. "Submodulare Funktion"@de . . "In mathematics, a submodular set function (also known as a submodular function) is a set function whose value, informally, has the property that the difference in the incremental value of the function that a single element makes when added to an input set decreases as the size of the input set increases. Submodular functions have a natural diminishing returns property which makes them suitable for many applications, including approximation algorithms, game theory (as functions modeling user preferences) and electrical networks. Recently, submodular functions have also found immense utility in several real world problems in machine learning and artificial intelligence, including automatic summarization, multi-document summarization, feature selection, active learning, sensor placement, image collection summarization and many other domains."@en . . . . . . . . . "Fonction sous-modulaire"@fr . . . . . . . . . . . . . . . . . . "Submodular set function"@en . . . . "Eine submodulare Funktion ist eine Mengenfunktion, die die Rangfunktion eines Matroids verallgemeinert. Submodulare Funktionen spielen in der kombinatorischen Optimierung eine wichtige Rolle."@de . "En optimisation combinatoire, les fonctions sous-modulaires sont des fonctions d'ensemble particuli\u00E8res. Soient E un ensemble et f une fonction qui \u00E0 tout sous-ensemble X de E associe un r\u00E9el f(X), on dit que f est sous-modulaire si l'in\u00E9galit\u00E9 suivante est v\u00E9rifi\u00E9e pour tout sous-ensemble X et Y de E Les fonctions sous-modulaire peuvent \u00EAtre vues comme l'analogue discret des fonctions convexes."@fr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "In mathematics, a submodular set function (also known as a submodular function) is a set function whose value, informally, has the property that the difference in the incremental value of the function that a single element makes when added to an input set decreases as the size of the input set increases. Submodular functions have a natural diminishing returns property which makes them suitable for many applications, including approximation algorithms, game theory (as functions modeling user preferences) and electrical networks. Recently, submodular functions have also found immense utility in several real world problems in machine learning and artificial intelligence, including automatic summarization, multi-document summarization, feature selection, active learning, sensor placement, imag"@en . . . . "33273315"^^ . . . . "\u52A3\u30E2\u30B8\u30E5\u30E9\u95A2\u6570"@ja . . . "\u6570\u5B66\u306E\u5206\u91CE\u306B\u304A\u3044\u3066\u52A3\u30E2\u30B8\u30E5\u30E9\u95A2\u6570 (\u82F1: submodular function) \u3068\u306F\u96C6\u5408\u95A2\u6570\u306E\u4E00\u7A2E\u3067\u3001\u7C21\u5358\u306B\u3044\u3046\u3068\u3001\u95A2\u6570\u306B\u6E21\u3055\u308C\u308B\u96C6\u5408\u306B1\u3064\u8981\u7D20\u304C\u52A0\u308F\u3063\u305F\u5834\u5408\u306B\u5897\u3048\u308B\u95A2\u6570\u306E\u5024\u304C\u3001\u3082\u3068\u306E\u96C6\u5408\u304C\u5927\u304D\u304F\u306A\u308B\u306B\u3064\u308C\u5C0F\u3055\u304F\u306A\u308B\u3088\u3046\u306A\u95A2\u6570\u3092\u6307\u3059\u3002\u96C6\u5408\u95A2\u6570\u3067\u3042\u308B\u3053\u3068\u3092\u660E\u793A\u3057\u3066\u52A3\u30E2\u30B8\u30E5\u30E9\u96C6\u5408\u95A2\u6570\u3068\u3044\u3046\u3053\u3068\u3082\u3042\u308B\u3002\u52A3\u30E2\u30B8\u30E5\u30E9\u95A2\u6570\u306E\u6982\u5FF5\u306F\u4E00\u822C\u306E\u30D9\u30AF\u30C8\u30EB\u5024\u95A2\u6570\u306B\u304A\u3051\u308B\u51F8\u95A2\u6570\u306E\u6982\u5FF5\u3068\u985E\u4F3C\u3057\u305F\u6027\u8CEA\u3092\u6301\u3064\u305F\u3081\u3001\u8FD1\u4F3C\u30A2\u30EB\u30B4\u30EA\u30BA\u30E0\u3084\u30B2\u30FC\u30E0\u7406\u8AD6\u3001\u6A5F\u68B0\u5B66\u7FD2\u306A\u3069\u306E\u5E45\u5E83\u3044\u5FDC\u7528\u3092\u6301\u3064\u3002"@ja . "En optimisation combinatoire, les fonctions sous-modulaires sont des fonctions d'ensemble particuli\u00E8res. Soient E un ensemble et f une fonction qui \u00E0 tout sous-ensemble X de E associe un r\u00E9el f(X), on dit que f est sous-modulaire si l'in\u00E9galit\u00E9 suivante est v\u00E9rifi\u00E9e pour tout sous-ensemble X et Y de E Les fonctions sous-modulaire peuvent \u00EAtre vues comme l'analogue discret des fonctions convexes."@fr . . . . "Eine submodulare Funktion ist eine Mengenfunktion, die die Rangfunktion eines Matroids verallgemeinert. Submodulare Funktionen spielen in der kombinatorischen Optimierung eine wichtige Rolle."@de . . . . . . . . . "\u6570\u5B66\u306E\u5206\u91CE\u306B\u304A\u3044\u3066\u52A3\u30E2\u30B8\u30E5\u30E9\u95A2\u6570 (\u82F1: submodular function) \u3068\u306F\u96C6\u5408\u95A2\u6570\u306E\u4E00\u7A2E\u3067\u3001\u7C21\u5358\u306B\u3044\u3046\u3068\u3001\u95A2\u6570\u306B\u6E21\u3055\u308C\u308B\u96C6\u5408\u306B1\u3064\u8981\u7D20\u304C\u52A0\u308F\u3063\u305F\u5834\u5408\u306B\u5897\u3048\u308B\u95A2\u6570\u306E\u5024\u304C\u3001\u3082\u3068\u306E\u96C6\u5408\u304C\u5927\u304D\u304F\u306A\u308B\u306B\u3064\u308C\u5C0F\u3055\u304F\u306A\u308B\u3088\u3046\u306A\u95A2\u6570\u3092\u6307\u3059\u3002\u96C6\u5408\u95A2\u6570\u3067\u3042\u308B\u3053\u3068\u3092\u660E\u793A\u3057\u3066\u52A3\u30E2\u30B8\u30E5\u30E9\u96C6\u5408\u95A2\u6570\u3068\u3044\u3046\u3053\u3068\u3082\u3042\u308B\u3002\u52A3\u30E2\u30B8\u30E5\u30E9\u95A2\u6570\u306E\u6982\u5FF5\u306F\u4E00\u822C\u306E\u30D9\u30AF\u30C8\u30EB\u5024\u95A2\u6570\u306B\u304A\u3051\u308B\u51F8\u95A2\u6570\u306E\u6982\u5FF5\u3068\u985E\u4F3C\u3057\u305F\u6027\u8CEA\u3092\u6301\u3064\u305F\u3081\u3001\u8FD1\u4F3C\u30A2\u30EB\u30B4\u30EA\u30BA\u30E0\u3084\u30B2\u30FC\u30E0\u7406\u8AD6\u3001\u6A5F\u68B0\u5B66\u7FD2\u306A\u3069\u306E\u5E45\u5E83\u3044\u5FDC\u7528\u3092\u6301\u3064\u3002"@ja . . "20470"^^ . "1121394132"^^ . . . . .