, Pour améliorer davantage la performance prédictive de l'algorithme des K-moyennes prédictives du premier type, le modèle LVQ pourrait être utilisé. Ce dernier prendrait en entrée les centres générés par l'algorithme des K-moyennes prédictives après convergence

, nous avons suivi une méthode uni-variée où chaque variable est traitée indépendamment des autres. Dans ce cas, nous n'avons pas étudié les interactions qui peuvent exister entre les variables. En effet, dans certains cas, une variable descriptives n'est importante qu'en présence d'une ou d'autres variables, Mesure d'importance des variables : dans les travaux réalisé à ce sujet (voir l'annexe E)

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V. Oumaima-alaoui-ismaili, A. Lemaire, and . Cornuéjols, Evaluation of predictive clustering quality, MBC2, on Model Based clustering and classification, vol.2, 2016.

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V. Oumaima-alaoui-ismaili, A. Lemaire, and . Cornuéjols, Classification à base de clustering ou comment décrire et prédire simultanément, Rencontres des Jeunes Chercheurs en Intelligence Artificielle (RJCIA), pp.7-12, 2015.

V. Oumaima-alaoui-ismaili, A. Lemaire, and . Cornuéjols, Une méthode basée sur des effectifs pour calculer la contribution des variables à un clustering, Atelier CluCo de la conférence Extraction et Gestion des Connaissances (EGC 2014)

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, Les aires sous les courbes de MSE

C. Le-tableau, 7) présente les performances moyennes en termes d'ALC-MSE de l'algorithme des K-moyennes standard précédé par Conditional Info (respectivement Rank Normalization) et en utilisant les différentes méthodes d'initialisation. Les résultats présentés dans les deux tableaux (C.6 et C.7) sont obtenus lorsque l'algorithme des K-moyennes est exécuté une

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L. Dans-la, Cette problématique de mesure de contribution, de mesure d'importance, dans un clustering peut être divisée en deux sousproblèmes que l'on peut respectivement caractériser de global ou local. L'importance globale a pour but de mesurer l'impact que la variable a eu sur la structure entière du partitionnement et non pas l'impact qu'elle a eu sur un cluster en particulier. Par contre, l'importance locale a pour objectif de savoir quelle variable a été déterminante dans la formation d'un cluster en particulier. Nous nous intéressons dans cet article uniquement à l'importance globale. Parmi les méthodes de l'état de l'art permettant de mesurer cette importance on trouvera de nombreux indices tels que : (i) l', plusieurs indices de qualité de clustering ont été développés afin de mesurer la contribution d'une variable au résultat d'un clustering, 1987.

. Halkidi, , 2000.

. S_dbw, , 2001.

, La plupart de ces méthodes utilisent le théorème de Huygens et la décomposition de l'inertie totale en la somme de l'inertie intra cluster et de l'inertie inter cluster. La contribution d'une variable est alors, par exemple, calculée en mesurant la valeur de l'inertie inter calculée uniquement avec cette variable vis-à-vis de la somme des inerties inter calculée sur toutes les variables, 1983.

, Notre proposition Notre but est l'ordonnancement du tableau 1 selon la contribution des variables à l'affection

, Nous décidons alors de poser le problème comme un problème de classification supervisée

, Le but sera d'essayer d'apprendre à prédire le cluster d'appartenance d'un individu (l'id-cluster du tableau 1) en utilisant une seule variable (classification univariée)

, En effet on ne souhaite pas mesurer l'importance des variables dans un nouvel espace mais l'importance des variables avec la représentation supervisée obtenue juste avant la création des clusters. Le but est l'aide à l'interprétation du clustering de manière à permettre à l'analyste de concentrer son attention sur les variables les plus importantes vis-à-vis du clustering obtenu. Parmi les méthodes capables d'utiliser la représentation issue de nos prétraitements supervisés et le tableau d'effectifs qui sert à présenter les résultats on choisit d'utiliser la méthode MODL qui mesure le pouvoir prédictif (appelé "level") d'une variable numérique dans, Comme on désire trier les variables selon le résultat de clustering initialement obtenu on s'interdira les classifieurs qui créent une nouvelle représentation des données, 2004.

. Dans-le-cas-d'une-variable-numérique, Nos prétraitements supervisés nous donnent les intervalles [les groupes de modalités] et la projection des individus sur les clusters (tableau 1) nous permettent d'avoir en notre possession les effectifs. L'ensemble des éléments nécessaire au calcul du level par variable est donc disponible pour toutes les variables explicatives. 1. exécuter l'algorithme de clustering afin d'obtenir un premier partitionnement. 2. trier les variables selon leur importance

, estimer la qualité de ce partitionnement à l'aide des critères EVA et AUC

, On peut alors tracer la courbe des valeurs, 2004.

, L'examen des résultats peut alors être fait visuellement en observant l'évolution de la courbe des valeurs d'EVA (respectivement AUC) et/ou en calculant l'aire sous la courbe des valeurs d'EVA (respectivement AUC) (ALC = Area Under Learning Curve, 2011.

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