Julien Jacques

Sensitivity analysis in presence of model uncertainty and correlated inputs

The first motivation of this work is to take into account model uncertainty in sensitivity analysis (SA). We present with some examples, a methodology to treat uncertainty due to a mutation of the studied model. Development of this methodology has highlighted an important problem, frequently encountered in SA: how to interpret sensitivity indices when random inputs are non-independent? This paper suggests a strategy for the problem of SA of models with non-independent random inputs. We propose a new application of the multidimensional generalization of classical sensitivity indices, resulting from group sensitivities (sensitivity of the output of the model to a group of inputs), and describe an estimation method based on Monte-Carlo simulations. Practical and theoretical applications illustrate the interest of this method.

Functional data clustering: a survey

Clustering techniques for functional data are reviewed. Four groups of clustering algorithms for functional data are proposed. The first group consists of methods working directly on the evaluation points of the curves. The second groups is defined by filtering methods which first approximate the curves into a finite basis of functions and second perform clustering using the basis expansion coefficients. The third groups is composed of methods which perform simultaneously dimensionality reduction of the curves and clustering, leading to functional representation of data depending on clusters. The last group consists of distance-based methods using clustering algorithms based on specific distances for functional data. A software review as well as an illustration of the application of these algorithms on real data are presented.

Model-based clustering for multivariate functional data

The first model-based clustering algorithm for multivariate functional data is proposed. After introducing multivariate functional principal components analysis (MFPCA), a parametric mixture model, based on the assumption of normality of the principal component scores, is defined and estimated by an EM-like algorithm. The main advantage of the proposed model is its ability to take into account the dependence among curves. Results on simulated and real datasets show the efficiency of the proposed method.

Model-based clustering of time series in group-specific functional subspaces

This work develops a general procedure for clustering functional data which adapts the clustering method high dimensional data clustering (HDDC), originally proposed in the multivariate context. The resulting clustering method, called funHDDC, is based on a functional latent mixture model which fits the functional data in group-specific functional subspaces. By constraining model parameters within and between groups, a family of parsimonious models is exhibited which allow to fit onto various situations. An estimation procedure based on the EM algorithm is proposed for determining both the model parameters and the group-specific functional subspaces. Experiments on real-world datasets show that the proposed approach performs better or similarly than classical two-step clustering methods while providing useful interpretations of the groups and avoiding the uneasy choice of the discretization technique. In particular, funHDDC appears to always outperform HDDC applied on spline coefficients.

Funclust: A curves clustering method using functional random variables density approximation

A new method for clustering functional data is proposed under the name Funclust. This method relies on the approximation of the notion of probability density for functional random variables, which generally does not exist. Using the Karhunen-Loeve expansion of a stochastic process, this approximation leads to define an approximation for the density of functional variables. Based on this density approximation, a parametric mixture model is proposed. The parameter estimation is carried out by an EM-like algorithm, and the maximum a posteriori rule provides the clusters. The efficiency of Funclust is illustrated on several real datasets, as well as for the characterization of the Mars surface.

A generative model for rank data based on insertion sort algorithm

An original and meaningful probabilistic generative model for full rank data modelling is proposed. Rank data arise from a sorting mechanism which is generally unobservable for statisticians. Assuming that this process relies on paired comparisons, the insertion sort algorithm is known as being the best candidate in order to minimize the number of potential paired misclassifications for a moderate number of objects to be ordered. Combining this optimality argument with a Bernoulli event during a paired comparison step, a model that possesses desirable theoretical properties, among which are unimodality, symmetry and identifiability is obtained. Maximum likelihood estimation can also be performed easily through an EM or a SEM-Gibbs algorithm (depending on the number of objects to be ordered) by involving the latent initial presentation order of the objects. Finally, the practical relevance of the proposal is illustrated through its adequacy with several real data sets and a comparison with a standard rank data model.

