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Topological data analysis (TDA) is an emergent field of data analysis. The critical step of TDA is computing the persistent Betti numbers. Existing classical algorithms for TDA are limited if we want to learn from high-dimensional…

$\renewcommand{\Re}{\mathbb{R}}$ We develop a general randomized technique for solving "implic it" linear programming problems, where the collection of constraints are defined implicitly by an underlying ground set of elements. In many…

The Continuous p-Dispersion Problem (CpDP) with boundary constraints asks for the placement of a fixed number of points in a compact subset of Euclidean space such that the minimum distance between any two points, as well as the points and…

Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems. As a…

A fast nonparametric procedure for classifying functional data is introduced. It consists of a two-step transformation of the original data plus a classifier operating on a low-dimensional hypercube. The functional data are first mapped…

The paper presents a new method of depth estimation dedicated for free-viewpoint television (FTV). The estimation is performed for segments and thus their size can be used to control a trade-off between the quality of depth maps and the…

In the absence of governing equations, dimensional analysis is a robust technique for extracting insights and finding symmetries in physical systems. Given measurement variables and parameters, the Buckingham Pi theorem provides a procedure…

Statistical depths provide a fundamental generalization of quantiles and medians to data in higher dimensions. This paper proposes a new type of globally defined statistical depth, based upon control theory and eikonal equations, which…

We introduce "TriMap"; a dimensionality reduction technique based on triplet constraints, which preserves the global structure of the data better than the other commonly used methods such as t-SNE, LargeVis, and UMAP. To quantify the global…

The concept of data depth in non-parametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. Halfspace depth is a measure of data depth. Given a set S of points and a point p, the…

The single-step explicit time integration methods have long been valuable for solving large-scale nonlinear structural dynamic problems, classified into single-solve and multi-sub-step approaches. However, no existing explicit single-solve…

Recent advances have markedly improved the cross-scene generalization of relative depth estimation, yet its practical applicability remains limited by the absence of metric scale, local inconsistencies, and low computational efficiency. To…

3D data is a valuable asset the computer vision filed as it provides rich information about the full geometry of sensed objects and scenes. Recently, with the availability of both large 3D datasets and computational power, it is today…

Transformer-based methods have swept the benchmarks on 2D and 3D detection on images. Because tokenization before the attention mechanism drops the spatial information, positional encoding becomes critical for those methods. Recent works…

The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…

Automated detection of visually salient regions is an active area of research in computer vision. Salient regions can serve as inputs for object detectors as well as inputs for region based registration algorithms. In this paper we consider…

Multidimensional imaging techniques provide powerful ways to examine various kinds of scientific questions. The routinely produced datasets in the terabyte-range, however, can hardly be analyzed manually and require an extensive use of…

Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…

We analyze the performance of the Tukey median estimator under total variation (TV) distance corruptions. Previous results show that under Huber's additive corruption model, the breakdown point is 1/3 for high-dimensional…

We study empirical variants of the halfspace (Tukey) depth of a probability measure $\mu$, which are obtained by replacing $\mu$ with the corresponding weighted empirical measure. We prove analogues of the Marcinkiewicz--Zygmund strong law…