In this master thesis I recapitulated several methods for clustering input data. Two well known clustering algorithms, concretely K-means algorithm and Fuzzy C-means (FCM) algorithm, were described in the submitted work. I presented several methods, which could help estimate the optimal number of clusters. Further, I described Kohonen maps and two models of Kohonen's maps with dynamically changing structure, namely Kohonen map with growing grid and the model of growing neural gas. At last I described quite new model of radial basis function neural networks. I presented several learning algorithms for this model of neural networks. In the end of this work I made some clustering experiments with real data. This data describes the international trade among states of the whole world.

Ce manuscrit étudie dans un premier temps la dépendance de la distorsion, ou erreur en quantification, du quantificateur construit à partir d'un n-échantillon d'une distribution de probabilité via l'algorithme des k-means. Plus précisément, l'objectif de ce travail est de donner des bornes en probabilité sur l'écart entre la distorsion de ce quantificateur et la plus petite distorsion atteignable parmi les quantificateurs, à nombre d'images k fixé, décrivant l'influence des divers paramètres de ce problème: support de la distribution de probabilité à quantifier, nombre d'images k, dimension de l'espace vectoriel sous-jacent, et taille de l'échantillon servant à construire le quantificateur k-mean. Après un bref rappel des résultats précédents, cette étude établit l'équivalence des diverses conditions existantes pour établir une vitesse de convergence rapide en la taille de l'échantillon de l'écart de distorsion considéré, dans le cas des distributions à densité, à une condition technique ressemblant aux conditions requises en classification supervisée pour l'obtention de vitesses rapides de convergence. Il est ensuite prouvé que, sous cette condition technique, une vitesse de convergence de l'ordre de 1/n pouvait être atteinte en espérance. Ensuite, cette thèse énonce une condition facilement interprétable, appelée condition de marge, suffisante à la satisfaction de la condition technique établie précédemment. Plusieurs exemples classiques de distributions satisfaisant cette condition sont donnés, tels les mélanges gaussiens. Si cette condition de marge se trouve satisfaite, une description précise de la dépendance de l'écart de distorsion étudié peut être donné via une borne en espérance: la taille de l'échantillon intervient via un facteur 1/n, le nombre d'images k intervient via différentes quantités géométriques associées à la distribution à quantifier, et de manière étonnante la dimension de l'espace sous-jacent semble ne jouer aucun rôle. Ce dernier point nous a permis d'étendre nos résultats au cadre des espaces de Hilbert, propice à la quantification des courbes. Néanmoins, la quantification effective en grande dimension nécessite souvent en pratique une étape de réduction du nombre de variables, ce qui nous a conduit dans un deuxième temps à étudier une procédure de sélection de variables associée à la quantification. Plus précisément, nous nous sommes intéressés à une procédure de type Lasso adaptée au cadre de la quantification vectorielle, où la pénalité Lasso porte sur l'ensemble des points images du quantificateur, dans le but d'obtenir des points images parcimonieux. Si la condition de marge introduite précédemment est satisfaite, plusieurs garanties théoriques sont établies concernant le quantificateur issu d'une telle procédure, appelé quantificateur Lasso k-means, à savoir que les points images de ce quantificateur sont proches des points images d'un quantificateur naturellement parcimonieux, réalisant un compromis entre erreur en quantification et taille du support des points images, et que l'écart en distorsion du quantificateur Lasso k-means est de l'ordre de 1/n^(1/2) en la taille de l'échantillon. Par ailleurs la dépendance de cette distorsion en les différents autres paramètres de ce problème est donnée explicitement. Ces prédictions théoriques sont illustrées par des simulations numériques confirmant globalement les propriétés attendues d'un tel quantificateur parcimonieux, mais soulignant néanmoins quelques inconvénients liés à l'implémentation effective de cette procédure. / The distortion of the quantizer built from a n-sample of a probability distribution over a vector space with the famous k-means algorithm is firstly studied in this thesis report. To be more precise, this report aims to give oracle inequalities on the difference between the distortion of the k-means quantizer and the minimum distortion achievable by a k-point quantizer, where the influence of the natural parameters of the quantization issue should be precisely described. For instance, some natural parameters are the distribution support, the size k of the quantizer set of images, the dimension of the underlying Euclidean space, and the sample size n. After a brief summary of the previous works on this topic, an equivalence