Related papers: Exact computation of the halfspace depth
We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite…
We report on the implementation of an algorithm for computing the set of all regular triangulations of finitely many points in Euclidean space. This algorithm, which we call down-flip reverse search, can be restricted, e.g., to computing…
Clouds classification is a great challenge in meteorological research. The different types of clouds, currently known and present in our skies, can produce radioactive effects that impact on the variation of atmospheric conditions, with the…
The aim of this paper is to introduce a method for computing Hilbert decompositions (and consequently the Hilbert depth) of a finitely generated multigraded module $M$ over the polynomial ring $K[X_1,..., X_n]$ by reducing the problem to…
Three-dimensional (3D) point cloud analysis has become one of the attractive subjects in realistic imaging and machine visions due to its simplicity, flexibility and powerful capacity of visualization. Actually, the representation of scenes…
Shapley additive explanations (SHAP) are widely recognised as computationally intractable for neural networks, since they induce an exponential search space over the input features. In this work, we take a first step towards scaling exact…
We show that, for any set of n points in d dimensions, there exists a hyperplane with regression depth at least ceiling(n/(d+1)). as had been conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n hyperplanes in d dimensions…
Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A multivariate depth function is a function which, given a…
Analyzing the geometric and semantic properties of 3D point clouds through the deep networks is still challenging due to the irregularity and sparsity of samplings of their geometric structures. This paper presents a new method to define…
Orienting surface normals correctly and consistently is a fundamental problem in geometry processing. Applications such as visualization, feature detection, and geometry reconstruction often rely on the availability of correctly oriented…
For the registration of partially overlapping point clouds, this paper proposes an effective approach based on both the hard and soft assignments. Given two initially posed clouds, it firstly establishes the forward correspondence for each…
In this paper, we present a significant improvement of Quick Hypervolume algorithm, one of the state-of-the-art algorithms for calculating exact hypervolume of the space dominated by a set of d-dimensional points. This value is often used…
We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…
Big data analytics has gathered immense research attention lately because of its ability to harness useful information from heaps of data. Cloud computing has been adjudged as one of the best infrastructural solutions for implementation of…
We study the theoretical and practical aspects of computing braids described by approximate descriptions of paths in the plane. Exact algorithms rely on the lexicographic ordering of the points in the plane, which is unstable under…
Current point cloud processing algorithms do not have the capability to automatically extract semantic information from the observed scenes, except in very specialized cases. Furthermore, existing mesh analysis paradigms cannot be directly…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
Point cloud completion aims to recover the complete shape based on a partial observation. Existing methods require either complete point clouds or multiple partial observations of the same object for learning. In contrast to previous…
Hierarchical clustering is a fundamental task often used to discover meaningful structures in data, such as phylogenetic trees, taxonomies of concepts, subtypes of cancer, and cascades of particle decays in particle physics. Typically…
Simulation of turbulent flows, especially at the edges of clouds in the atmosphere, is an inherently challenging task. Hitherto, the best possible computational method to perform such experiments is the Direct Numerical Simulation (DNS).…