15 accepted papers
Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection. Sparse PCA algorithms are usually expressed as a trade-off be…
This work deals with elliptical Wishart distributions on the set of symmetric positive definite matrices. It contains two major contributions. First, the information geometry associated with elliptical Wishart distributions is derived. Second, this geometry is leveraged to propose Riemannian-optimiz…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian mixture model (GMM). Numerical instability and convergence pr…
The multivariate power exponential (MEP) distribution can model a broad range of signals. In noisy scenarios, the robust estimation of the MEP parameters has been traditionally addressed by a fixed-point approach associated with a nonconvex optimization problem. Establishing convergence properties f…
Linear and Quadratic Discriminant Analysis are well-known classical methods but can heavily suffer from non-Gaussian distributions and/or contaminated datasets, mainly because of the underlying Gaussian assumption that is not robust. To fill this gap, this paper presents a new robust discriminant an…
A popular regularized (shrinkage) covariance estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward its grand mean. In this paper, a more general approach is considered in which the SCM is replaced by an M-est…
This paper aims at providing an original Riemannian geometry to derive robust covariance matrix estimators in spiked models (i.e. when the covariance matrix has a low-rank plus identity structure). The considered geometry is the one induced by the product of the Stiefel manifold and the manifold of…
This paper introduces an improved Low Rank Adaptive Normalized Matched Filter (LR-ANMF) detector in a high dimensional (HD) context where the observation dimension is large and of the same order of magnitude than the sample size. To that end, the statistical analysis of the LR-ANMF, in a context whe…
In this paper, we propose a new regularized (penalized) covariance matrix estimator which encourages grouping of the eigenvalues by penalizing large differences (gaps) between successive eigenvalues. This is referred to as fusing eigenvalues (eFusion). The proposed penalty function utilizes Tukey's…
This paper presents a new algorithm to estimate the number of sources embedded in a correlated Complex Elliptically Distributed (CES) noise in the context of large dimensional regime. The proposed method is a two-steps ones: first the data covariance matrix is estimated with a robust and consistent…
The paper addresses the problem of approximating the detector distribution used in target detection embedded in a disturbance composed of a low rank Gaussian noise and a white Gaussian noise. In this context, it is interesting to use an adaptive version of the Low Rank Normalized Matched Filter (LR-…
This paper presents two approaches to derive an asymptotic distribution of the robust Adaptive Normalized Matched Filter (ANMF). More precisely, the ANMF has originally been derived under the assumption of Gaussian distributed noise where the variance is different between the observation under test…
This paper introduces a Bayesian non parametric (BNP) model associated with a Markov random field (MRF) for detecting changes between remote sensing images acquired by homogeneous or heterogeneous sensors. The proposed model is built for an analysis window which takes advantage of the spatial inform…
This paper lies in the lineage of recent works studying the asymptotic behaviour of robust-scatter estimators in the case where the number of observations and the dimension of the population covariance matrix grow at infinity with the same pace. In particular, we analyze the fluctuations of bilinear…