between the conditions previously stated for the excess distortion to decrease fast with respect to the sample size and a technical condition is stated, in the continuous density case. Interestingly, this condition looks like a technical condition required in statistical learning to achieve fast rates of convergence. Then, it is proved that the excess distortion achieves a fast convergence rate of 1/n in expectation, provided that this technical condition is satisfied. Next, a so-called margin condition is introduced, which is easier to understand, and it is established that this margin condition implies the technical condition mentioned above. Some examples of distributions satisfying this margin condition are exposed, such as the Gaussian mixtures, which are classical distributions in the clustering framework. Then, provided that this margin condition is satisfied, an oracle inequality on the excess distortion of the k-means quantizer is given. This convergence result shows that the excess distortion decreases with a rate 1/n and depends on natural geometric properties of the probability distribution with respect to the size of the set of images k. Suprisingly the dimension of the underlying Euclidean space seems to play no role in the convergence rate of the distortion. Following the latter point, the results are directly extended to the case where the underlying space is a Hilbert space, which is the adapted framework when dealing with curve quantization. However, high-dimensional quantization often needs in practical a dimension reduction step, before proceeding to a quantization algorithm. This motivates the following study of a variable selection procedure adapted to the quantization issue. To be more precise, a Lasso type procedure adapted to the quantization framework is studied. The Lasso type penalty applies to the set of image points of the quantizer, in order to obtain sparse image points. The outcome of this procedure is called the Lasso k-means quantizer, and some theoretical results on this quantizer are established, under the margin condition introduced above. First it is proved that the image points of such a quantizer are close to the image points of a sparse quantizer, achieving a kind of tradeoff between excess distortion and size of the support of image points. Then an oracle inequality on the excess distortion of the Lasso k-means quantizer is given, providing a convergence rate of 1/n^(1/2) in expectation. Moreover, the dependency of this convergence rate on different other parameters is precisely described. These theoretical predictions are illustrated with numerical experimentations, showing that the Lasso k-means procedure mainly behaves as expected. However, the numerical experimentations also shed light on some drawbacks concerning the practical implementation of such an algorithm.

Le projet Européen « GENIUS » ambitionne de développer les méthodologies génériques pour le diagnostic de systèmes piles à combustible à haute température de type oxyde solide (SOFC). Le travail de cette thèse s’intègre dans ce projet ; il a pour objectif la mise en oeuvre d’un outil de diagnostic en utilisant le stack comme capteur spécial pour détecter et identifierles défaillances dans les sous-systèmes du stack SOFC.Trois algorithmes de diagnostic ont été développés, se basant respectivement sur la méthode de classification k-means, la technique de décomposition du signal en ondelettes ainsi que la modélisation par réseau Bayésien. Le premier algorithme sert au diagnostic ex-situ et est appliqué pour traiter les donnés issues des essais de polarisation. Il permet de déterminer les variables de réponse significatives qui indiquent l’état de santé du stack. L’indice Silhouette a été calculé comme mesure de qualité de classification afin de trouver le nombre optimal de classes dans la base de données.La détection de défaut en temps réel peut se réaliser par le deuxième algorithme. Puisque le stack est employé en tant que capteur, son état de santé doit être vérifié préalablement. La transformée des ondelettes a été utilisée pour décomposer les signaux de tension de la pile SOFC dans le but de chercher les variables caractéristiques permettant d’indiquer l’état desanté de la pile et également assez discriminatives pour différentier les conditions d’opération normales et anormales.Afin d’identifier le défaut du système lorsqu’une condition d’opération anormale s’est détectée, les paramètres opérationnelles réelles du stack doivent être estimés. Un réseau Bayésien a donc été développé pour accomplir ce travail.Enfin, tous les algorithmes ont été validés avec les bases de données expérimentales provenant de systèmes SOFC variés, afin de tester leur généricité. / The EU-project “GENIUS” is targeted at the investigation of generic diagnosis methodologies for different Solid Oxide Fuel Cell (SOFC) systems. The Ph.D study presented in this thesis was integrated into this project; it aims to develop a diagnostic tool for SOFC system fault detection and identification based on validated diagnostic