger set due to synonymy. The consequence of the rank lowering is that some dimensions are combined and depend on more than one term: {(car), (truck), (flower)} --> {(1.3452 car + 0.2828 truck), (flower)} This mitigates the problem of identifying synonymy, as the rank lowering is expected to merge the dimensions associated with terms that have similar meanings. It also mitigates the problem with polysemy, since components of polysemous words that point in the \"right\" direction are added to the components of words that share a similar meaning. Conversely, components that point in other directions tend to either simply cancel out, or, at worst, to be smaller than components in the directions corresponding to the intended sense. Derivation Let <math>X be a matrix where element <math>(i,j) describes the occurrence of term <math>i in document <math>j (this can be, for example, the frequency). <math>X will look like this: \\begin{matrix} \\textbf{d}_j \\downarrow \\textbf{t}_i^T \\rightarrow \\begin{bmatrix} x_{1,1} \\dots x_{1,n} \\vdots \\ddots \\vdots x_{m,1} \\dots x_{m,n} \\end{bmatrix} \\end{matrix} Now a row in this matrix will be a vector corresponding to a term, giving its relation to each document: \\textbf{t}_i^T \\begin{bmatrix} x_{i,1} \\dots x_{i,n} \\end{bmatrix} Likewise, a column in this matrix will be a vector corresponding to a document, giving its relation to each term: \\textbf{d}_j \\begin{bmatrix} x_{1,j} \\vdots x_{m,j} \\end{bmatrix} Now the dot product <math>\\textbf{t}_i^T \\textbf{t}_p between two term vectors gives the correlation between the terms over the documents. The matrix product <math>X X^T contains all these dot products. Element <math>(i,p) (which is equal to element <math>) contains the dot product <math>\\textbf{t}_i^T \\textbf{t}_p (<math> \\textbf{t}_p^T \\textbf{t}_i). Likewise, the matrix <math>X^T X contains the dot products between all the document vectors, giving their correlation over the terms: <math>\\textbf{d}_j^T \\textbf{d}_q \\textbf{d}_q^T \\textbf{d}_j. Now assume that there exists a decomposition of <math>X such that <math>U and <math>V are orthonormal matrices and <math>\\Sigma is a diagonal matrix. This is called a singular value decomposition (SVD): X U \\Sigma V^T The matrix products giving us the term and document correlations then become \\begin{matrix} X X^T (U \\Sigma V^T) (U \\Sigma V^T)^T (U \\Sigma V^T) (V^{T^T} \\Sigma^T U^T) U \\Sigma V^T V \\Sigma^T U^T U \\Sigma \\Sigma^T U^T X^T X (U \\Sigma V^T)^T (U \\Sigma V^T) (V^{T^T} \\Sigma^T U^T) (U \\Sigma V^T) V \\Sigma U^T U \\Sigma V^T V \\Sigma^T \\Sigma V^T \\end{matrix} Since <math>\\Sigma \\Sigma^T and <math>\\Sigma^T \\Sigma are diagonal we see that <math>U must contain the eigenvectors of <math>X X^T, while <math>V must be the eigenvectors of <math>X^T X. Both products have the same non-zero eigenvalues, given by the non-zero entries of <math>\\Sigma \\Sigma^T, or equally, by the non-zero entries of <math>\\Sigma^T\\Sigma. Now the decomposition looks like this: \\begin{matrix} X U \\Sigma V^T (\\textbf{d}_j) (\\hat \\textbf{d}_j) \\downarrow \\downarrow (\\textbf{t}_i^T) \\rightarrow \\begin{bmatrix} x_{1,1} \\dots x_{1,n} \\vdots \\ddots \\vdots x_{m,1} \\dots x_{m,n} \\end{bmatrix} (\\hat \\textbf{t}_i^T) \\rightarrow \\begin{bmatrix} \\begin{bmatrix} \\, \\, \\textbf{u}_1 \\, \\,\\end{bmatrix} \\dots \\begin{bmatrix} \\, \\, \\textbf{u}_l \\, \\, \\end{bmatrix} \\end{bmatrix} \\cdot \\begin{bmatrix} \\sigma_1 \\dots 0 \\vdots \\ddots \\vdots 0 \\dots \\sigma_l \\end{bmatrix} \\cdot \\begin{bmatrix} \\begin{bmatrix} \\textbf{v}_1 \\end{bmatrix} \\vdots \\begin{bmatrix} \\textbf{v}_l \\end{bmatrix} \\end{bmatrix} \\end{matrix} The values <math>\\sigma_1, \\dots, \\sigma_l are called the singular values, and <math>u_1, \\dots, u_l and <math>v_1, \\dots, v_l the left and right singular vectors. Notice how the only part of <math>U that contributes to <math>\\textbf{t}_i is the <math>i\\textrm{'th} row. Let this row vector be called <math>\\hat \\textrm{t}_i. Likewise, the only part of <math>V^T that contributes to <math>\\textbf{d}_j is the <math>j\\textrm{'th} column, <math>\\hat \\textrm{d}_j. These are not the eigenvectors, but depend on all the eigenvectors. It turns out that when you select the <math>k largest singular values, and their corresponding singular vectors from <math>U and <math>V, you get the rank <math>k