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Invariant Coordinate Selection (ICS) is a multivariate technique that relies on the simultaneous diagonalization of two scatter matrices. It serves various purposes, including its use as a dimension reduction tool prior to clustering or…

Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…

Invariant coordinate selection (ICS) is a dimension reduction method, used as a preliminary step for clustering and outlier detection. It has been primarily applied to multivariate data. This work introduces a coordinate-free definition of…

For multivariate data, tandem clustering is a well-known technique aiming to improve cluster identification through initial dimension reduction. Nevertheless, the usual approach using principal component analysis (PCA) has been criticized…

In high reliability standards fields such as automotive, avionics or aerospace, the detection of anomalies is crucial. An efficient methodology for automatically detecting multivariate outliers is introduced. It takes advantage of the…

Invariant coordinate selection (ICS) and projection pursuit (PP) are two methods that can be used to detect clustering directions in multivariate data by optimizing criteria sensitive to non-normality. In particular, ICS finds clustering…

This work presents sparse invariant coordinate selection, SICS, a new method for sparse and robust independent component analysis. SICS is based on classical invariant coordinate selection, which is presented in such a form that a…

Independent component selection (ICS), introduced by Tyler et al. (2009, JRSS B), is a powerful tool to find potentially interesting projections of multivariate data. In some cases, some of the projections proposed by ICS come close to…

Given a dataset and an existing clustering as input, alternative clustering aims to find an alternative partition. One of the state-of-the-art approaches is Kernel Dimension Alternative Clustering (KDAC). We propose a novel Iterative…

Inclusive deep inelastic scattering factorization combines two features that are often treated separately: an asymptotic reconstruction of the current-current matrix element from hard and long-distance data, and an invariance under finite…

The Minimum Covariance Determinant (MCD) approach robustly estimates the location and scatter matrix using the subset of given size with lowest sample covariance determinant. Its main drawback is that it cannot be applied when the dimension…

This paper revisits the classic iterative proportional scaling (IPS) from a modern optimization perspective. In contrast to the criticisms made in the literature, we show that based on a coordinate descent characterization, IPS can be…

Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…

Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty.…

In this article, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend…

Even when starting with a very poor initial guess, the iterative configuration interaction (iCI) approach can converge from above to full CI very quickly by constructing and diagonalizing a small Hamiltonian matrix at each…

Annotation of medical images, such as MRI and CT scans, is crucial for evaluating treatment efficacy and planning radiotherapy. However, the extensive workload of medical professionals limits their ability to annotate large image datasets,…

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…

Distributed scatterers in InSAR (DS-InSAR) processing are essential for retrieving surface deformation in areas lacking strong point targets. Conventional workflows typically involve selecting statistically homogeneous pixels based on…

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and…