algorithms, through applying theSOFC stack as a sensor.In this context, three algorithms, based on the k-means clustering technique, the wavelet transform and the Bayesian method, respectively, have been developed. The first algorithm serves for ex-situ diagnosis. It works on the classification of the polarization measurements of the stack, aiming to figure out the significant response variables that are able to indicate the state of health of the stack. The parameter “Silhouette” has been used to evaluate the classification solutions in order to determine the optimal number of classes/patterns to retain from the studied database.The second algorithm allows the on-line fault detection. The wavelet transform has been used to decompose the SOFC’s voltage signals for the purpose of finding out the effective feature variables that are discriminative for distinguishing the normal and abnormal operating conditions of the system. Considering the SOFC as a sensor, its reliability must be verifiedbeforehand. Thus, the feature variables are also required to be indicative to the state of health of the stack.When the stack is found being operated improperly, the actual operating parameters should be estimated so as to identify the system fault. To achieve this goal, a Bayesian network has been proposed serving as a meta-model of the stack to accomplish the estimation. At the end, the databases originated from different SOFC systems have been used to validate these three algorithms and assess their generalizability.

Made available in DSpace on 2017-07-21T14:19:24Z (GMT). No. of bitstreams: 1 Lays Veloso.pdf: 1140015 bytes, checksum: c544c69a03612a2909b7011c936788ee (MD5) Previous issue date: 2015-04-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This study aimed to investigate the use of a parallel K-means clustering algorithm,based on parallel MapReduce model, to improve the response time of the data mining. The parallel K-Means was implemented in three phases, performed in each iteration: assignment of samples to groups with nearest centroid by Mappers, in parallel; local grouping of samples assigned to the same group from Mappers using a Combiner and update of the centroids by the Reducer. The performance of the algorithm was evaluated in respect to SpeedUp and ScaleUp. To achieve this, experiments were run in single-node mode and on a Hadoop cluster consisting of six of-the-shelf computers. The data were clustered comprise flux towers measurements from agricultural regions and belong to Ameriflux. The results showed performance gains with increasing number of machines and the best time was obtained using six machines reaching the speedup of 3,25. To support our results, ANOVA analysis was applied from repetitions using 3, 4 and 6 machines in the cluster, respectively. The ANOVA show low variance between the execution times obtained for the same number of machines and a significant difference between means of each number of machines. The ScaleUp analysis show that the application scale well with an equivalent increase in data size and the number of machines, achieving similar performance. With the results as expected, this paper presents a parallel and scalable implementation of the K-Means to run on a Hadoop cluster and improve the response time of clustering to large databases. / Este trabalho teve como objetivo investigar a utilização de um algoritmo de agrupamento K-Means paralelo, com base no modelo paralelo MapReduce, para melhorar o tempo de resposta da mineração de dados. O K-Means paralelo foi implementado em três fases, executadas em cada iteração: atribuição das amostras aos grupos com centróide mais próximo pelos Mappers, em paralelo; agrupamento local das amostras atribuídas ao mesmo grupo pelos Mappers usando um Combiner e atualização dos centróides pelo Reducer. O desempenho do algoritmo foi avaliado quanto ao SpeedUp e ScaleUp. Para isso foram executados experimentos em modo single-node e em um cluster Hadoop formado por seis computadores de hardware comum. Os dados agrupados são medições de torres de fluxo de regiões agrícolas e pertencem a Ameriflux. Os resultados mostraram que com o aumento do número de máquinas houve ganho no desempenho, sendo que o melhor tempo obtido foi usando seis máquinas chegando ao SpeedUp de 3,25. Para apoiar nossos resultados foi construída uma tabela ANOVA a partir de repetições usando 3, 4 e 6 máquinas no cluster, pespectivamente. Os resultados da análise ANOVA mostram que existe pouca variância entre os tempos de execução obtidos com o mesmo número de máquinas e existe uma diferença significativa entre as médias para cada número de máquinas. A partir dos experimentos para analisar o ScaleUp verificou-se que a aplicação escala bem com o aumento equivalente do tamanho dos dados e do número de máquinas no cluster,atingindo um desempenho próximo. Com os resultados conforme esperados, esse trabalho apresenta uma implementação paralela e escalável do K-Means para ser executada em um cluster Hadoop e melhorar o tempo de resposta do agrupamento de grandes bases de dados.

