arXiv subjects

Marie Chavent

Publications and source records attributed to Marie Chavent.

7 recordsLinked to original sources

arXiv2024

mDAE : modified Denoising AutoEncoder for missing data imputation

This paper introduces a methodology based on Denoising AutoEncoder (DAE) for missing data imputation. The proposed methodology, called mDAE hereafter, results from a modification of the loss function and a straightforward procedure for choosing the hyper-parameters. An ablation study shows on several UCI Machine Learning Repository datasets, the benefit of using this modified loss function and an overcomplete structure, in terms of Root Mean Squared Error (RMSE) of reconstruction. This numerical study is completed by comparing the mDAE methodology with eight other methods (four standard and four more recent). A criterion called Mean Distance to Best (MDB) is proposed to measure how a method performs globally well on all datasets. This criterion is defined as the mean (over the datasets) of the distances between the RMSE of the considered method and the RMSE of the best method. According to this criterion, the mDAE methodology was consistently ranked among the top methods (along with SoftImput and missForest), while the four more recent methods were systematically ranked last. The Python code of the numerical study will be available on GitHub so that results can be reproduced or generalized with other datasets and methods.

cs.LG↗

arXiv2024

From explained variance of correlated components to PCA without orthogonality constraints

Block Principal Component Analysis (Block PCA) of a data matrix A, where loadings Z are determined by maximization of AZ 2 over unit norm orthogonal loadings, is difficult to use for the design of sparse PCA by 1 regularization, due to the difficulty of taking care of both the orthogonality constraint on loadings and the non differentiable 1 penalty. Our objective in this paper is to relax the orthogonality constraint on loadings by introducing new objective functions expvar(Y) which measure the part of the variance of the data matrix A explained by correlated components Y = AZ. So we propose first a comprehensive study of mathematical and numerical properties of expvar(Y) for two existing definitions Zou et al. [2006], Shen and Huang [2008] and four new definitions. Then we show that only two of these explained variance are fit to use as objective function in block PCA formulations for A rid of orthogonality constraints.

stat.ML↗

arXiv2022

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 to this type of data standard multivariate analysis methods which allow description, exploration and visualization of the 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 proposes a unified mathematical presentation of the different methods with common notations, as well as providing a summarised presentation of the three algorithms, with details to help the user understand graphical and numerical outputs of the corresponding R functions. This then allows the user to easily provide relevant interpretations of the results obtained. 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.

stat.CO↗

arXiv2021

Optimal Projected Variance Group-Sparse Block PCA

We address the problem of defining a group sparse formulation for Principal Components Analysis (PCA) - or its equivalent formulations as Low Rank approximation or Dictionary Learning problems - which achieves a compromise between maximizing the variance explained by the components and promoting sparsity of the loadings. So we propose first a new definition of the variance explained by non necessarily orthogonal components, which is optimal in some aspect and compatible with the principal components situation. Then we use a specific regularization of this variance by the group-$\ell_{1}$ norm to define a Group Sparse Maximum Variance (GSMV) formulation of PCA. The GSMV formulation achieves our objective by construction, and has the nice property that the inner non smooth optimization problem can be solved analytically, thus reducing GSMV to the maximization of a smooth and convex function under unit norm and orthogonality constraints, which generalizes Journee et al. (2010) to group sparsity. Numerical comparison with deflation on synthetic data shows that GSMV produces steadily slightly better and more robust results for the retrieval of hidden sparse structures, and is about three times faster on these examples. Application to real data shows the interest of group sparsity for variables selection in PCA of mixed data (categorical/numerical) .

stat.ML↗

arXiv2018

Combining clustering of variables and feature selection using random forests

Standard approaches to tackle high-dimensional supervised classification problem often include variable selection and dimension reduction procedures. The novel methodology proposed in this paper combines clustering of variables and feature selection. More precisely, hierarchical clustering of variables procedure allows to build groups of correlated variables in order to reduce the redundancy of information and summarizes each group by a synthetic numerical variable. Originality is that the groups of variables (and the number of groups) are unknown a priori. Moreover the clustering approach used can deal with both numerical and categorical variables (i.e. mixed dataset). Among all the possible partitions resulting from dendrogram cuts, the most relevant synthetic variables (i.e. groups of variables) are selected with a variable selection procedure using random forests. Numerical performances of the proposed approach are compared with direct applications of random forests and variable selection using random forests on the original p variables. Improvements obtained with the proposed methodology are illustrated on two simulated mixed datasets (cases n>p and n<p, where n is the sample size) and on a real proteomic dataset. Via the selection of groups of variables (based on the synthetic variables), interpretability of the results becomes easier.

math.ST↗

arXiv2017

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 $α\in [0,1]$. 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 $α$ 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.

stat.CO↗

arXiv2008

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.

stat.CO↗