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Cluster analysis

Cluster analysis
The result of a cluster analysis shown as the coloring of the squares into three clusters. Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters). It is a main task of exploratory data mining, and a common technique for statistical data analysis, used in many fields, including machine learning, pattern recognition, image analysis, information retrieval, and bioinformatics. Besides the term clustering, there are a number of terms with similar meanings, including automatic classification, numerical taxonomy, botryology (from Greek βότρυς "grape") and typological analysis. Definition[edit] According to Vladimir Estivill-Castro, the notion of a "cluster" cannot be precisely defined, which is one of the reasons why there are so many clustering algorithms.[4] There is a common denominator: a group of data objects.

Partitionnement de données Un article de Wikipédia, l'encyclopédie libre. Exemple de clustering hiérarchique Pour obtenir un bon partitionnement, il convient d'à la fois : minimiser l'inertie intra-classe pour obtenir des grappes (cluster en anglais) les plus homogènes possibles.maximiser l'inertie inter-classe afin d'obtenir des sous-ensembles bien différenciés. Vocabulaire[modifier | modifier le code] La communauté scientifique francophone utilise différents termes pour désigner cette technique. Intérêt et applications[modifier | modifier le code] Le partitionnement de données est une méthode de classification non supervisée (différente de la classification supervisée où les données d'apprentissage sont déjà étiquetées), et donc parfois dénommée comme telle. Applications : on en distingue généralement trois sortes[1] Algorithmes[modifier | modifier le code] Il existe de multiples méthodes de partitionnement des données, parmi lesquelles : Logiciels associés[modifier | modifier le code] Anil K.

Fuzzy clustering Fuzzy clustering is a class of algorithms for cluster analysis in which the allocation of data points to clusters is not "hard" (all-or-nothing) but "fuzzy" in the same sense as fuzzy logic. Explanation of clustering[edit] Data clustering is the process of dividing data elements into classes or clusters so that items in the same class are as similar as possible, and items in different classes are as dissimilar as possible. In hard clustering, data is divided into distinct clusters, where each data element belongs to exactly one cluster. One of the most widely used fuzzy clustering algorithms is the Fuzzy C-Means (FCM) Algorithm (Bezdek 1981). into a collection of c fuzzy clusters with respect to some given criterion. and a partition matrix , where each element wij tells the degree to which element xi belongs to cluster cj . which differs from the k-means objective function by the addition of the membership values uij and the fuzzifier m. Fuzzy c-means clustering[edit] See also[edit]

Welcome — Theano 0.7rc1 documentation Theano is a Python library that allows you to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. Theano features: tight integration with NumPy – Use numpy.ndarray in Theano-compiled functions.transparent use of a GPU – Perform data-intensive computations much faster than on a CPU.efficient symbolic differentiation – Theano does your derivatives for functions with one or many inputs.speed and stability optimizations – Get the right answer for log(1+x) even when x is really tiny.dynamic C code generation – Evaluate expressions faster.extensive unit-testing and self-verification – Detect and diagnose many types of errors. Theano has been powering large-scale computationally intensive scientific investigations since 2007. 2017/11/15: Release of Theano 1.0.0. You can watch a quick (20 minute) introduction to Theano given as a talk at SciPy 2010 via streaming (or downloaded) video: git clone How to Seek Help¶

Algoritmo de agrupamiento Generalmente, los vectores de un mismo grupo (o clústers) comparten propiedades comunes. El conocimiento de los grupos puede permitir una descripción sintética de un conjunto de datos multidimensional complejo. De ahí su uso en minería de datos. Esta descripción sintética se consigue sustituyendo la descripción de todos los elementos de un grupo por la de un representante característico del mismo. En algunos contextos, como el de la minería de datos, se lo considera una técnica de aprendizaje no supervisado puesto que busca encontrar relaciones entre variables descriptivas pero no la que guardan con respecto a una variable objetivo. Aplicaciones[editar] Las técnicas de agrupamiento encuentran aplicación en diversos ámbitos. Algoritmos[editar] Existen dos grandes técnicas para el agrupamiento de casos: Existen diversas implementaciones de algoritmos concretos. Referencias[editar] Volver arriba ↑ Rousseeuw, P.J.; Kaufman, L. (1990). Enlaces externos[editar]

Expectation–maximization algorithm In statistics, an expectation–maximization (EM) algorithm is an iterative method for finding maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter-estimates are then used to determine the distribution of the latent variables in the next E step. EM clustering of Old Faithful eruption data. The random initial model (which due to the different scales of the axes appears to be two very flat and wide spheres) is fit to the observed data. History[edit] The convergence analysis of the Dempster-Laird-Rubin paper was flawed and a correct convergence analysis was published by C.

Very Brief Introduction to Machine Learning for AI — Notes de cours IFT6266 Hiver 2010 The topics summarized here are covered in these slides. Intelligence The notion of intelligence can be defined in many ways. Here we define it as the ability to take the right decisions, according to some criterion (e.g. survival and reproduction, for most animals). Artificial Intelligence Computers already possess some intelligence thanks to all the programs that humans have crafted and which allow them to “do things” that we consider useful (and that is basically what we mean for a computer to take the right decisions). Formalization of Learning First, let us formalize the most common mathematical framework for learning. with the being examples sampled from an unknown process . which takes as argument a decision function and an example , and returns a real-valued scalar. under the unknown generating process Supervised Learning In supervised learning, each examples is an (input,target) pair: and takes an as argument. Local Generalization is close to input example , then the corresponding outputs .

Knowledge Management, management des connaissances - L'Analyse des Réseaux Sociaux Si nous admettons que l’individu agit fortement sur son groupe social et que le groupe crée une contrainte qui pèse en retour sur les choix, les orientations, les comportements, les opinions des individus, alors il devient important de mieux analyser ces réseaux humains : leur structure, leurs normes, et la position de chaque individu. C’est l’objectif d’une science relativement récente : l’Analyse des Réseaux Sociaux (ARS ou SNA pour Social Network Analysis en anglais). Pour l’introduire, prenons un exemple simple : Dans le schéma ci-dessus, 11 personnes ont été positionnées ; une flèche relie deux acteurs à chaque fois qu’ils ont déclaré se connaître (ou travailler ensemble). A première vue, on pourrait penser que Cécile, qui est celle qui connaît le plus de monde (6 liens) est la plus influente. - un leadership implicite du groupe, des « leaders d’opinion », - des affinités/inimitiés entre personnes, les flux les plus actifs, - des communautés informelles, réseaux d’influence,

File:EM-Gaussian-data.svg From Wikimedia Commons, the free media repository Summary[edit] Licensing[edit] File history Click on a date/time to view the file as it appeared at that time. You cannot overwrite this file. File usage on other wikis The following other wikis use this file: Introduction to Deep Learning Algorithms — Notes de cours IFT6266 Hiver 2010 See the following article for a recent survey of deep learning: Yoshua Bengio, Learning Deep Architectures for AI, Foundations and Trends in Machine Learning, 2(1), 2009 Depth The computations involved in producing an output from an input can be represented by a flow graph: a flow graph is a graph representing a computation, in which each node represents an elementary computation and a value (the result of the computation, applied to the values at the children of that node). The flow graph for the expression could be represented by a graph with two input nodes and , one node for the division taking as input (i.e. as children), one node for the square (taking only as input), one node for the addition (whose value would be and taking as input the nodes , and finally one output node computing the sinus, and with a single input coming from the addition node. A particular property of such flow graphs is depth: the length of the longest path from an input to an output. Insufficient depth can hurt

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