In this master thesis I recapitulated several methods for data clustering. Two well known clustering algorithms, concretely K-means algorithm and Fuzzy C-means (FCM) algorithm, were described in the submitted work. I presented several methods, which could help estimate the optimal number of clusters. Further, I described Kohonen maps and two models of Kohonen's maps with dynamically changing structure, namely Kohonen map with growing grid and the model of growing neural gas. At last I described quite new model of radial basis function neural networks. I presented several learning algorithms for this model of neural networks, RAN, RANKEF, MRAN, EMRAN and GAP. In the end of this work I made some clustering experiments with real data. This data describes the international trade among states of the whole world.

Made available in DSpace on 2017-05-12T14:46:57Z (GMT). No. of bitstreams: 1 Kelyn Schenatto.pdf: 4212903 bytes, checksum: 0ba04350cc25aff5e6acb249938e5375 (MD5) Previous issue date: 2014-02-04 / Despite the benefits offered by the technology of precision agriculture (PA), the necessity of dense sampling grids and use of sophisticated equipment for the soil and plant handling make it financially unfeasible in many cases, especially for small producers. With the aimof making viable the PA, the definition of management zones (MZ) consists in dividing the plotin subregions that have similar physicochemical features, where it is possible to work in the conventional manner (without site-specific input application), differing them from the other sub-regions of the field. Thus we use concepts from PA, but adapting some procedures to the reality of the producer, not requiring the replacement of machinery traditionally used.Therefore, yield is usually correlated with physical and chemical properties through statistical and geostatistical methods, and attributes are selected to generate thematic maps, which are then used to define the MZ. In the generation of thematic maps step, are commonly used traditional interpolation methods (Inverse Distance - ID , inverse of the square distance - ISD, and kriging - KRI), and it is important to assess if the quality of thematic maps generated influences in the MZ drafting process and can not justify the interpolation data using robust methods such as KRI. Thus, the present study aimed to evaluate three interpolation methods (ID , ISD and KRI ) for generation of thematic maps used in the generation of MZ by clustering methods K-Means and Fuzzy C-Meas, in two experimental areas (9.9 ha and 15.5 ha), and been used data from four seasons (three crops of soybeans and one of corn). The KRI interpolation and ID showed similar UM. The agreement between the maps decreased when an increase in the number of classes, but with greater intensity with the Fuzzy C-Means method. Clustering algorithms K-Means and Fuzzy C-Means performed similar division on two UM. The best interpolation method was KRI following the ID, what justifies the choice of a more robust interpolation (KRI) to generate UM / Apesar dos benefícios proporcionados pela tecnologia de agricultura de precisão (AP), a necessidade de grades amostrais densas e uso de equipamentos sofisticados para o manejo do solo e da planta tornam o seu cultivo em muitos casos inviável financeiramente, principalmente para pequenos produtores. Com a finalidade de viabilizar a AP, a definição de unidades de manejo (UM) consiste em dividir o talhão em sub-regiões que possuam características físico-químicas semelhantes, onde se pode trabalhar de forma convencional (sem aplicação localizada de insumos), diferenciando-se das outras sub-regiões do talhão. Dessa forma, utilizam-se conceitos de AP, mas adaptam-se alguns procedimentos para a realidade do produtor, não havendo necessidade da substituição de máquinas tradicionalmente utilizadas. Para isso, são geralmente correlacionados atributos físicos e químicos com a produtividade das culturas e, por meio de métodos estatísticos e geoestatísticos, selecionam-se atributos que darão origem a mapas temáticos posteriormente utilizados para definição das UM. Na etapa de geração dos mapas temáticos, são normalmente utilizados métodos tradicionais de interpolação (inverso da distância ID, inverso da distância ao quadrado IDQ e krigagem KRI) e é importante avaliar se a qualidade dos mapas temáticos gerados influencia no processo de definição das UM, podendo desta forma não se justificar a interpolação de dados a partir do uso de métodos robustos como a KRI. O presente trabalho teve como objetivo a avaliação de três métodos de interpolação (ID, IQD e KRI) para definição dos mapas temáticos utilizados na confecção de UM pelos métodos de agrupamento K-Means e Fuzzy C-Means, em duas áreas experimentais (de 9,9 ha e 15,5 ha), sendo utilizados dados de quatro safras (três safras de soja e uma de milho). Os interpoladores ID e KRI apresentaram UM similares. A concordância entre os mapas diminuiu quando houve aumento do número de classes, mas teve maior intensidade com o método Fuzzy C-Means. Os algoritmos de agrupamento K-Means e Fuzzy C-Means se apresentaram similares na divisão em duas UM. O melhor método de interpolação foi a KRI, seguida do ID, o que justifica a escolha do interpolador mais robusto (KRI) na geração de UM

