Un problème de confinement pour une coque membranaire linéairement élastique de type elliptique

We identify, and rigorously justify by an asymptotic analysis, the variational inequalities of the two-dimensional problem satisfied by the displacement field of a linearly elastic membrane shell of elliptic type subjected to a confinement condition inside a half-space. This type of condition substantially differs from the Signorini condition usually imposed on the “lower face” of the shell.     

Factor probabilistic distance clustering (FPDC): a new clustering method

Factor clustering methods have been developed in recent years thanks to improvements in computational power. These methods perform a linear transformation of data and a clustering of the transformed data, optimizing a common criterion. Probabilistic distance (PD)-clustering is an iterative, distribution free, probabilistic clustering method. Factor PD-clustering (FPDC) is based on PD-clustering and involves a linear transformation of the original variables into a reduced number of orthogonal ones using a common criterion with PD-clustering. This paper demonstrates that Tucker3 decomposition can be used to accomplish this transformation. Factor PD-clustering alternatingly exploits Tucker3 decomposition and PD-clustering on transformed data until convergence is achieved. This method can significantly improve the PD-clustering algorithm performance; large data sets can thus be partitioned into clusters with increasing stability and robustness of the results. Real and simulated data sets are used to compare FPDC with its main competitors, where it performs equally well when clusters are elliptically shaped but outperforms its competitors with non-Gaussian shaped clusters or noisy data.     

Composite Likelihood Inference in a Discrete Latent Variable Model for Two-Way “Clustering-by-Segmentation” Problems

We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g., exchangeable observational units or features) and contiguous groups, or segments, along the other (e.g., consecutively ordered times or locations). The model relies on a hidden Markov structure but, given its complexity, cannot be estimated by full maximum likelihood. Therefore, we introduce a composite likelihood methodology based on considering different subsets of the data. The proposed approach is illustrated by simulation, and with an application to genomic data.