 # 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 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. There is a common denominator: a group of data objects. Related:  Machine LearningAI

Multidimensional scaling Types Classical multidimensional scaling Also known as Principal Coordinates Analysis, Torgerson Scaling or Torgerson–Gower scaling. Takes an input matrix giving dissimilarities between pairs of items and outputs a coordinate matrix whose configuration minimizes a loss function called strain. Metric multidimensional scaling A superset of classical MDS that generalizes the optimization procedure to a variety of loss functions and input matrices of known distances with weights and so on. Non-metric multidimensional scaling In contrast to metric MDS, non-metric MDS finds both a non-parametric monotonic relationship between the dissimilarities in the item-item matrix and the Euclidean distances between items, and the location of each item in the low-dimensional space. Louis Guttman's smallest space analysis (SSA) is an example of a non-metric MDS procedure. Generalized multidimensional scaling Details The data to be analyzed is a collection of The goal of MDS is, given Δ, to find

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 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 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 See also

Statistical classification In machine learning and statistics, classification is the problem of identifying to which of a set of categories (sub-populations) a new observation belongs, on the basis of a training set of data containing observations (or instances) whose category membership is known. An example would be assigning a given email into "spam" or "non-spam" classes or assigning a diagnosis to a given patient as described by observed characteristics of the patient (gender, blood pressure, presence or absence of certain symptoms, etc.). In the terminology of machine learning, classification is considered an instance of supervised learning, i.e. learning where a training set of correctly identified observations is available. The corresponding unsupervised procedure is known as clustering, and involves grouping data into categories based on some measure of inherent similarity or distance. Terminology across fields is quite varied. Relation to other problems Frequentist procedures Algorithms

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¶

Correspondence analysis Correspondence analysis (CA) is a multivariate statistical technique proposed by Hirschfeld and later developed by Jean-Paul Benzécri. It is conceptually similar to principal component analysis, but applies to categorical rather than continuous data. In a similar manner to principal component analysis, it provides a means of displaying or summarising a set of data in two-dimensional graphical form. All data should be nonnegative and on the same scale for CA to be applicable, and the method treats rows and columns equivalently. It is traditionally applied to contingency tables — CA decomposes the chi-squared statistic associated with this table into orthogonal factors. Because CA is a descriptive technique, it can be applied to tables whether or not the statistic is appropriate. Details Preprocessing From table C, compute a sets of weights for the columns and the rows (sometimes called masses), where row weights are and column weights are where and are

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 The convergence analysis of the Dempster-Laird-Rubin paper was flawed and a correct convergence analysis was published by C.

Machine learning Machine learning is a subfield of computer science that evolved from the study of pattern recognition and computational learning theory in artificial intelligence. Machine learning explores the construction and study of algorithms that can learn from and make predictions on data. Such algorithms operate by building a model from example inputs in order to make data-driven predictions or decisions,:2 rather than following strictly static program instructions. Machine learning is closely related to and often overlaps with computational statistics; a discipline that also specializes in prediction-making. It has strong ties to mathematical optimization, which deliver methods, theory and application domains to the field. When employed in industrial contexts, machine learning methods may be referred to as predictive analytics or predictive modelling. Overview Tom M. Types of problems and tasks History and relationships to other fields Relation to statistics

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 .

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