De nombreux travaux se sont intéressés aux facteurs sociaux et scolaires du décrochage situés au niveau de l’école élémentaire ou du début du collège (e.g., difficultés scolaires liées à une origine sociale défavorisée). En complément, un besoin de recherche existe pour mieux comprendre le décrochage au lycée et le « processus de stress » qui le sous-tend (Dupéré et al., 2015). Les travaux de cette thèse visent à combler ce besoin en analysant les données administratives et auto-rapportées portant sur des lycéens des filières professionnelles et générales ou technologiques suivis pendant trois ans à partir de la classe de 2nde (N > 1900, dont 17% de décrocheurs). Premièrement, nos analyses multiniveaux montrent que, à caractéristiques comparables en termes d’origine sociale et de parcours scolaire en amont du lycée, le processus de stress au début du lycée augmente le risque de décrochage scolaire en diminuant les perceptions de justice scolaire, de contrôle sur la scolarité et de soutien enseignant (i.e., ressources et besoins protecteurs face au stress), ainsi que l’engagement et les résultats scolaires (i.e., facteurs proximaux du stress). Deuxièmement, quel que soit le parcours de vie de l’élève, le fait d’intégrer une spécialité de formation offrant des perspectives d’emploi plus défavorables facilite le décrochage. De même, intégrer une spécialité moins prestigieuse augmente le risque de décrocher, mais uniquement chez les élèves qui perçoivent peu de contrôle ou de justice au lycée. Troisièmement, des analyses de trajectoires scolaires indiquent l’existence de 4 profils de décrocheurs qui se distinguent aussi bien au niveau de leur parcours de vie que de leur processus de stress. La majorité d’entre eux (60%) présentent des profils d’élèves « dans la norme » au cours du lycée et s’avèrent surreprésentés dans les filières plus défavorisées. Globalement, ces résultats suggèrent que le décrochage au lycée n’est pas réductible aux facteurs de risque précoces mis en avant dans la littérature, mais qu’il tient aussi à l’existence de formations peu porteuses en termes d’emploi et au processus de stress qui résulte, pour certains élèves, de la relégation socio-scolaire. Des implications sont tirées concernant la manière de concevoir et de lutter contre le décrochage dans une approche combinant ces dimensions (i.e., l’orientation scolaire et le développement individuel). / A number of studies have delved into the social or school factors of dropping out rooted in the contexts of elementary or middle school (e.g., school difficulties associated with a low socioeconomic background). As a complement, more research is needed to better understand dropping out during high school and its underlying « stress process » (Dupéré et al., 2015). The present thesis responds to this need by analysing administrative and self-reported data from vocational and academic students followed during three years starting at the first year of high school (N > 1900, including 17% dropouts). Firstly, our multilevel analyses show that, regardless of students’ social and school background before high school, the stress process at the beginning of high school increases the odds of dropping out by diminishing perceptions of school justice and control and teacher support (i.e., resources and needs that protect against stress) as well as school engagement and grades (i.e., proximal factors of stress). Secondly, regardless of students’ background, being admitted into a vocational track that offers poorer employment prospects facilitates dropping out. Likewise, entering a less prestigious track contributes to dropout, but only among students who feel little control or justice in the high school context. Thirdly, analyses of school trajectories point to the existence of 4 dropout profiles that can be differentiated according to their life course and stress process. Most dropouts (60%) show “normative” student profiles during high school and are overrepresented in the most unfavourable tracks. Overall, these results suggest that high school dropout cannot be reduced to the early risk factors that are highlighted in the literature, but that it is also due to the existence of tracks that show little promise for future employment and to the stress process that results, for some students, from school and social relegation. Implications are drawn regarding the way dropping out can be conceived of and tackled from an approach that combines these dimensions (i.e., school tracking and individual development).