approximation to X with the smallest error. This approximation has a minimal error. But more importantly we can now treat the term and document vectors as a \"concept space\". The vector <math>\\hat \\textbf{t}_i then has <math>k entries, each giving the occurrence of term <math>i in one of the <math>k concepts. Likewise, the vector <math>\\hat \\textbf{d}_j gives the relation between document <math>j and each concept. We write this approximation as X_k U_k \\Sigma_k V_k^T You can now do the following: See how related documents <math>j and <math>q are in the concept space by comparing the vectors <math>\\hat \\textbf{d}_j and <math>\\hat \\textbf{d}_q. This gives you a clustering of the documents. Comparing terms <math>i and <math>p by comparing the vectors <math>\\hat \\textbf{t}_i and <math>\\hat \\textbf{t}_p, giving you a clustering of the terms in the concept space. Given a query, view this as a mini document, and compare it to your documents in the concept space. To do the latter, you must first translate your query into the concept space. It is then intuitive that you must use the same transformation that you use on your documents: \\textbf{d}_j U_k \\Sigma_k \\hat \\textbf{d}_j \\hat \\textbf{d}_j \\Sigma_k^{-1} U_k^T \\textbf{d}_j This means that if you have a query vector <math>q, you must do the translation <math>\\hat \\textbf{q} \\Sigma_k^{-1} U_k^T \\textbf{q} before you compare it with the document vectors in the concept space. You can do the same for pseudo term vectors: \\textbf{t}_i^T \\hat \\textbf{t}_i^T \\Sigma_k V_k^T \\hat \\textbf{t}_i^T \\textbf{t}_i^T V_k^{-T} \\Sigma_k^{-1} \\textbf{t}_i^T V_k \\Sigma_k^{-1} \\hat \\textbf{t}_i \\Sigma_k^{-1} V_k^T \\textbf{t}_i Implementation The SVD is typically computed using large matrix methods but may also be computed incrementally and with greatly reduced resources via a neural network-like approach, which does not require the large, full-rank matrix to be held in memory. A fast, incremental, low-memory, large-matrix SVD algorithm has recently been developed. Unlike Gorrell and Webb's (2005) stochastic approximation, Brand's (2006) algorithm provides an exact solution. Limitations Some of LSA's drawbacks include: The resulting dimensions might be difficult to interpret. For instance, in {(car), (truck), (flower)} --> {(1.3452 car + 0.2828 truck), (flower)} the (1.3452 car + 0.2828 truck) component could be interpreted as \"vehicle\". However, it is very likely that cases close to {(car), (bottle), (flower)} --> {(1.3452 car + 0.2828 bottle), (flower)} will occur. This leads to results which can be justified on the mathematical level, but have no interpretable meaning in natural language. LSA cannot capture Polysemy (i.e. , multiple meanings of a word), because it represents each word as a single point in space. The probabilistic model of LSA does not match observed data: LSA assumes that words and documents form a joint Gaussian model, while a Poisson distribution has been observed. Thus, a newer alternative is probabilistic latent semantic analysis, based on a multinomial model, which is reported to give better results than standard LSA. Commercial Applications LSA has been used to assist in performing prior art searches for patents. See also Compound term processing Latent Dirichlet allocation Latent semantic mapping Latent Semantic Structure Indexing Principal components analysis Probabilistic latent semantic analysis Spamdexing Vectorial semantics Coh-Metrix External links Latent Semantic Analysis, a scholarpedia article on LSA written by Tom Landauer, one of the creators of LSA. The Semantic Indexing Project, an open source program for latent semantic indexing SenseClusters, an open source package for Latent Semantic Analysis and other methods for clustering similar contexts S-Space Package, an open source Java library that includes Latent Semantic Analysis and other algorithms for generating Statistical semantics from a text corpus References -- a MATLAB implementation of Brand's algorithm is available Original article where the model was first exposed. PDF. Illustration of the application of LSA to document retrieval."