ClustGeo: an R package for hierarchical clustering with spatial constraints

In this paper, we propose a Ward-like hierarchical clustering algorithm including spatial/geographical constraints. Two dissimilarity matrices $D_0$ and $D_1$ are inputted, along with a mixing parameter $\alpha \in [0,1]$. The dissimilarities can be non-Euclidean and the weights of the observations can be non-uniform. The first matrix gives the dissimilarities in the "feature space" and the second matrix gives the dissimilarities in the "constraint space". The criterion minimized at each stage is a convex combination of the homogeneity criterion calculated with $D_0$ and the homogeneity criterion calculated with $D_1$. The idea is then to determine a value of $\alpha$ which increases the spatial contiguity without deteriorating too much the quality of the solution based on the variables of interest i.e. those of the feature space. This procedure is illustrated on a real dataset using the R package ClustGeo

Image Segmentation with Multidimensional Refinement Indicators

We transpose an optimal control technique to the image segmentation problem. The idea is to consider image segmentation as a parameter estimation problem. The parameter to estimate is the color of the pixels of the image. We use the adaptive parameterization technique which builds iteratively an optimal representation of the parameter into uniform regions that form a partition of the domain, hence corresponding to a segmentation of the image. We minimize an error function during the iterations, and the partition of the image into regions is optimally driven by the gradient of this error. The resulting segmentation algorithm inherits desirable properties from its optimal control origin: soundness, robustness, and flexibility

Multivariate Analysis of Mixed Data: The R Package PCAmixdata

Mixed data arise when observations are described by a mixture of numerical and categorical variables. The R package PCAmixdata extends standard multivariate analysis methods to incorporate this type of data. The key techniques/methods included in the package are principal component analysis for mixed data (PCAmix), varimax-like orthogonal rotation for PCAmix, and multiple factor analysis for mixed multi-table data. This paper gives a synthetic presentation of the three algorithms with details to help the user understand graphical and numerical outputs of the corresponding R functions. The three main methods are illustrated on a real dataset composed of four data tables characterizing living conditions in different municipalities in the Gironde region of southwest France

A Fully Equivalent Global Pressure Formulation for Three-Phase Compressible Flow

We introduce a new global pressure formulation for immiscible three-phase compressible flows in porous media which is fully equivalent to the original equations, unlike the one introduced in \cite{CJ86}. In this formulation, the total volumetric flow of the three fluids and the global pressure follow a classical Darcy law, which simplifies the resolution of the pressure equation. However, this global pressure formulation exists only for Total Differential (TD) three-phase data, which depend only on two functions of saturations and global pressure: the global capillary pressure and the global mobility. Hence we introduce a class of interpolation which constructs such TD-three-phase data from any set of three two-phase data (for each pair of fluids) which satisfy a TD-compatibility condition

The output least squares identifiability of the diffusion coefficient from an H1H^1-observation in a 2-D elliptic equation

Output least squares stability for the diffusion coefficient in an elliptic equation in dimension two is analyzed. This guarantees Lipschitz stability of the solution of the least squares formulation with respect to perturbations in the data independently of their attainability. The analysis shows the influence of the flow direction on the parameter to be estimated. A scale analysis for multi-scale resolution of the unknown parameter is provided

On central tendency and dispersion measures for intervals and hypercubes

The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for interval-valued datasets. We propose a geometrical approach in the determination of summary statistics (central tendency and dispersion measures) for interval-valued variables

Approche bloc en ACP group-sparse: le package sparsePCA

International audienc

A semiparametric approach for a multivariate sample selection model

International audienceMost of the common estimation methods for sample selection models rely heavily on parametric and normality assumptions. We consider in this paper a multivariate semiparametric sample selection model and develop a geometric approach to the estimation of the slope vectors in the outcome equation and in the selection equation. Contrary to most existing methods, we deal symmetrically with both slope vectors. Moreover, the estimation method is link-free and distributionfree. It works in two main steps: a multivariate sliced inverse regression step, and a canonical analysis step. We establish pn-consistency and asymptotic normality of the estimates. We describe how to estimate the observation and selection link functions. The theory is illustrated with a simulation study

Classification

National audienceLa classification a pour objet de regrouper des données en classes possédant des caractéristiques similaires. La classification peut être supervisée lorsque l'on dispose d'un ensemble d'apprentissage labellisé, semi-supervisée ou non supervisée. Elle apparaît dans de nombreuses applications telles que la fouille de texte, la reconnaissance vocale ou l'analyse de données génomiques. L'objectif de cette session est d'offrir un panorama des approches statistiques pour la classification de données (modèles de mélange, SVM, processus de Dirichlet, etc.) et d'en présenter diverses applications