本研究使用TFIDF文字探勘技術分析樣本公司年度財務報告裡面的重要非量化資訊，與三項量化財務比率比較，欲探討公司年報在不同市場裡文字敘述與財務表現之一致性。研究結果顯示，根據從2003年至2010年上市半導體公司之年度報告，美國公司的年報較會對財務表現做出誇大的文字敘述，本研究亦發現在文字敘述上，市場較不成熟的中國公司所發布之年報較偏向低估他們的財務表現。 / This study presented a way to extract useful information out of unstructured qualitative textual data with the use of the TFIDF text mining technique, which was used to help us explore for consistencies between financial performance in the form of quantitative financial ratios and qualitative narrative disclosures in the annual report between countries with different levels of market development. The results show that, based on listed semiconductor companies' annual reports between 2003 to 2010, companies in the United States have a high tendency to exaggerate and overstate about their performance in the MD&A, while less developed markets such as China turned out to have the lowest tendency to exaggerate and was more likely to understate about its performance in their Director's Report.

Made available in DSpace on 2015-05-08T14:53:37Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 3740949 bytes, checksum: 4b4bb1e725e28d0a9a489835e70b4e60 (MD5) Previous issue date: 2014-02-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Find emergency public services falls into one of the classic optimization problems where points are available for candidates who are chosen, among them, those that optimize the efficiency criteria established, to find a limited number of facilities. The set of candidate sites have great influence on the final solution generated by a model location . In the research, three strategies were used to elect local candidates to position the cars of police : decision of the Security Manager , p-median model and method of clustering k-means. With the support of Geographical Information Systems (GIS ) it was possible to georeference the occurrences of crimes , to visualize the distribution of selected local candidates and identify the presence of hotspots of crime. Aiming to solve the problem of allocating vehicles adopted two approaches : exact and heuristic . Therefore, two hybrid meta - heuristics were implemented - GRASP combined with VND and GRASP with exact model. They obtained same or very approximate solutions of the optimal solution . It was developed a system of spatial decision support based on the solution of the formulation of the problem of locating facilities with restricted coverage and backup coverage. It is a Web tool built with by WebGIS technology / Localizar serviços públicos emergenciais se enquadra em um dos problemas clássicos de otimização onde pontos candidatos são disponibilizados para que sejam escolhidos, dentre eles, aqueles que otimizem o critério de eficiência estabelecido, visando localizar um número limitado de facilidades. O conjunto de locais candidatos tem grande influência sobre a solução final gerada por um modelo de localização. Na pesquisa, foram definidas três estratégias para eleger os locais candidatos ao posicionamento de viaturas policiais: decisão do gestor de segurança, modelo de Pmedianas e método de clusterização k-means. Com apoio de Sistemas de Informação Geográfica (SIG) foi possível georreferenciar as ocorrências de crimes, visualizar a distribuição dos locais candidatos selecionados e identificar a presença de hotspots de crimes. Visando resolver o problema de alocação de viaturas adotou-se duas abordagens: exata e heurística. Para tanto, duas meta-heurísticas híbridas foram implementadas - GRASP combinado com VND e GRASP com modelo exato, as quais obtiveram soluções iguais ou muito aproximadas da solução ótima. Foi desenvolvido um sistema de apoio a decisão espacial baseado na solução da formulação do problema de localização de facilidades com restrições de cobertura e cobertura backup. Trata-se de uma ferramenta WEB construída com base os padrões usados pela tecnologia WebGIS