@en , "Latent Semantic Indexing (kurz LSI, englisch f\u00FCr schwache Bedeutungseinordnung) ist ein Verfahren des Information Retrieval, das 1990 zuerst von Deerwester et al. erw\u00E4hnt wurde. Verfahren wie das LSI sind insbesondere f\u00FCr die Suche auf gro\u00DFen Datenmengen wie dem Internet von Interesse. Das Ziel von LSI ist es, Hauptkomponenten von Dokumenten zu finden. Diese Hauptkomponenten (Konzepte) kann man sich als generelle Begriffe vorstellen. So ist Pferd zum Beispiel ein Konzept, das Begriffe wie M\u00E4hre, Klepper oder Gaul umfasst. Somit ist dieses Verfahren zum Beispiel dazu geeignet, aus sehr vielen Dokumenten (wie sie beispielsweise im Internet stehen), diejenigen herauszufinden, in denen es um Autos geht, auch wenn in ihnen das Wort Auto nicht explizit vorkommt. Des Weiteren kann LSI dabei helfen, Artikel, in denen es wirklich um Autos geht, von denen zu unterscheiden, in denen nur das Wort Auto erw\u00E4hnt wird (wie zum Beispiel bei Seiten, auf denen ein Auto als Gewinn angepriesen wird)."@de ; rdfs:comment ""@ja , ""@zh , "\u041B\u0430\u0442\u0435\u043D\u0442\u043D\u043E-\u0441\u0435\u043C\u0430\u043D\u0442\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u0430\u043D\u0430\u043B\u0438\u0437 (\u041B\u0421\u0410) - \u044D\u0442\u043E \u043C\u0435\u0442\u043E\u0434 \u043E\u0431\u0440\u0430\u0431\u043E\u0442\u043A\u0438 \u0438\u043D\u0444\u043E\u0440\u043C\u0430\u0446\u0438\u0438 \u043D\u0430 \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u043E\u043C \u044F\u0437\u044B\u043A\u0435, \u0430\u043D\u0430\u043B\u0438\u0437\u0438\u0440\u0443\u044E\u0449\u0438\u0439 \u0432\u0437\u0430\u0438\u043C\u043E\u0441\u0432\u044F\u0437\u044C \u043C\u0435\u0436\u0434\u0443 \u043A\u043E\u043B\u043B\u0435\u043A\u0446\u0438\u0435\u0439 \u0434\u043E\u043A\u0443\u043C\u0435\u043D\u0442\u043E\u0432 \u0438 \u0442\u0435\u0440\u043C\u0438\u043D\u0430\u043C\u0438 \u0432 \u043D\u0438\u0445 \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044E\u0449\u0438\u043C\u0438\u0441\u044F, \u0441\u043E\u043F\u043E\u0441\u0442\u0430\u0432\u043B\u044F\u0449\u0438\u0439 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0435 \u0444\u0430\u043A\u0442\u043E\u0440\u044B (\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438) \u0432\u0441\u0435\u043C \u0434\u043E\u043A\u0443\u043C\u0435\u043D\u0442\u0430\u043C \u0438 \u0442\u0435\u0440\u043C\u0430\u043C."@ru , "L\u2019analyse s\u00E9mantique latente ou indexation s\u00E9mantique latente est un proc\u00E9d\u00E9 de traitement des langues naturelles, dans le cadre de la s\u00E9mantique vectorielle. La LSA fut brevet\u00E9e en 1988 et publi\u00E9e en 1990. Elle permet d'\u00E9tablir des relations entre un ensemble de documents et les termes qu'ils contiennent, en construisant des \u00AB concepts \u00BB li\u00E9s aux documents et aux termes."@fr , "Latent semantic analysis (LSA) is a technique in natural language processing, in particular in vectorial semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms. LSA was patented in 1988 by Scott Deerwester, Susan Dumais, George Furnas, Richard Harshman, Thomas Landauer, Karen Lochbaum and Lynn Streeter."@en , "Latent semantisk analys (eng. Latent Semantic Analysis, LSA) \u00E4r en indexeringsmetod inom spr\u00E5kteknologi som beskriver relationen mellan termer (ord) och dokument i ett korpus. Metoden placerar alla dokument i ett h\u00F6gdimensionellt vektorrum s\u00E5 att konceptuellt besl\u00E4ktade dokument \u00E4ven \u00E4r n\u00E4rliggande i vektorrummet. Ett av metodens fr\u00E4msta m\u00E5l \u00E4r att kunna h\u00E4mta ut alla relevanta dokument vid en s\u00F6kning, \u00E4ven de som inte inneh\u00E5ller just de termer som anv\u00E4ndes i s\u00F6kfrasen."@sv , "Latent Semantic Indexing (kurz LSI, englisch f\u00FCr schwache Bedeutungseinordnung) ist ein Verfahren des Information Retrieval, das 1990 zuerst von Deerwester et al. erw\u00E4hnt wurde. Verfahren wie das LSI sind insbesondere f\u00FCr die Suche auf gro\u00DFen Datenmengen wie dem Internet von Interesse. Das Ziel von LSI ist es, Hauptkomponenten von Dokumenten zu finden. Diese Hauptkomponenten (Konzepte) kann man sich als generelle Begriffe vorstellen."@de . @prefix skos: . @prefix ns8: . dbpedia:Latent_semantic_analysis skos:subject ns8:Natural_language_processing , ns8:Information_retrieval , ns8:Latent_variable_models . @prefix ns9: . dbpedia:Latent_semantic_analysis dbpprop:wikiPageUsesTemplate ns9:dubious ; dbpprop:date "December 2008"@en . @prefix ns10: . dbpedia:Latent_semantic_analysis dbpprop:hasPhotoCollection ns10:Latent_semantic_analysis . dbpedia:Infoscale dbpprop:redirect dbpedia:Latent_semantic_analysis .