Gaussian mixture models for the classification of high-dimensional vibrational spectroscopy data

In this work, a family of generative Gaussian models designed for the supervised classification of high‐dimensional data is presented as well as the associated classification method called High‐Dimensional Discriminant Analysis (HDDA). The features of these Gaussian models are as follows: i) the representation of the input density model is smooth; ii) the data of each class are modeled in a specific subspace of low dimensionality; iii) each class may have its own covariance structure; iv) model regularization is coupled to the classification criterion to avoid data over‐fitting. To illustrate the abilities of the method, HDDA is applied on complex high‐dimensional multi‐class classification problems in mid‐infrared and near‐infrared spectroscopy and compared to state‐of‐the‐art methods. Copyright

The discriminative functional mixture model for a comparative analysis of bike sharing systems

Bike sharing systems (BSSs) have become a means of sustainable intermodal transport and are now proposed in many cities worldwide. Most BSSs also provide open access to their data, particularly to real-time status reports on their bike stations. The analysis of the mass of data generated by such systems is of particular interest to BSS providers to update system structures and policies. This work was motivated by interest in analyzing and comparing several European BSSs to identify common operating patterns in BSSs and to propose practical solutions to avoid potential issues. Our approach relies on the identification of common patterns between and within systems. To this end, a model-based clustering method, called FunFEM, for time series (or more generally functional data) is developed. It is based on a functional mixture model that allows the clustering of the data in a discriminative functional subspace. This model presents the advantage in this context to be parsimonious and to allow the visual-ization of the clustered systems. Numerical experiments confirm the good behavior of FunFEM, particularly compared to state-of-the-art methods. The application of FunFEM to BSS data from JCDecaux and the Transport for London Initiative allows us to identify 10 general patterns, including pathological ones, and to propose practical improvement strategies based on the system comparison. The visual-ization of the clustered data within the discriminative subspace turns out to be particularly informative regarding the system efficiency. The proposed methodology is implemented in a package for the R software , named funFEM, which is available on the CRAN. The package also provides a subset of the data analyzed in this work. 1. Introduction. This work was motivated by the will to analyze and compare bike sharing systems (BSSs) to identify their common strengths and weaknesses. This type of study is possible because most BSS operators, in dozens of cities worldwide, provide open access to real-time status reports on their bike stations (e.g., the number of available bikes, the number of free bike stands). The implementation of bike sharing systems is one of the urban mobility services proposed in cities across the world as an additional means

Adaptive linear models for regression: Improving prediction when population has changed

The general setting of regression analysis is to identify a relationship between a response variable Y and one or several explanatory variables X by using a learning sample. In a prediction framework, the main assumption for predicting Y on a new sample of observations is that the regression model Y=f(X)+@e is still valid. Unfortunately, this assumption is not always true in practice and the model could have changed. We therefore propose to adapt the original regression model to the new sample by estimating a transformation between the original regression function f(X) and the new one f^*(X). The main interest of the proposed adaptive models is to allow the build of a regression model for the new population with only a small number of observations using the knowledge on the reference population. The efficiency of this strategy is illustrated by applications on artificial and real datasets, including the modeling of the housing market in different U.S. cities. A package for the R software dedicated to the adaptive linear models is available on the authors web page.

Protein similarity search with subset seeds on a dedicated reconfigurable hardware

With a sharp increase of available DNA and protein sequence data, new precise and fast similarity search methods are needed for large-scale genome and proteome comparisons. Modern seed-based techniques of similarity search (spaced seeds, multiple seeds, subset seeds) provide a better sensitivity/specificity ratio. We present an implementation of such a seed-based technique on a parallel specialized hardware embedding reconfigurable architecture (FPGA), where the FPGA is tightly connected to large capacity Flash memories. This parallel system allows large databases to be fully indexed and rapidly accessed. Compared to traditional approaches presented by the Blastp software, we obtain both a significant speed-up and better results. To the best of our knowledge, this is the first attempt to exploit efficient seed-based algorithms for parallelizing the sequence similarity search.