Made available in DSpace on 2017-07-10T19:23:44Z (GMT). No. of bitstreams: 1 Kelyn Schenatto.pdf: 4212903 bytes, checksum: 0ba04350cc25aff5e6acb249938e5375 (MD5) Previous issue date: 2014-02-04 / Despite the benefits offered by the technology of precision agriculture (PA), the necessity of dense sampling grids and use of sophisticated equipment for the soil and plant handling make it financially unfeasible in many cases, especially for small producers. With the aimof making viable the PA, the definition of management zones (MZ) consists in dividing the plotin subregions that have similar physicochemical features, where it is possible to work in the conventional manner (without site-specific input application), differing them from the other sub-regions of the field. Thus we use concepts from PA, but adapting some procedures to the reality of the producer, not requiring the replacement of machinery traditionally used.Therefore, yield is usually correlated with physical and chemical properties through statistical and geostatistical methods, and attributes are selected to generate thematic maps, which are then used to define the MZ. In the generation of thematic maps step, are commonly used traditional interpolation methods (Inverse Distance - ID , inverse of the square distance - ISD, and kriging - KRI), and it is important to assess if the quality of thematic maps generated influences in the MZ drafting process and can not justify the interpolation data using robust methods such as KRI. Thus, the present study aimed to evaluate three interpolation methods (ID , ISD and KRI ) for generation of thematic maps used in the generation of MZ by clustering methods K-Means and Fuzzy C-Meas, in two experimental areas (9.9 ha and 15.5 ha), and been used data from four seasons (three crops of soybeans and one of corn). The KRI interpolation and ID showed similar UM. The agreement between the maps decreased when an increase in the number of classes, but with greater intensity with the Fuzzy C-Means method. Clustering algorithms K-Means and Fuzzy C-Means performed similar division on two UM. The best interpolation method was KRI following the ID, what justifies the choice of a more robust interpolation (KRI) to generate UM / Apesar dos benefícios proporcionados pela tecnologia de agricultura de precisão (AP), a necessidade de grades amostrais densas e uso de equipamentos sofisticados para o manejo do solo e da planta tornam o seu cultivo em muitos casos inviável financeiramente, principalmente para pequenos produtores. Com a finalidade de viabilizar a AP, a definição de unidades de manejo (UM) consiste em dividir o talhão em sub-regiões que possuam características físico-químicas semelhantes, onde se pode trabalhar de forma convencional (sem aplicação localizada de insumos), diferenciando-se das outras sub-regiões do talhão. Dessa forma, utilizam-se conceitos de AP, mas adaptam-se alguns procedimentos para a realidade do produtor, não havendo necessidade da substituição de máquinas tradicionalmente utilizadas. Para isso, são geralmente correlacionados atributos físicos e químicos com a produtividade das culturas e, por meio de métodos estatísticos e geoestatísticos, selecionam-se atributos que darão origem a mapas temáticos posteriormente utilizados para definição das UM. Na etapa de geração dos mapas temáticos, são normalmente utilizados métodos tradicionais de interpolação (inverso da distância ID, inverso da distância ao quadrado IDQ e krigagem KRI) e é importante avaliar se a qualidade dos mapas temáticos gerados influencia no processo de definição das UM, podendo desta forma não se justificar a interpolação de dados a partir do uso de métodos robustos como a KRI. O presente trabalho teve como objetivo a avaliação de três métodos de interpolação (ID, IQD e KRI) para definição dos mapas temáticos utilizados na confecção de UM pelos métodos de agrupamento K-Means e Fuzzy C-Means, em duas áreas experimentais (de 9,9 ha e 15,5 ha), sendo utilizados dados de quatro safras (três safras de soja e uma de milho). Os interpoladores ID e KRI apresentaram UM similares. A concordância entre os mapas diminuiu quando houve aumento do número de classes, mas teve maior intensidade com o método Fuzzy C-Means. Os algoritmos de agrupamento K-Means e Fuzzy C-Means se apresentaram similares na divisão em duas UM. O melhor método de interpolação foi a KRI, seguida do ID, o que justifica a escolha do interpolador mais robusto (KRI) na geração de UM